Publication list, long version Karl Schlechta February 12, 2017

Contents

(February 12, 2017) Books, published or accepted ----------------------------

2017 ---[Sch17]

Karl Schlechta: "Formal Methods for Nonmonotonic and Related Logics" Springer, Heidelberg (graduate level textbook, appr. 650-700 pages, in preparation)

2016 ---[GS16]

Dov Gabbay, Karl Schlechta: "A new perspective on non-monotonic logics" Springer, Heidelberg, ISBN 978-331-946-8150 Nov. 14, 2016 1 Introduction 1 1 Overview 1 2 Introduction to the main concepts 1 3 Abstract constructions 2 Basic algebraic and logical definitions 2 1 Overview of this chapter 2 2 The definitions 3 Defeasible inheritance 3 1 Conceptual analysis 3 2 Basic discussion 3 3 Directly sceptical split validity upward chaining off-path inheritance 3 4 Review of other approaches and problems 3 5 Discussion of their properties 4 Reiter defaults and autoepistemic logic 4 1 Introduction 4 2 Autoepistemic logic 4 3 Discussion 5 Preferential structures and related concepts 1

2 5 1 Preferential Structures 5 2 Laws About Size 5 3 Discussion 6 Deontic logic, contrary-to-duty obligations 6 1 Deontic logic 6 2 Contrary-to-duty obligations 6 3 A-ranked structures 6 4 Application of A-ranked structures to contrary-to-duty conditionals 7 Theory revision, theory contraction, and conditionals 7 1 Introduction 7 2 Theory revision 7 3 Theory contraction 7 4 Conditionals and update 8 Independence and interpolation 8 1 Monotone and Antitone Interpolation 8 2 Interpolation for Non-Monotonic Logic and Size 9 Probabilistic and abstract independence 9 1 Introduction 9 2 Probabilistic and set independence 9 3 Basic results for set and function independence 9 4 Examples of new rules 9 5 There is no finite characterization 9 6 Systematic construction of new rules 10 Formal construction 10 1 Introduction 10 2 Discussion of various properties 10 3 Desiderata 10 4 The solution 10 5 Version 1 10 6 Version 2 10 7 Discussion 10 8 Extensions 10 9 Formal properties 11 The Talmudic KAL Vachomer rule 11 1 Introduction 11 2 The AGS approach 11 3 A problem with the original AGS algorithm 11 4 The arrow counting approach 12 Equational CTD 12 1 Summary 12 2 Methodological orientation 12 3 Equational modelling of contrary to duty obligations 12 4 Equational semantics for general CTD sets 12 5 Proof theory for CTDs 12 6 Comparing with Makinson and Torre’s input output logic 12 7 Comparing with Governatori and Rotolo’s logic of violations 12 8 Conclusion 13 Neurology 13 1 Summary of work by Edelman et al. 13 2 Abstract constructions - another part of human reasoning 14 Conclusion

2011 ---[GS10]

Dov Gabbay, Karl Schlechta: "Conditionals and modularity in general logics" Springer, Heidelberg, August 2011, ISBN 978-3-642-19067-4, a preliminary version is accessible via arXiv.org, same title 1 Introduction 1.1 The main subjects of this book

3 1.1.1 An example 1.1.1.1 An abstract description of both cases in above example 1.1.2 Connections 1.2 Main definitions and results 1.2.1 The monotone case 1.2.2 The non-monotonic case 1.3 Overview of this introduction 1.4 Basic definitions 1.5 Towards a uniform picture of conditionals 1.5.1 Discussion and classification 1.5.2 Additional structure on language and truth values 1.5.3 Representation for general revision, update, and counterfactuals 1.6 Interpolation 1.6.1 Introduction 1.6.2 Problem and Method 1.6.3 Monotone and antitone semantic and syntactic interpolation 1.6.4 Laws about size and interpolation in non-monotonic logics 1.6.5 Summary 1.7 Neighbourhood semantics 1.7.1 Defining neighbourhoods 1.7.2 Additional requirements 1.7.3 Connections between the various properties 1.7.4 Various uses of neighbourhood semantics 1.8 An abstract view on modularity and independence 1.8.1 Introduction 1.8.2 Abstract definition of independence 1.8.3 Other aspects of independence 1.9 Conclusion and outlook 1.10 Previously published material, acknowledgements 2 Basic definitions 2.1 Introduction 2.1.1 Overview of this chapter 2.2 Basic algebraic and logical definitions 2.2.1 Countably many disjoint sets 2.2.2 Introduction to many-valued logics 2.3 Preferential structures 2.3.1 The minimal variant 2.3.2 The limit variant 2.3.3 Preferential structures for many-valued logics 2.4 IBRS and higher preferential structures 2.4.1 General IBRS 2.4.2 Higher preferential structures 2.5 Theory revision 2.5.0.8A remark on intuition 2.5.1 Theory revision for many-valued logics 3 Towards a uniform picture of conditionals 3.1 Introduction 3.1.1 Overview of this chapter 3.2 An abstract view on conditionals 3.2.1 A general definition as arbitrary operator 3.2.2 Properties of choice functions 3.2.3 Evaluation of systems of sets 3.2.4 Conditionals based on binary relations 3.2.4.1 Short discussion of above examples 3.3 Conditionals and additional structure on language and truth values 3.3.1 Introduction 3.3.2 Operations on language and truth values 3.3.3 Operations on language elements and truth values within one language 3.3.4 Operations on several languages 3.3.5 Operations on definable model sets 3.3.6 Softening concepts 3.3.7 Aspects of modularity and independence in defeasible inheritance 3.4 Representation for general revision, update, and counterfactuals 3.4.1 Importance of theory revision for general structures, reactivity, and its solution

4 3.4.2 Introduction 3.4.3 Semantic representation for generalized distance based theory revision 3.4.4 Semantic representation for generalized update and counterfactuals 3.4.5 Syntactic representation for generalized revision, update, counterfactuals 4 Monotone and antitone semantic and syntactic interpolation 4.1 Introduction 4.1.1 Overview 4.1.2 Problem and Method 4.1.3 Monotone and antitone semantic and syntactic interpolation 4.2 Monotone and antitone semantic interpolation 4.2.1 The two-valued case 4.2.2 The many-valued case 4.3 The interval of interpolants in monotonic or antitonic logics 4.3.1 Introduction 4.3.2 Examples and a simple fact 4.3.3 + and - as new semantic and syntactic operators 4.4 Monotone and antitone syntactic interpolation 4.4.1 Introduction 4.4.2 The classical propositional case 4.4.3 Finite (intuitionistic) Goedel logics 5 Laws about size and interpolation in non-monotonic logics 5.1 Introduction 5.1.1 A succinct description of our main ideas and results in this chapter 5.1.2 Various concepts of size and non-monotonic logics 5.1.3 Additive and multiplicative laws about size 5.1.4 Interpolation and size 5.1.5 Hamming relations and size 5.1.6 Equilibrium logic 5.1.7 Interpolation for revision and argumentation 5.1.8 Language change to obtain products 5.2 Laws about size 5.2.1 Additive laws about size 5.2.2 Multiplicative laws about size 5.2.3 Hamming relations and distances 5.2.4 Summary of properties 5.2.5 Language change in classical and non-monotonic logic 5.3 Semantic interpolation for non-monotonic logic 5.3.1 Discussion 5.3.2 Interpolation of the form A~B-C 5.3.3 Interpolation of the form A-B~C 5.3.4 Interpolation of the form A~B~C 5.3.5 Interpolation for distance based revision 5.3.6 The equilibrium logic EQ 5.4 Context and structure 5.5 Interpolation for argumentation 6 Neighbourhood semantics 6.1 Introduction 6.1.1 Defining neighbourhoods 6.1.2 Additional requirements 6.1.3 Connections between the various properties 6.1.4 Various uses of neighbourhood semantics 6.2 Detailed overview 6.2.1 Motivation 6.2.2 Tools to define neighbourhoods 6.2.3 Additional requirements 6.2.4 Interpretation of the neighbourhoods 6.2.5 Overview of the different lines of reasoning 6.2.6 Extensions 6.3 Tools and requirements for neighbourhoods and how to obtain them 6.3.1 Tools to define neighbourhoods 6.3.2 Obtaining such tools 6.3.3 Additional requirements for neighbourhoods 6.3.4 Connections between the various concepts 6.4 Neighbourhoods in deontic and default logic 6.4.1 Introduction

5 6.4.2 Two important examples for deontic logic 6.4.3 Neighbourhoods for deontic systems 7 Conclusion and outlook 7.1 Conclusion 7.1.1 Semantic and syntactic interpolation 7.1.2 Independence and interpolation for monotonic logic 7.1.3 Independence and interpolation for non-monotonic logic 7.1.4 Neighbourhood semantics 7.2 Outlook 7.2.1 The dynamics of reasoning 7.2.2 A revision of basic concepts of logic: justification

