Adaptive Logics and Dynamic Proofs. Mastering the Dynamics of Reasoning, with Special Attention to Handling Inconsistency.

Transcription

1 Adaptive Logics and Dynamic Proofs. Mastering the Dynamics of Reasoning, with Special Attention to Handling Inconsistency. Diderik Batens October 11, 2010

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3 Contents Preface 1 1 Introduction What is an Adaptive Logic? Dynamic Reasoning Forms Specific Features Languages Static Proofs Semantics for Logics that Have Static Proofs Classical Logic Example: Handling Inconsistency A Paradigmatic Problem A Regular Paraconsistent Logic Enter Dynamics A Failing Strategy The Reliability Strategy The Minimal Abnormality Strategy The Predicative Cases Final Derivability Semantics The Classical Symbols Concluding Comments Appendix: Proof of Theorems and Example: Inductive Generalization Promises A First Logic of Inductive Generalization Heuristic Matters and Further Comments Two Alternatives Combined Adaptive Logics Handling Background Knowledge Conjectures Some Comments in Conclusion v

4 vi CONTENTS 4 The Standard Format Introduction The Definition Excursion on the Classical Symbols Proofs Semantics The Upper Limit Logic Dynamic Proofs Adaptive Dynamic Proofs and Dialogues Reliability Minimal Abnormality Excursion: Classical Disjunctions in Dab-formulas Dynamic Semantics Modifications to Adaptive Logics from Previous Chapters Metatheory of The Standard Format Some Facts about Choice Sets Strong Reassurance Soundness and Completeness The Adequacy of Final Derivability Punctual Uniformity Some Further Properties Equivalent Premise Sets Maximality of the Lower Limit Logic Border Cases Some Negative Theorems Strategies and Combinations Other Strategies Simple Blindness Normal Selections The Flip-flop Strategy Counting Combined Adaptive Logics Unions of Sets of Abnormalities Sequential Superpositions Examples and Metatheoretic Problems Closed Unions of Consequence Sets Ordered Fusions of Adaptive Logics More Ways to Handle Inconsistency The Need for Variants Some More Regular Paraconsistent Logics The Corresponding Adaptive Logics As Normal As Possible Identifying Inconsistent Objects

5 CONTENTS vii 8 Corrective Adaptive Logics Not Only Inconsistency-Adaptive Logics Variants and Combinations Ambiguity-Adaptive Logics Adaptive Zero Logic Strength of Paraconsistency and Ambiguity Flip-flop Criteria Integration within the Adaptive Program Aim Compatibility Inconsistent Compatibility Integrating Normal Selections Integrating the Flip-flop Strategy Integrating Counting Rescher Manor RM and their Enrichment Aim A Failure A Second Failure Other Proposal / Heuristic Considerations Direct Proofs Formula-Preferential Systems Computational and Philosophical Computational Complexity Criteria for Final Derivability Criteria: Tableau Methods Tableaux for the Lower Limit Logic Tableaux for the Adaptive Logics Criteria: Proof Procedures Reliability Minimal Abnormality Reasoning in the Absence of a Criterion Interesting Open Problems References 329 Note on the Index 339 Index 340 A afspraken Dirk + TE DOEN 349 A.1 talen A.2 Add: Defeasible Reasoning and Adaptive Logics A.3 Urgent: REVISE A.4 NIET VERGETEN A.5 GP

6 viii CONTENTS B Notes on Some Concepts 353 B.1 The Consequence Relation B.2 Proofs B.3 Semantics C Notes 357 C.1 Consistency by Brute Force C.2 Extensional Logics C.3 Infinite proofs C.4 Troubles with Φ(Γ) C.4.1 Infinite extensions required C.4.2 Uncountable Φ(Γ) C.4.3 Need the proof be infinite? C.4.4 The Way Premise sets are Given C.4.5 Criteria for Uncountable Φ(Γ) C.5 Arguments for Inserting Lines C.6 Examples of Simple Defeasible Mechanisms C.7 Interpretation of Expectancies D More Notes 365 D.1 Henkin and Compactness D.2 Prospective Dynamics and Axiom schemata D.3 Content-Guided Choice of an Adaptive Logic D.4 Adaptive Logics Defined by Rules D.5 Relation with argumentation E Verwijderd 369 E.1 Idea behind the Technical Treatment E.2 Flip-flops: stuk uit flipflop-afdeling E.3 LP flip-flop / deels fout E.4 Tijdelijk E.5 Direct bewijs van Corr E.6 oude versie eigenschappen