2009 ---[GS09f]

Dov Gabbay, Karl Schlechta: "Logical tools for handling change in agent-based systems" Springer, ISBN 978-3642044069 a (condensed) preliminary version is accessible via arXiv.org, same title 1 Introduction and Motivation 1.1 Program 1.2 Short overview of the different logics 1.2.1 Nonmonotonic logics 1.2.2 Theory revision 1.2.3 Theory update 1.2.4 Deontic logic 1.2.5 Counterfactual conditionals 1.2.6 Modal logic 1.2.7 Intuitionistic logic 1.2.8 Inheritance systems 1.2.9 A summarizing table for the semantics 1.3 A discussion of concepts 1.3.1 Basic semantic entities, truth values, and operators 1.3.2 Algebraic and structural semantics 1.3.3 Restricted operators and relations 1.3.4 Copies in preferential models 1.3.5 Further remarks on universality of representation proofs 1.3.6 ~ in the object language? 1.3.7 Various considerations on abstract semantics 1.3.8 A comparison with Reiter defaults 1.4 IBRS 1.4.1 Definition and comments 1.4.2 The power of IBRS 1.4.3 Abstract semantics for IBRS and its engineering realization 2 Basic definitions and results 2.1 Algebraic definitions 2.2 Basic logical definitions 2.3 Basic definitions and results for nonmonotonic logics 3 Abstract semantics by size 3.1 The first order setting 3.2 General size semantics 3.2.1 Introduction 3.2.2 Main table 3.2.3 Coherent systems 4 Preferential structures - Part I 4.1 Introduction 4.1.1 Remarks on nonmonotonic logics and preferential semantics 4.1.2 Basic definitions 4.2 Preferential structures without domain conditions 4.2.1 General discussion

6 4.2.2 Detailed discussion 5 Preferential structures - Part II 5.1 Simplifications by domain conditions, logical properties 5.1.1 Introduction 5.1.2 Smooth structures 5.1.3 Ranked structures 5.1.4 The logical properties with definability preservation 5.2 A-ranked structures 5.2.1 Representation results for A-ranked structures 5.3 Two sequent calculi 5.3.1 Introduction 5.3.2 Plausibility Logic 5.3.3 A comment on the work by Arieli and Avron 5.4 Blurred observation - absence of definability preservation 5.4.1 Introduction 5.4.2 General and smooth structures without definability preservation 5.4.3 Ranked structures 5.5 The limit variant 5.5.1 Introduction 5.5.2 The algebraic limit 5.5.3 The logical limit 6 Higher preferential structures 6.1 Introduction 6.2 The general case 6.3 Discussion of the totally smooth case 6.4 The essentially smooth case 6.5 Translation to logic 7 Deontic logic and hierarchical conditionals 7.1 Semantics of deontic logic 7.1.1 Introductory remarks 7.1.2 Basic definitions 7.1.3 Philosophical discussion of obligations 7.1.4 Examination of the various cases 7.1.5 What is an obligation? 7.1.6 Conclusion 7.2 A comment on work by Aqvist 7.2.1 Introduction 7.2.2 There are (at least) two solutions 7.2.3 Outline 7.3 Hierarchical conditionals 7.3.1 Introduction 7.3.2 Formal modelling and summary of results 7.3.3 Overview 7.3.4 Connections with other concepts 7.3.5 Formal results and representation for hierarchical conditionals 8 Theory update and theory revision 8.1 Update 8.1.1 Introduction 8.1.2 Hidden dimensions 8.2 Theory revision 8.2.1 Introduction to theory revision 8.2.2 Booth revision 8.2.3 Revision and independence 8.2.4 Preferential modelling of defaults 8.2.5 Remarks on independence 9 An analysis of defeasible inheritance systems 9.1 Introduction 9.1.1 Terminology 9.1.2 Inheritance and reactive diagrams 9.1.3 Conceptual analysis 9.2 Introduction to nonmonotonic inheritance 9.2.1 Basic discussion 9.2.2 Directly sceptical split validity upward chaining off-path inheritance 9.2.3 Review of other approaches and problems 9.3 Defeasible inheritance and reactive diagrams 9.3.1 Summary of our algorithm 9.3.2 Overview 9.3.3 Compilation and memorization 9.3.4 Executing the algorithm 9.3.5 Signposts

7 9.3.6 Beyond inheritance 9.4 Interpretations 9.4.1 Introduction 9.4.2 Informal comparison of inheritance with the systems P and R 9.4.3 Inheritance as information transfer 9.4.4 Inheritance as reasoning with prototypes 9.5 Detailed translation of inheritance to modified systems of small sets 9.5.1 Normality 9.5.2 Small sets

2004 ---[Sch04]

Karl Schlechta: Coherent systems Vol. 2 of the Series: Studies in Logic and Practical Reasoning, Elsevier, Amsterdam, Sept. 2004, pp. 468, ISBN 0-444-51789-8 see also: LIF TR 14-2003 for a preliminary version Abstract: We discuss several types of common sense reasoning, reduce them to a small number of basic semantical concepts, and show several (in-)completeness results for such logics.

TABLE OF CONTENTS ================= Foreword (by David Makinson) Summary Acknowledgements Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter

1 2 3 4 5 6 7 8 9

: : : : : : : : :

Introduction Concepts Preferences Distances Definability preservation Sums Size Integration Conclusion and outlook

Bibliography Index CHAPTER 1 : INTRODUCTION ======================== 1.1 1.1.1 1.1.2 1.1.3 1.1.4 1.2 1.3 1.4 1.4.1 1.4.2 1.4.3 1.4.4

The main topics of the book Conceptual analysis Generalized modal logic and integration Formal results Various remarks Historical remarks Organisation of the book Overview of the chapters The conceptual part (Chapter 2) The formal part (Chapters 3-7) Integration (Chapter 8) Problems, ideas and techniques

8 1.5 1.6 1.6.1 1.6.2 1.6.2.1

Specific remarks on propositional logic Basic definitions The algebraic part The logical part Results on the absence of representation

CHAPTER 2 : CONCEPTS ==================== 2.1 2.2 2.2.1 2.2.1.1 2.2.1.2 2.2.1.3 2.2.2 2.2.3 2.2.4 2.2.5 2.2.6 2.2.7 2.2.8 2.2.9 2.2.10 2.2.10.1 2.2.10.2 2.2.11 2.2.12 2.3 2.3.1 2.3.2 2.3.3 2.3.3.1 2.4

Introduction Reasoning types Traditional non-monotonic logics Normal, important, or interesting cases The majority of cases As many as possible (Reiter defaults) Prototypical and ideal cases Extreme cases and interpolation Clustering Certainty Quality of an answer, approximation, and complexity Useful reasoning Inheritance and argumentation Dynamic systems Theory revision General discussion The AGM approach Update Counterfactual conditionals Basic semantical concepts Preference Distance Size Sums and products Coherence

CHAPTER 3 : PREFERENCES ======================= 3.1 3.1.1 3.1.2 3.2 3.2.1 3.2.2 3.2.3 3.2.4 3.3 3.3.1 3.3.2 3.4 3.4.1 3.5 3.5.1 3.6 3.6.1 3.6.1.1 3.7 3.7.1 3.7.2 3.7.2.1 3.7.2.2 3.7.2.3 3.8 3.9 3.9.1 3.9.1.1

Introduction General discussion The basic definitions and results General preferential structures General minimal preferential structures Transitive minimal preferential structures One copy version A (very) short remark on X-logics Smooth minimal preferential structures Smooth minimal preferential structures with arbitrarily many copies Smooth and transitive minimal preferential structures The logical characterization of general and smooth preferential models Simplifications of the general transitive limit case A counterexample to the KLM-system The formal results A non-smooth model of cumulativity The formal results A non-smooth injective structure validating P, (WD), -(NR) Plausibility logic - problems without closure under finite union Introduction Completeness and incompleteness results for plausibility logic (PlI)+(PlRM)+(PlCC) is complete (and sound) for preferential models Incompleteness of full plausibility logic for smooth structures Discussion and remedy The role of copies in preferential structures A new approach to preferential structures Introduction Main concepts and results

9 3.9.1.2 3.9.1.3 3.9.1.4 3.9.2 3.9.3 3.9.3.1 3.9.3.2 3.9.4 3.10 3.10.1 3.10.1.1 3.10.1.2 3.10.2 3.10.2.1 3.10.2.2 3.10.3 3.10.3.1 3.10.3.2

Motivation and overview Basic definitions and facts Outline of our representation results and technique Validity in traditional and in our preferential structures The disjoint union of models and the problem of multiple copies Disjoint unions and preservation of validity in disjoint unions Multiple copies Representation in the finite case Ranked preferential structures Introduction Detailed discussion of this section Introductory facts and definitions The minimal variant Some introductory results Characterizations The limit variant without copies Representation Partial equivalence of limit and minimal ranked structures

CHAPTER 4 : DISTANCES ===================== 4.1 4.1.1 4.1.2 4.1.3 4.2 4.2.1 4.2.2 4.2.2.1 4.2.2.2 4.2.2.3 4.2.3 4.2.3.1 4.2.3.2 4.2.3.3 4.2.4 4.2.5 4.2.5.1 4.2.5.2 4.2.5.3 4.3 4.3.1 4.3.1.1 4.3.2 4.3.2.1 4.3.2.2 4.3.2.3

Introduction Theory Revision Counterfactuals Summary Revision by symmetrical and not necessarily symmetric distance Introduction The algebraic results Introduction and pseudo-distances The representation results for the symmetric case The representation result for the finite not necessarily symmetric case The logical results Introduction The symmetric case The finite not necessarily symmetric case There is no finite characterization The limit case Introduction Remarks on the logics of the revision limit case Equivalence of the minimal and the limit case for formulas Local and global metrics for the semantics of counterfactuals Introduction Basic definitions The results Outline of the construction for Proposition 4.3.1 Detailed proof of Proposition 4.3.1 The limit variant

CHAPTER 5 : DEFINABILITY PRESERVATION ===================================== 5.1 5.1.1 5.1.2 5.1.2.1 5.1.2.2 5.1.2.3 5.1.3 5.1.3.1 5.1.3.2 5.1.3.3 5.1.4 5.2

Introduction The problem The remedy Preferential structures Theory revision Summary Basic definitions and results General part Results for the definability preserving case and counterfactuals Discussion of the technical development A remark on definability preservation and modal logic Preferential structures

10 5.2.1 5.2.1.1 5.2.1.2 5.2.1.3 5.2.2 5.2.3 5.3 5.3.1 5.3.2

The algebraic results The conditions The general case The smooth case The logical results The general case and the limit version cannot be characterized Revision The algebraic result The logical result

CHAPTER 6 : SUMS ================ 6.1 6.1.1 6.1.2 6.1.3 6.1.4 6.1.5 6.2 6.3 6.3.1 6.3.2 6.3.3 6.3.3.1 6.3.3.2 6.3.4 6.3.4.1 6.3.4.2 6.4 6.4.1 6.4.1.1 6.4.1.2 6.4.2 6.4.2.1 6.4.2.2 6.4.3 6.5 6.5.1

Introduction The general situation and the Farkas algorithm Update by minimal sums Comments on "Belief revision with unreliable observations" "Between" and "behind" Summary The Farkas algorithm A representation result for update by minimal sums Introduction An abstract result Representation Introduction The result There is no finite representation for our type of update possible Outline The details Comments on "Belief revision with unreliable observations" Introduction The situation Basic definitions and results A characterization of Markov systems (in the finite case) Outline and introduction The representation result for the finite case There is no finite representation possible "Between" and "Behind" There is no finite representation for "between" and "behind"

CHAPTER 7 : SIZE ================ 7.1 7.1.1 7.2 7.2.1 7.2.2 7.3 7.3.1 7.3.2 7.3.2.1 7.3.2.2 7.3.2.3 7.3.3 7.3.3.1 7.3.4 7.4 7.4.1 7.4.2 7.4.2.1 7.4.2.2

Introduction The details Generalized quantifiers Introduction Results Comparison of three abstract coherent systems based on size Introduction Presentation of the three systems The system of Ben-David/Ben-Eliyahu The system of the author The system of Friedman/Halpern Comparison of the systems of Ben-David/Ben-Eliyahu and the author Equivalence of both systems Comparison of the systems of Ben-David/Ben-Eliyahu and of Friedman/Halpern Theory revision based on model size Introduction Results Pre-EE relations and epistemic entrenchment relations Stable sets

11 7.4.2.3

Revision based on model size

CHAPTER 8 : INTEGRATION ======================= 8.1 8.1.1 8.1.2 8.2 8.3 8.3.1 8.3.2 8.3.3

Introduction Rules or object language? Various levels of reasoning Reasoning types and concepts Formal aspects Classical modal logic Classical propositional operators have no unique interpretation Combining individual completeness results

CHAPTER 9 : CONCLUSION AND OUTLOOK ==================================

1997 ---[Sch97-2]

K.Schlechta : "Nonmonotonic logics - Basic Concepts, Results, and Techniques" Springer Lecture Notes series, LNAI 1187, Jan. 1997, 243pp Table of contents: 1 1.1 1.2 1.2.1 1.2.2 1.2.3 1.2.4 1.2.5 1.2.6 1.3 1.3.1 1.3.2 1.3.3 1.3.4 1.3.5 1.3.6 1.3.7 1.3.8 1.3.9 1.3.10 1.3.11 1.4 1.5 2 2.1 2.1.1 2.1.2 2.1.3 2.1.4 2.1.5 2.1.6 2.1.7 2.2

Introduction Preliminaries Our philosophical position Logic as a tool Basic semantical notions Abstract semantics Restricted monotony and irrelevance Logic and structural information Summary and program Introduction to nonmonotonic logics and its problems History and an example Some basic differences A (simplified) introduction to Reiter’s theory of defaults Static and dynamic aspects of defaults Introduction to preferential structures Introduction to defaults as generalized quantifiers A two stage approach Introduction to logic and analysis Introduction to theory revision Introduction to structured reasoning in diagrams The problem of irrelevant information Basic definitions and notation Acknowledgements Preferential structures and related logics Preferential structures Introduction and basic definitions Orderings on &L and completeness results Defaults and preferential models Supraclassicality + cumulativity + distributivity does not entail classical representability A representation theorem for preferential models General smoothness Limit preferential models Local and global metrics for the semantics of counterfactual conditionals

12 2.3

Extension by finite approximation from below

3 3.1 3.2 3.3

Defaults as generalized quantifiers Introduction Defaults as generalized quantifiers Sceptical revision of partially ordered defaults

4 4.1 4.2

Logic and analysis Overview, motivation, and basic definitions Technical development

5 5.1 5.2 5.3

Theory revision and probability Introduction Epistemic preference relations Measuring theories, and an outlook for a different treatment of theory revision

6 6.1 6.1.1 6.1.2

6.1.6 6.2

Structured reasoning Inheritance diagrams Introduction A detailed survey of inheritance la Thomason et al. Review of other approaches and problems A parallel definition for the sceptical and the extension-based approach Directly sceptical inheritance cannot capture the intersection of extensions A semantics for defeasible inheritance Networks of inference : J. Pearl’s book

7

References

6.1.3 6.1.4 6.1.5

Articles in international journals, published or accepted ---------------------------------------------------------

2010 ---[GS09c]

D.Gabbay, K.Schlechta: "Semantic Interpolation" Journal of Applied Non-classical Logics, Vol 20/4, 2010, pp. 345-371 Abstract: We define semantic interpolation and show that it always exists for monotone or antitone (propositional) logics. We show that it sometimes, but not always, carries over to syntactic interpolation. Finally, we investigate several forms of semantic interpolation for non-monotonic logic.

2009 ---[GS09a]

D.Gabbay, K.Schlechta: "Size and Logic" Review of Symbolic Logic, Vol. 2, No. 2, pp. 396-413, 2009 Abstract: We show how to develop a multitude of rules of nonmonotonic logic from very simple and natural

13 notions of size, using them as building blocks. [GS09b]

D.Gabbay, K.Schlechta: "Independence - revision and defaults", Studia Logica (2009) 92, pp. 381-394, Abstract: We investigate different aspects of independence here, in the context of theory revision, generalizing slightly work by Chopra, Parikh, and Rodrigues, and in the context of preferential reasoning.

[GS08b]

D.Gabbay, K.Schlechta: "Reactive preferential structures and nonmonotonic consequence", Review of Symbolic Logic, Vol. 2, No. 2, pp. 414-450, 2009 Abstract: We introduce Information Bearing Relation Systems (IBRS) as an abstraction of many logical systems. We then define a general semantics for IBRS, and show that a special case of IBRS generalizes in a very natural way preferential semantics and solves open representation problems for weak logical systems. This is possible, as we can "break" the strong coherence properties of preferential structures by higher arrows, i.e. arrows, which do not go to points, but to arrows themselves.

[GS08h]

D.Gabbay, K.Schlechta: "A comment on work by Booth and co-authors", Studia Logica, 2010, 94:403-432 Abstract: We solve a representation problem left open in an article by Booth and co-authors.

2008 ---[GS08a]

D.Gabbay, K.Schlechta: "Cumulativity without closure of the domain under finite unions", Review of Symbolic Logic, 1 (3): 372-392, 2008 Abstract: For nonmonotonic logics, Cumulativity is an important logical rule. We show here that Cumulativity fans out into an infinity of different conditions, if the domain is not closed under finite unions.

[GS08d]

D.Gabbay, K.Schlechta: "A theory of hierarchical consequence and conditionals", Journal of Logic, Language and Information, 19:1, 3-32, 2010 Abstract: We introduce A-ranked preferential structures and combine them with an accessibility relation. A-ranked

14 preferential structures are intermediate between simple preferential structures and ranked structures. The additional accessibilty relation allows us to consider only parts of the overall A-ranked structure. This framework allows us to formalize contrary to duty obligations, and other pictures where we have a hierarchy of situations, and maybe not all are accessible to all possible worlds. Representation results are proved. [GS08e]

D.Gabbay, K.Schlechta: "Defeasible inheritance systems and reactive diagrams", Logic Journal of the IGPL, 17:1-54, 2009 Abstract: We give a conceptual analysis of (defeasible or nonmonotonic) inheritance diagrams, and compare our analysis to the "small" and "big sets" of preferential and related reasoning. In our analysis, we consider nodes as information sources and truth values, direct links as information, and valid paths as information channels and comparisons of truth values. This results in an upward chaining, split validity, off-path preclusion inheritance formalism of a particularly simple type. We show that the small and big sets of preferential reasoning have to be relativized if we want them to conform to inheritance theory, resulting in a more cautious approach, perhaps closer to actual human reasoning. Finally, we interpret inheritance diagrams as theories of prototypical reasoning, based on two distances: set difference, and information difference. We will also see that some of the major distinctions between inheritance formalisms are consequences of deeper and more general problems of treating conflicting information.

[GS08c]

D.Gabbay, K.Schlechta: "Roadmap for preferential logics", Journal of applied nonclassical logics, Vol. 19/1, pp. 43-95, 2009, Abstract: We give a systematic overview of semantical and logical rules in nonmonotonic and related logics. We show connections and sometimes subtle differences, and also compare such rules to uses of the notion of size.

2001 ----

15 [LMS01]

D.Lehmann, M.Magidor, K.Schlechta: "Distance Semantics for Belief Revision", Journal of Symbolic Logic, Vol.66, No. 1, March 2001, p. 295-317 Abstract: A vast and interesting family of natural semantics for belief revision is defined. Suppose one is given a distance d between any two models. One may then define the revision of a theory K by a formula alpha as the theory defined by the set of all those models of alpha that are closest, by d, to the set of models of K. This family is characterized by a set of rationality postulates that extends the AGM postulates. The new postulates describe properties of iterated revisions.

[SD01]

K.Schlechta, J.Dix: "Explaining updates by minimal sums", Theoretical Computer Science, 266 (2001), pp. 819-838 Abstract: Human reasoning about developments of the world involves always an assumption of inertia. We discuss two approaches for formalizing such an assumption, based on the concept of an explanation: (1) there is a general preference relation given on the set of all explanations, (2) there is a notion of a distance between models and explanations are preferred if their sum of distances is minimal. We show exactly under which conditions the converse is true as well and therefore both approaches are equivalent modulo these conditions. Our main result is a general representation theorem in the spirit of Kraus, Lehmann and Magidor.

2000 ---[Sch00-1]

K.Schlechta: "New techniques and completeness results for preferential structures" Journal of Symbolic Logic, Vol. 65, No. 2, pp. 719-746, June 2000 Abstract : Preferential structures are probably the best examined semantics for nonmonotonic and deontic logics, but also provide semantical approaches to theory revision and update, and other fields where a preference relation between models is a natural interpretation. They have been widely used to differentiate the various systems of such logics, and their construction is one of the main subjects in the formal investigation of these logics. We introduce new techniques to construct preferential structures for completeness proofs. Since our main interest is to provide general techniques, which can be applied in various situations and for various base logics (propositional and other), we take a purely algebraic approach, which can be translated into logics by easy lemmata. In particular, we give a clean construction via indexing by trees for transitive structures, this allows to simplify the proofs of [Sch92] and in particular of [Sch96-1], and to extend the results given there.

16

[SGMRT00]

K.Schlechta, L.Gourmelen, S.Motre, O.Rolland, B.Tahar: "A new approach to preferential structures", Fundamenta Informaticae, Vol. 42, No. 3-4, pp. 391-410, April-May 2000 Abstract: This paper deals with some fundamental concepts and questions of preferential structures. A model for preferential reasoning will, in this article, be a total order on the models of the underlying classical language. Instead of working in completeness proofs with a canonical preferential structure as done traditionally, we work with sets of such total orders. We thus stay close to the way completeness proofs are done in classical logic. Our new approach will also justify multiple copies (or labelling functions) present in most work on preferential structures. A representation result for the finite case is given.

[Sch00-2]

K.Schlechta: "Unrestricted preferential structures", Journal of Logic and Computation, Vol.10, No.4, pp.573-581, 2000 Abstract: We solve in this short, technical paper one of the perhaps major open problems of preferential structures, and give an unrestricted representation result. Up to now - to the author’s knowledge - all representation results for preferential structures were subject to some restriction: definability preservation (the author’s terminology, fullness in Lehmann’s terminology) or some kind of finiteness. The results presented here are valid without any restrictions.

1999 ---[BLS99]

S.Berger, D.Lehmann, K.Schlechta: "Preferred History Semantics for Iterated Updates", Journal of Logic and Computation, Vol.9, No.6, pp.817-833, 1999 Abstract: We give a semantics to iterated update by a preference relation on possible developments. An iterated update is a sequence of formulas, giving (incomplete) information about successive states of the world. A development is a sequence of models, describing a possible trajectory through time. We assume a principle of inertia and prefer those developments, which are compatible with the information, and avoid unnecessary changes. The logical properties of the updates defined in this way are considered, and a representation result is proved.

[Sch99]

K.Schlechta: "A topological construction of a non-smooth model of cumulativity" Journal of Logic and Computation, Vol.9, No.4, pp.457-462, 1999 Abstract : To solve a problem posed by Bezzazi, Makinson, Perez (Bezzazi, Makinson, Perez: "Beyond Rational

17 Monotony: Some Strong Non-Horn Rules for Nonmonotonic Inference Relations", JLC Vol. 7, No.5, p.605, 1997), we construct an injective, non-smooth preferential model of Cumulativity and Weak Determinacy, in which Negation Rationality fails. We make essential use of infinite sequences of models approaching sets of models. To our knowledge, this is the first time that such topological constructions are used in the context of preferential models. [ALS99]

L.Audibert, C.Lhoussaine, K.Schlechta: "Distance based revision of preferential logics" Logic Journal of the Interest Group in Pure and Applied Logics (1999), Vol. 7, No. 4, July 1999, pp. 429-446 Abstract : We first analyze AGM revision as conditions on choice functions for sets of models. This abstraction seems to us to capture the essentials of classical revision, it also immediately reveals the connection between revision and ranked preferential models, and gives further insight into the distance semantics for revision as developped by Lehmann, Magidor, and Schlechta. Our analysis shows how to apply the essential ideas of revision to other situations than classical theories and formulas, we exemplify this by examining preferential databases. We revise one preferential logic or database, L, with another one, L’. The basic idea is to describe such a logic as a partial order, either as the order of a preferential model which defines the logic, or as the order between formulas defined by the logic. A partial order can be seen as the set of total orders which extend it, and, given a distance on the set of total orders, we can define a revision as follows: L*L’ will be the logic corresponding to the partial order generated by those total orders extending (the order of) L’, which are closest to the set of total orders extending (the order of) L. We thus give a semantical approach to the problem. A representation result is proven.

1997 ---[Sch97-1]

K.Schlechta : "A Reduction of the Theory of Confirmation to the Notions of Distance and Measure", Logic Journal of the Interest Group in Pure and Applied Logics, Vol.5, No.1, pp.49-64, 1997 Abstract : We present an analysis and formalization of confirmation of a theory through observation. The basic ideas are, first, to carry the results of single observations over to neighbouring cases by analogy, using an abstract distance relation as in the Stalnaker/Lewis semantics for counterfactual conditionals. A theory is then, in a second step, considered confirmed iff we have thus concluded positively for a "large" part of the universe - where "large" is interpreted by a weak filter. Formal semantics as well as sound and complete axiomatizations for the (trivial) first order and the propositional case are given.

18 [Sch97-3]

K.Schlechta : "Symmetrical Theory Revision", (Non-prioritized belief revision based on distances between models), Theoria, Vol. 63, Part 1-2, pp. 34-53, 1997 (appeared in 1999) Abstract : We base Theory Revision on a notion of distance between the models of the underlying logic. Revisions constructed from such distances have nice properties: The AGM postulates are (with a minor exception) satisfied, and additional properties, e.g. for iterated revision, hold. The present article adapts this idea to non-prioritized Theory Revision. Some motivation and comparison to other, similar approaches are given, and so is a representation result.

[BGHPSW97]

D.Bellot, C.Godefroid, P.Han, J.P.Prost, K.Schlechta, E.Wurbel: "A semantical approach to the concept of screened revision", Theoria, Vol. 63, Part 1-2, pp. 24-33, 1997 (appeared in 1999) Abstract : We interpret Makinson’s concept of screened revision as a special form of iterated revision, and give it a formal definition based on a distance semantics. Differences between Makinson’s and our approach are discussed, and a representation result is given.

[Sch97-4]

K.Schlechta: "Filters and Partial Orders", Journal of the Interest Group in Pure and Applied Logics, Vol. 5, No. 5, p. 753-772, 1997 Abstract : We discuss several abstract semantics for nonmonotonic logics. We present their motivations, their development and some historical origins, and show that the three systems considered are essentially equivalent: (a) the coherent systems of filters of S.Ben-David and R.Ben-Eliahu, (b) the coherent systems of filters developed by the author, (c) the partial order semantics of N.Friedman and J.Halpern.

1996 ---[Sch96-1]

K.Schlechta : "Some Completeness Results for Stoppered and Ranked Classical Preferential Models", Journal of Logic and Computation, Oxford, Vol. 6, No. 4, pp. 599-622, 1996 Abstract : We extend the work begun in [Sch92] to stoppered (or smooth) and ranked classical preferential models, giving several soundness and completeness results for these structures. In addition, we discuss the number of copies of models needed to represent arbitrary logics defined by preferential structures.

19 [Sch96-3]

K.Schlechta : "Completeness and Incompleteness for Plausibility Logic", Journal of Logic, Language and Information, 5:2, 1996, p.177-192, Kluwer, Dordrecht Abstract : Plausibility Logic was introduced by Daniel Lehmann. We show - among some other results completeness of a subset of Plausibility Logic for Preferential Models, and incompleteness of full Plausibility Logic for smooth Preferential Models.

[Sch96-2]

K.Schlechta : "A Two-Stage Approach to First Order Default Reasoning", Fundamenta Informaticae, Vol. 28, No. 3-4, pp. 377-402, 1996 Abstract : Our subject is the representation and analysis of simple first-order default statements of ordinary language, such as "normally, birds fly". There are, among other approaches, two kinds of analysis, both semantic in style. One interprets "normally, birds fly" along the lines of "for every item x in the domain of discourse, the most normal models of "x is a bird" are models of "x flies"". This is the preferential models approach, first outlined by Bossu/Siegel and Shoham, and studied by Kraus, Lehmann, Magidor and others. The other interprets "normally, birds fly" along the lines of "there is an important subset of the birds, all of whose elements fly". This is the generalized quantifier approach, formulated and developed by the author. The purpose of the present paper is to show how the two approaches may usefully be combined into a single two-stage approach, and how such a combination provides an elegant account of certain problematic examples.

1995 ---[Sch95-1]

K.Schlechta : "Defaults as Generalized Quantifiers", Journal of Logic and Computation, Oxford, Vol.5, No.4, p.473-494, 1995 Abstract : We interpret (open normal) defaults as generalized FOL-quantifiers, give a semantics and a corresponding sound and complete axiom system. Nested and negated defaults are admissible and have a clear meaning. Moreover, the logic provides a notion of consistency for default theories, which is used for a theory revision approach in an order sorted language.

[Sch95-2]

K.Schlechta : "Logic, Topology, and Integration", Journal of Automated Reasoning, 14:353-381, 1995, Kluwer Abstract : The central notion will be that of closeness of (or difference between) two theories. In the first part, we give intuitive arguments in favour of considering topologies on the set of theories, continuous logics, and the average difference

20 between two logics, i.e. the integral of their difference. We continue by arguing for the importance of the difference between theories in a wide range of applications and problems. In the second part, we give some basic definitions and results for one such type of topology. In particular, separation properties and compactness will be discussed, and examples given. The techniques employed for constructing the topology will also be used for defining a sigma-algebra of measurable sets on the set of theories, leading to the usual definition of the Lebesgue integral, and a precise definition of the average difference of two logics. [Sch95-3]

K.Schlechta : "Preferential Choice Representation Theorems for Branching Time Structures" Journal of Logic and Computation, Oxford, Vol.5, pp.783-800, 1995 Abstract : The idea of preferential choice is applied here to dynamic structures in two directions : 1. We show that a deontic choice function of "good" developments can be represented by a ranked, stoppered preferential relation on all developments. 2. We generalize the Katsuno/Mendelzon Update Semantics to preferences between developments and obtain a representation theorem for arbitrarily many time points.

[Sch95-5]

K.Schlechta : "Some Completeness Results for Propositional Conditional Logics", Bulletin of the IGPL, Vol.3, No.1, March 1995, p.111-115 Abstract : We consider three different measures of distance between classical propositional models, and provide sound and complete axiomatisations for the ensuing conditional semantics, by translating conditional formulas into equivalent classical ones.

1994 ---[SM94]

K.Schlechta, D.Makinson : "Local and Global Metrics for the Semantics of Counterfactual Conditionals", Journal of Applied Non-Classical Logics, Vol.4, No.2, pp.129-140, Hermes, Paris, 1994 Abstract : The semantics for counterfactual conditionals employs indexed relations <[a] between possible worlds, with x<[a]y read intuitively as "x is closer to a than is y". This paper considers the question how far these different "closeness" relations of a model may be derived from a common source. Despite some well-known negative observations, we show that there is also quite a strong positive answer. Our main result is that for any model equipped with modular relations derived from multiple metrics d[a] via the equation x<[a]y iff d[a](a,x)
21 metric d, via the equation x<[a]y iff d(a,x)
1993 ---[Sch93]

K.Schlechta : "Directly Sceptical Inheritance Cannot Capture the Intersection of Extensions", Journal of Logic and Computation, Oxford, Vol.3, No.5 (1993), p. 455-467 Abstract : We show that, under some very weak assumptions about the definitions of sceptical and extension-based defeasible inheritance, directly sceptical inheritance cannot capture the intersection of extensions.

1992 ---[Sch92]

K.Schlechta : "Some Results on Classical Preferential Models", Journal of Logic and Computation, Oxford, Vol.2, No.6 (1992), p. 675-686 Abstract : We first show that a result of Kraus, Lehmann, Magidor on classical preferential models does not carry over to the general infinite case. We further show that - in the absence of all restrictions on finiteness - "logically nice" (definability preserving) classical preferential models correspond essentially to infinite conditionalisation.

1991 ---[MS91]

D.Makinson, K.Schlechta : "Floating Conclusions and Zombie Paths", (On principles and problems of defeasible inheritance), Artificial Intelligence 48 (1991), p. 199-209 Abstract : We discuss two difficulties in the "directly sceptical" approach to inference in defeasible inheritance nets, as developed by Horty, Thomason and Touretzky. We suggest that as a result of the general architecture of the approach, it is intrinsically unable to deal with a phenomenon of "floating conclusions", and has great difficulty in accommodating a phenomenon of "zombie paths". The conclusion drawn is that the directly sceptical approach cannot hope to do the work of an approach via the family of all extensions.

[Sch91-1]

K.Schlechta : "Theory Revision and Probability", Notre Dame Journal of Formal Logic 32, No.2 (1991), p. 307-319 Abstract : The problem of Theory Revision is to "add" a

22 formula to a theory, while preserving consistency, or to "subtract" a formula from a theory. In the process, only - in some sense minimal changes are to be made to the given theory and certain plausible conditions to be satisfied. In general, however, logic, minimality, and those conditions do not uniquely determine the process. Uniqueness can be achieved in a natural way by imposing an order on the formulae, as done by Gardenfors and Makinson : Given such a suitable order of "epistemic entrenchment", dependant on the theory considered, it is easy to define a unique revision process for that theory. We improve their results in the following way : We show how to define orders, which give rise to unique revision processes too, but in addition, 1) are well compatible with logic and thus have nice logical properties, 2) do not depend on the theory considered, so it suffices to fix one order for iterated revision, and are thus especially well suited for computational purposes, 3) have a natural probabilistic construction. In conclusion, we show that the completeness problems of Theory Revision, discussed by Alchourron, Gardenfors and Makinson, carry over to a certain extent to an approach of Theory Revision based on revising axiom systems. WARNING: Proposition 2.4 is wrong. This was pointed out by Hans Rott. (The proof of (K-1) is wrong.) (This is my only published sin I am aware of - but perhaps you find more of them.) [Sch91-2]

K.Schlechta : "Results on Infinite Extensions", Journal of Applied Non-Classical Logics, Hermes, Paris, Vol. 1, No. 1 (1991), p. 65-72 Abstract : In a joint paper M.Freund, D.Lehmann, D.Makinson (M.Freund, D.Lehmann, D.Makinson : Canonical Extensions to the Infinite Case of Finitary Nonmonotonic Inference Relations. in : Proceedings, 1. German Workshop on Non-Monotonic Reasoning, GMD St.Augustin 1989, G.Brewka, H.Freitag Eds., [FLM]) have examined a natural extension of finitary inference rules to the infinite case. We present here some results related to this problem. The first shows that the extension does not preserve cautious monotony. This was formulated as a question in the original version of [FLM] , the new version cites our result, though without proof. The second shows that two versions of distributivity are equivalent - as shown in [FLM], distributivity plus cautious monotony is strong enough to carry cautious monotony through to the extension. The third result gives a partial (induction through regular cardinals) answer to a natural question concerning a parallel problem in the infinite. The fourth result cautions against one kind of weakening of the basic construction. Basically, the weakened approach corresponds to convergent partial sequences, the original one to totally converging sequences. It is not surprising that the former can give funny logics. The fifth presents another technique for constructing still quite well-behaved non-monotonic logics.

1990 ----

23 [JS90]

R.B.Jensen, K.Schlechta : "Results on the Generic Kurepa Hypothesis", Archive for Mathematical Logic, Vol. 30 (1990), p. 13-27 Abstract : K.J.Devlin has extended Jensen’s construction of a model of ZFC and CH without Souslin trees to a model without Kurepa trees either. We modify the construction again to obtain a model with these properties, but in addition, without Kurepa trees in ccc-generic extensions. We use a partially defined box-sequence, given by a fine structure lemma. We also show that the usual collapse of kappa Mahlo to omega_2 will give a model without Kurepa trees not only in the model itself, but also in ccc-extensions.

Articles submitted (or soon to be submitted) to international journals ----------------------------------------------------------------------

2009 ----

Articles submitted to international conferences, proceedings etc.: ------------------------------------------------------------------

Manuscripts (to be submitted): ------------------------------

In preparation: ---------------

Articles in refereed books with international participation -----------------------------------------------------------

2014

24 ---[Sch14]

K.Schlechta: "Non-monotonic logic: preferential versus algebraic semantics" in: "David Makinson on classical methods for non-classical problems", S.O.Hansson Ed., Springer, Heidelberg, 2014

2007 ---[Sch07]

K.Schlechta: "Nonmonotonic logics - a preferential approach", in: "Handbook of the history of logic", vol.8: "The many-valued and non-monotonic turn in logic", D.Gabbay, J.Woods eds., Elsevier, 2007, pp. 451-516

2002 ---[Sch02-1]

K.Schlechta : "Considrations subjectives sur la smantique de la rvision des thories" (trad. P.Livet), in "Rvision des croyances", P.Livet ed., Herms/Lavoisier, Paris, 2002, p. 167-180 Abstract : Nous allons nous contrer sur un mode de pense que l’on pourrait peut-tre nommer "philosophie de la formalisation" de la thorie de la rvision, en comparant sans exigences trop strictes les diffrentes proprits et les structures smantiques, et en vitant autant que possible de trop rentrer dans les dtails techniques.

1995 ---[Sch95-4]

K.Schlechta : "Some Completeness Results for Classical Preferential Models", in "Logic, Action, and Information", A.Fuhrmann, H.Rott eds., De Gruyter, Berlin/New York, 1995/96, p. 229-237 Abstract : After giving basic definitions, facts and examples for preferential structures in Section 1, we present here without proof several completeness results for such preferential structures. In each case, our main technical result is combinatorial in character, the transfer to logic will always be more or less straightforward.

Articles in refereed proceedings of international conferences -------------------------------------------------------------

25

1999 ---[DS99]

J.Dix, K.Schlechta: Explaining updates by minimal sums, 19th. Intern. Conf. on Foundations of Software Technology and Theoretical Computer Science, 13-15 Dec. 1999, IIT Campus, Chennai, India, Springer LNCS 1738 Abstract: Human reasoning about developments of the world involves always an assumption of inertia. We discuss two approaches for formalizing such an assumption, based on the concept of an explanation: (1) there is a general preference relation given on the set of all explanations, (2) there is a notion of a distance between models and explanations are preferred if their sum of distances is minimal. We show exactly under which conditions the converse is true as well and therefore both approaches are equivalent modulo these conditions. Our main result is a general representation theorem in the spirit of Kraus, Lehmann and Magidor.

1998 ---[ALS99]

L.Audibert, C.Lhoussaine, K.Schlechta: "Distance based revision of preferential logics", in Belief Revision Workshop of KR98 (Knowledge Representation), Trento, Italy, 1998 (electronic proceedings) See [ALS99] (above).

[AS98]

L.Audibert, K.Schlechta: Defeasible inheritance and reference classes, to appear in the Proceeding of the Belief Revision Workshop of KR98 (Knowledge Representation), Trento, Italy, 1998, Hans Rott, Maryanne Williams eds. Abstract: We formalize how information from a reference class is used to augment the information of a base class. While theory revision operates on theories and formulas of the same language, the languages of the base and the reference class might be different. The information we consider is defeasible, and we examine two approaches, one working on preferential models expressing this information, the other working on the partial orders defined by the information. We show that our two approaches are equivalent. We finally apply these ideas to elucidate defeasible inheritance, choosing the reference classes via valid paths, and, conversely, we motivate the definition of valid paths with the reference class concept.

1996 ---[SLM96]

K.Schlechta, D.Lehmann, M.Magidor : "Distance Semantics for Belief Revision", in

26 Proceedings of: Theoretical Aspects of Rationality and Knowledge, Tark VI, 1996, ed. Y.Shoham, Morgan Kaufmann, San Francisco, 1996, p. 137-145 Abstract : A vast and interesting family of natural semantics for Belief Revision is defined. Suppose one is given a distance d between any two models. One may define the revision of a theory K by a formula a as the theory defined by the set of all those models of a that are closest, by d, to the set of models of K. This family is characterized by a set of rationality postulates that extends the AGM postulates. The new postulates describe properties of iterated revisions.

1995 ---[Sch95-6]

K.Schlechta : "A Two-Stage Approach to First Order Default Reasoning", in "Symbolic and Quantitative Approaches to Reasoning and Uncertainty" (Proceedings of ECSQARU-95, Fribourg, Suisse, July 1995), C.Froidevaux, J.Kohlas eds., p. 379-386, Springer Lecture Notes in AI, 1995 See [Sch96-2].

[Sch95-7]

K.Schlechta : "A Reduction of the Theory to the Notions of Distance and Measure", "Symbolic and Quantitative Approaches to Uncertainty" (Proceedings of ECSQARU-95, July 1995), C.Froidevaux, J.Kohlas eds., Springer Lecture Notes in AI, 1995

of Confirmation in Reasoning and Fribourg, Suisse, p. 387-394,

See [Sch97-1]. [Sch95-8]

K.Schlechta : "A Reduction of the Theory of Confirmation to the Notions of Distance and Measure", 10th International Congress of Logic, Methodology and Philosophy of Science, Firenze (Italy), August 1995 See [Sch97-1].

1993 ---[BS93]

F.Baader, K.Schlechta : "A Semantics for Open Normal Defaults via a Modified Preferential Approach", in "Symbolic and Quantitative Approaches to Reasoning and Uncertainty" (Proceedings of ECSQARU-93, Granada, Spain, November 1993), M.Clarke, R.Kruse, S.Moral eds., p. 9-16, Springer Lecture Notes in AI, 1993 1991 ----

[Sch91-3]

K.Schlechta : "Some Results on Theory Revision", "The Logic of Theory Change", A. Fuhrmann, M. Morreau eds., Springer Verlag 1991, p.72-92

[BMS91-1]

G.Brewka, D.Makinson, K.Schlechta : "JTMS and Logic Programming", "Proceedings International Workshop on Non-Monotonic Reasoning and Logic Programming", Washington, Juli 1991

27 Abstract : This paper makes three main points. We observe first that the inference relation induced by a set of JTMS justification rules (or equivalently, by a logic program with negation under the Gelfond-Lifschitz semantics) is not in general cumulative: the addition to a set of assumptions of some of the derivable conclusions may lead to a loss of others. We then show how cumulativity may be restored by adapting a technique recently applied by Brewka to default logic. The basic idea is to upgrade the universe of discourse: replace the elementary propositions, between which inference customarily takes place, by more complex items consisting of elementary propositions indexed by certain of the "reasons" that lead to their acceptance. However, as we finally show, the indexed JTMS still has a shortcoming: it does not give an adequate treatment of the phenomenon of "floating conclusions". The problem of finding an alternative aproach that handles floating conclusions adequately without losing cumulativity again, remains open. [BMS91-2]

G.Brewka, D.Makinson, K.Schlechta : "Cumulative Inference Relations for JTMS and Logic Programming", "Nonmonotonic and Inductive Logic", J.Dix, K.P.Jantke, P.Schmitt eds., Springer Verlag 1991, p.1-12 Abstract : This paper makes three main points. We observe first that the inference relation induced by a set of JTMS justification rules under the grounded model semantics (or equivalently, by a logic program with negation under the Gelfond-Lifschitz semantics) is not in general cumulative: the addition to a set of assumptions of some of the derivable conclusions may lead to a loss of others. We then show how cumulativity may be restored by adapting a technique recently applied by Brewka to default logic. The basic idea is to upgrade the universe of discourse: replace the elementary propositions, between which inference customarily takes place, by more complex items consisting of elementary propositions indexed by certain of the "reasons" that lead to their acceptance. However, as we finally show, the indexed JTMS still has a shortcoming: it does not give an adequate treatment of the phenomenon of "floating conclusions". The problem of finding an alternative aproach that handles floating conclusions adequately without losing cumulativity again, remains open.

1990 ---[Sch90]

K.Schlechta : "Semantics for Defeasible Inheritance", Proceedings ECAI 90, L.G.Aiello ed., London 1990, p.594-597 Abstract : We will propose a semantics for non-monotonic

28 inheritance which can handle preclusion. Our approach is based on formalizing the notion of a "normal" subset, allowing us to state e.g. "normally, all p are q". Since for preclusion, direct links are in a stronger way true than valid paths, we express this by different degrees of "normality", resulting in a many-valued semantics. Primarily, our semantics is intended for the directly sceptical approach; for extensions, we suggest a combination with possible worlds.

1989 ---[Sch89-1]

K.Schlechta : "Defeasible Inheritance : Coherence Properties and Semantics", "Proceedings of Tubingen Workshop on Semantic Networks and Non-Monotonic Reasoning", M.Morreau ed., SNS-Report 89-48, Seminar fur naturlichsprachliche Systeme, Universitaet Tubingen, (1989) Abstract : In Makinson, Schlechta: "Floating Conclusions and Zombie Paths", Artificial Intelligence 48 (1991), p.199-209 ([MS91]), we discussed problems of both the directly sceptical and the extensions approach to reasoning in defeasible inheritance systems. Here, we present and examine solutions to some of these problems, giving stability special attention. In addition, we present a (class of) semantics for defeasible inheritance, based on "normal" subsets.

[Sch89-2]

K.Schlechta : "Directly Sceptical Inheritance cannot Capture the Intersection of Extensions", "Proceedings Workshop Non-Monotonic Reasoning 1989", G.Brewka, H.Freitag eds., GMD-Report 443, Arbeitspapiere der Gesellschaft fur Mathematik und Datenverarbeitung (1989) See [Sch93].

Articles in refereed proccedings of national conferences --------------------------------------------------------

1988 ---[Sch88-1]

K.Schlechta : "Remarks on Shoham’s Temporal Logic", Proceedings der GWAI 88, W.Hoeppner ed., Springer Verlag 1988 (Informatik Fachberichte Nr. 181) Abstract : We describe a problem in Shoham’s system of temporal logic and present a solution.

[Sch88-2]

K.Schlechta : "Remarks on Consistency and Completeness of Circumscription" Proceedings der GWAI 88, W.Hoeppner ed.,

29 Springer Verlag 1988 (Informatik Fachberichte Nr. 181) Abstract : We discuss definable minimal models, the semantical counterpart of first order circumscription, examine the adequacy of Mott’s system of circumscription and show that some completeness results of Perlis and Minker fail in Mott’s system.

Technical reports and archive submissions -----------------------------------------

Note : 1. Some Technical Reports have also been submitted for publication elsewhere or appeared as such meanwhile. 2. "LIM" stands for: Laboratoire d’Informatique de Marseille, CNRS ESA 6077, Universite de Provence, CMI, 39, Rue Joliot-Curie, F-13453 Marseille Cedex 13, France 3. "LIF" stands for: Laboratoire d’Informatique Fondamentale de Marseille, CNRS UMR, Universite de Provence, CMI, 39, Rue Joliot-Curie, F-13453 Marseille Cedex 13, France www.lif.univ-mrs.fr

2010 ---[GS10-t1]

Dov Gabbay, Karl Schlechta: Critical analysis of the Carmo-Jones system of Contrary-to-Duty obligations arXiv.org 1002.3021, (submitted Feb. 16, 2010)

2006 ---[Sch06-t1]

Karl Schlechta: Domain closure conditions and definability preservation HAL ccsd-00084398, arXiv.org math.LO/0607189, 73 p., (submitted July 7, 2006) Abstract: We show the importance of closure of the domain under finite unions, in particular for Cumulativity, and representation results. We see that in the absence of this closure, Cumulativity fans out to an infinity of different conditions. We introduce the concept of an algebraic limit, and discuss its importance. We then present a representation result for a new concept of revision, introduced by Booth et al., using approximation by formulas. We analyse definability preservation problems, and show that intersection is the crucial step. We simplify older proofs for

30 the non-definability cases, and add a new result for ranked structures. AMS Classification: 03B42, 03B65, 03B70, 68T27, 68T30

[Sch06-t2]

Karl Schlechta: Remarks on inheritance systems HAL hal-00117112, arXiv.org math.LO/0611937 11 p., (submitted November 30, 2006) Abstract: We try a conceptual analysis of inheritance diagrams, first in abstract terms, and then compare to "normality" and the "small/big sets" of preferential and related reasoning. The main ideas are about nodes as truth values and information sources, truth comparison by paths, accessibility or relevance of information by paths, relative normality, and prototypical reasoning. AMS Classification: 68T27, 68T30

2003 ---[Sch03-t1]

Karl Schlechta: Coherent systems LIF TR 14-2003 (Preliminary version of [Sch04]) Abstract: We discuss several types of common sense reasoning, reduce them to a small number of basic semantical concepts, and show several (in-)completeness results for such logics.

2000 ---[SFBMS00]

Karl Schlechta, Enrico Formenti, Jean-Marc Batty, Jean Francois Morcillot, Sophie Sadok: "Comments on ’Belief revision with unreliable observations’ ", LIM Research Report 2000-362 Abstract: We discuss the article "Belief Revision with Unreliable Observations" by C.Boutilier, N.Friedman, and J.Halpern, and give a characterization of (a finite variant) of Markov systems, using an old algorithm, due to Farkas.

[Sch00-m1]

K.Schlechta: "Representation results for limit preferential structures", Research Report, 2000-8, Institut des Sciences Cognitives, 67 blvd. Pinel, F-69675 Bron Cedex, France

31

1999 ---[Sch00-1]

K.Schlechta: New techniques and completeness results for preferential structures Research Report, 1999-5, Institut des Sciences Cognitives, 67 blvd. Pinel, F-69675 Bron Cedex, France See [Sch00-1] (above).

[Sch97-t2]

K.Schlechta: Representation results for revision and update (in cooperation with D.Lehmann and M.Magidor) Research Report, 1999-4, Institut des Sciences Cognitives, 67 blvd. Pinel, F-69675 Bron Cedex, France Abstract : These notes are based on joint work with D.Lehmann and M.Magidor, Hebrew University, Jerusalem. Thus, they are coauthors in substance. We show a number of representation results for revision and update, all based on distances between models, or on ranked orders between sequences of models. Section 2: We first show an abstract representation result. It will be used for update (Proposition 5.4), and a close analogue will be used for one proof for the asymmetric revision case (Proposition 4.7). We can apply it to the symmetric revision case too, but there it does not seem to simplify the situation. Its main value is perhaps more psychological than mathematical: It gives a direction how to build the completeness proof, by pointing out which Lemmas to prove (Facts 4.5, 4.6, 4.10, 4.11, 5.2, 5.3). Section 3: We treat revision determined by a symmetric distance between models. As usual, we first (Section 3.1) work on (sets of) models, and turn then to logic (Section 3.2). Section 4: We treat revision determined by a not necessarily symmetric distance between models. We work in the finite case (finiteness is used repeatedly in the proofs), and only with sets of models. Translation to logic will be straightforward. After some initial remarks (Section 4.1), we give two proofs with slightly different conditions. The latter one (Section 4.3) is based on Daniel Lehmann’s conditions. Section 5: We treat update determined by a ranked order between sequences of developments, again we work in the finite case, and only with models. We first (Section 5.2) treat the case where subsequences are supposed to be better explanations. We give two representation results, with two somewhat different sets of conditions (Section 5.2.1, Section 5.2.2). Finally (Section 5.3), we treat the case where sequences are ordered by the sum of their differences - a distance between individual models being given.

[Sch99-t1]

K.Schlechta, "A new approach to preferential

32 structures", in "DGNMR99, Proceedings of the fourth Dutch-German workshop on nonmonotonic reasoning techniques and their applications", H.Rott, C.Albert, G.Brewka, C.Witteveen eds., Research Report, Institute for Logic, Language, and Computation, Amsterdam, The Netherlands See [SGMRT00] (above).

1998 ---[ALS98-t]

L.Audibert, C.Lhoussaine, K.Schlechta: "Distance based revision of preferential logics" LIM Research Report RR 262, 3/98 See [ALS99] (above).

[LMS01]

D.Lehmann, M.Magidor, K.Schlechta: "Distance Semantics for Belief Revision", Leibniz Center for Research in Computer Science, Technical Report TR-98-10, Institute of Computer Science, Hebrew University, Givat Ram, Jerusalem 91904, Israel See [LMS01] (above).

[BLS99]

S.Berger, D.Lehmann, K.Schlechta: "Preferred History Semantics for Iterated Updates", Leibniz Center for Research in Computer Science, Technical Report TR-98-11, Institute of Computer Science, Hebrew University, Givat Ram, Jerusalem 91904, Israel See [BLS99] (above).

[AS98]

L.Audibert, K.Schlechta: "Defeasible inheritance and reference classes" LIM Research Report RR 281, 9/98 See [AS98] (above).

1997 ---[BGHPSW97-t] D.Bellot, C.Godefroid, P.Han, J.P.Prost, K.Schlechta, E.Wurbel: "A semantical approach to the concept of screened revision", LIM Research Report RR 217, 3/97 See [BGHPSW97].

1996 ---[Sch96-t1]

K.Schlechta: Filters and Partial Orders LIM Research Report RR 140, 1/96 See [Sch97-4].

[Sch96-t2]

K.Schlechta : "On basic concepts and ideas of nonmonotonic logics",

33 LIM Research Report RR 192, 10/96 See [Sch97-2].

1995 ---[LMS95-t1]

D.Lehmann, M.Magidor, K.Schlechta : "A Semantics for Theory Revision", LIM Research Report 1995 - 126

[Sch95-t1]

K.Schlechta : "Inheritance - Language or Structure ?", LIM Research Report RR 138, 12/95 Abstract : We argue that logic and the structural information of inheritance diagrams might be quite different. We show how a seemingly reasonable attempt to give a semantics to inheritance diagrams via a coherent system of filters fails. We further argue that structural information should perhaps be considered as primitive. Given then such structural information, and theories valid for single nodes, structure can determine inheritance of these theories. Conflicts can be solved in a theory revision approach. Conflicts between theories of equal weight necessitate a modified (symmetric) revision operation. We give a possible solution of symmetric revision based on a distance semantics.

1994 ---[Sch94-t1]

K.Schlechta : "Limit Preferential Models", LIM Research Report RR 6, 03/94 Abstract : We show a representation theorem for a subclass of limit preferential models.

[Sch94-t2]

K.Schlechta : "Completeness and Incompleteness for Plausibility Logic", LIM Research Report RR 7, 04/94 See [Sch96-3].

[Sch92-n4]

K.Schlechta : "Some Completeness Results for Stoppered and Ranked Classical Preferential Models", LIM Research Report RR 15, 05/94 See [Sch96-1].

[Sch89-n1]

K.Schlechta : "Defaults as Generalized Quantifiers", LIM Research Report RR 16, 05/94 See [Sch95-1].

[Sch92-n9]

K.Schlechta : "Preferences in Dynamic Structures", LIM Research Report RR 17, 05/94 See [Sch95-3].

34 [Sch94-t3]

K.Schlechta : "Some Completeness Results for Propositional Conditional Logics", LIM Research Report RR 23, 06/94 See [Sch95-5].

[Sch94-t4]

K.Schlechta : "A Two-Stage Approach to First Order Default Reasoning", LIM Research Report RR 36, 09/94 See [Sch96-2].

[SM94]

K.Schlechta, D.Makinson : "Local and Global Metrics for the Semantics of Counterfactual Conditionals", LIM Research Report RR 37, 09/94 See [SM94].

[Sch94-t5]

K.Schlechta : "A Reduction of the Theory of Confirmation to the Notions of Distance and Measure", LIM Research Report RR 64, 12/94 See [Sch97-1].

1993 ---[BS93-t1]

F.Baader, K.Schlechta : "A Semantics for Open Normal Defaults via a Modified Preferential Approach", Internal Report RR-93-13, Deutsches Forschungszentrum fur Kunstliche Intelligenz (DFKI), Stuhlsatzenhausweg 3, D-66123 Saarbrucken, Germany, 1993

[Sch92-n1]

K.Schlechta : "Logic, Topology, and Integration", Tech. Rept. of Gesellschaft fur Mathematik und Datenverarbeitung, (GMD), POB 1240, D-53757 St.Augustin, Germany, 1993 See [Sch95-2].

1992 ---[Sch92-t1]

K.Schlechta : "Results on Non-Monotonic Logics", IWBS Report 204, IBM Germany, IWBS, POB 80 08 80, D-7000 Stuttgart 80, Germany, 1992 (Habilitation Thesis, University of Hamburg)

[SM89]

K.Schlechta, D.Makinson : "On Principles and Problems of Defeasible Inheritance", Internal Report RR-92-59, Deutsches Forschungszentrum fur Kunstliche Intelligenz (DFKI), Stuhlsatzenhausweg 3, D-66123 Saarbrucken, Germany, 1992 Abstract : We have two aims here: First, to discuss some basic principles underlying different approaches to Defeasible Inheritance; second, to examine problems of these approaches as they already appear in quite simple diagrams. We build upon, but go beyond, the discussion in the joint paper of Touretzky, Horty, and Thomason: A Clash of Intuitions (D.S.Touretzky, J.F.Horty, R.H.Thomason : A Clash of Intuitions : The Current State of Nonmonotonic Multiple

35 Inheritance Systems, IJCAI 1987). [Sch88-n1]

K.Schlechta : "Defaults, Preorder Semantics and Circumscription", Internal Report RR-92-60, Deutsches Forschungszentrum fur Kunstliche Intelligenz (DFKI), Stuhlsatzenhausweg 3, D-66123 Saarbrucken, Germany, 1992 Abstract : We examine questions related to translating defaults into circumscription. Imielinski has examined the concept of preorder semantics as an abstraction from specific systems of circumscription. We give precise definitions, characterize preorder semantics syntactically and examine the translatability of one default into preorder semantics. Finally, we give a rather bleak outlook on the translation of defaults into circumscription.

Talks at international conferences without proceedings (but with programm ------------------------------------------------------------------------committee or on invitation) ---------------------------

December 1989, Conference on defeasible inheritance, Tubingen on "Defeasible Inheritance" June 1990, Nonmonotonic Reasoning Workshop, Lake Tahoe on "Defaults as Generalized Quantifiers" September 1990, Conference on non-monotonic logics, Konstanz on "Preferential Models" Fall 1990, Deduktionstreffen, Lautenbach on "Defaults as Generalized Quantifiers" December 1990, NIL90, Karlsruhe on "Homogenousness in Defeasible Reasoning" December 1991, NIL91, Schloss Reinhardsbrunn on "Some Results for Preferential Structures" August 1992, Workshop Logic and Change, GWAI, Bonn on "New Results on Preferential Structures" October 1992, LogIn, Konstanz on "Preferential Structures" August 95, "Logic Colloquium 95", Haifa, Israel, invited talk August 95, "Seventh European Summer School in Logic", invited talk March 99, "Fourth Dutch-German Workshop on Nonmonotonic Reasoning Techniques and Their Applications", Amsterdam, invited talk

Various activities ------------------

Organization: August 95, "Seventh European Summer School in Logic", co-organizer of Workshop (with F.Baader) June 00, LiCS-Workshop, "Nonmonotonicity and Belief Revision", co-organizer (with D.Lehmann) I have invited (dates are approximate):

36 Yuri Gurevich, University of Michigan, USA, December 1994 Shai Ben-David, Technion, Haifa, Israel, February 1996 Menachem Magidor, Hebrew University, Jerusalem, Israel, June 1996 Daniel Lehmann, Hebrew University, Jerusalem, Israel, June 1997 Aron Avron, Tel Aviv, Israel, June 2005 David Makinson, London, May 2006 I was invited: Hebrew University, Jerusalem, Israel, April 1995, by Daniel Lehmann and Menachem Magidor Editor: I was Associate editor of the journal Studia Logica Reviewing: I have reviewed for various journals and conferences.