M.J. Cresswell

Indeholder "Preface", "Note on References", "Note to the Second Printing", "Part I. Modal Propositional Logic", "1. Non-modal Propositional Calculus", " Primitive symbols and formation rules of PC", " Interpretation", " Further operators", " Interpretation of ., ⊃, ≡", " Validity", " Testing for validity (i) the truth-table method", " Testing for validity (ii) the Reductio method", " Substitution of equivalents", " Conjunctive normalform", " Axiomatization of PC", " The system PM", " Consistency", " Completeness", "2. The System T", " The basic modal notions", " Systems of modal logic", " The system T", " Method of setting out proofs", " Proofs of theorems", " Consistency of T", " Exercises", "3. The Systems S4 and S5", " Introduction", " The system S4", " Modalities in S4", " The system S5", " Modalities in S5", " Modal functions and modal degree", " Modal conjunctive normal form", " MCNF theorem", " Modal functions in S4", " The Brouwerian system", " Consistency", " Collapsing into PC", " Exercises", "4. Validity in T, S4 and S5", " The PC game", " The T game", " The S4 game", " The S5 game", " Some results", " Formal definitions of validity", " The intuitive interpretation of models and validity", " Exercises", "5. T: Decision Procedure and Completeness", " Testing for T-validity", " Semantic diagrams as a decision procedure for T", " The completeness of T", " Exercises", "6. S4 and S5: Decision Procedures and Completeness", " S4-diagrams", " The completeness of S4", " S5-diagrams", " An alternative decision procedure for S5", " The completeness of S5", " Exercises", "7. Some Alternative Bases for T, S4 and S5", " Alternative bases for T", " Alternative bases for S4", " Alternative bases for S5", " Exercises", "Part II. Modal Predicate Logic", "8. The Lower Predicate Calculus", " The non-modal lower predicate calculus", " Interpretation", " Validity in LPC", " Axiomatization", " Modal lower predicate calculi", " The consistency of modal LPC", " Validity in modal LPC", " The monadic modal LPC", "9. The Completeness of Modal LPC", " The general structure of a Henkin proof", " Maximal consistent sets", " Some properties of maximal consistent sets", " The completeness of PM", " The completeness of T, S4 and S5", " The completeness of (non-modal) LPC", " The completeness of modal LPC", "10. Modality and Existence", " Validity without the Barcan formula", " Completeness without the Barcan formula", " Interpretation of modal LPC models", " Kripke's semantics for modal LPC", " Modality de dicta and modality de re", "11. Identity and Description in Modal LPC", " LPC with identity", " Modal LPC with identity", " Semantics for modal LPC with identity", " Contingent identity systems", " Semantics for T + I and S4 + I", " Descriptions", " Introducing descriptions by definition", " Sets and attributes", "Part III. A Survey of Modal Logic", "12. The Lewis Systems (I)", " Historical preamble", " The 'paradoxes of implication'", " The system SI", " SI and T compared", " 'T-principles' in SI", " The system S2", " The system S3", " The system S4", " The system S5", "13. The Lewis Systems (II)", " The distinctness of SI-S5", " Alternative bases for the Lewis systems", " The Lewis systems and T", "14. Other Modal Propositional Systems", " The system SO.5", " Systems with the Brouwerian axiom", " Systems with generalized S4 axioms", " Systems between S4 and S5", " Systems between S3 and S5", " Extensions of S4 not contained in S5", " Non-regular systems", " Other modal predicate calculi", "15. Validity and Decision Procedures for Various Systems", " Validity in S2 and S3", " Decision procedures for S2 and S3", " Validity in S6-S8", " Decision procedures for S6-S8", " The systems S3.5 and S9", " The system SO.5", " Systems containing T", " The existence postulate", "16. Non-standard Systems", " Systems with primitives other than L or M", " The system E", " Systems without the axiom of necessity", " Systems without any theses of the form Lα", " A system without the interdefinability of L and M", " Systems based on non-classical propositional calculi", " The Ł-modal system", "17. Boolean Algebra and Modal Logic", " Boolean algebras", " Boolean algebra and PC", " Boolean algebras with added operators", " Boolean algebras and the system T", " Boolean algebras and T-validity", "Appendix 1. Natural Deduction and Modal Systems", "Appendix 2. Entailment and Strict Implication", "Appendix 3. Axiomatic Bases for Propositional Modal Systems", "Appendix 4. Notation", "Appendix 5. Kripke's Model Structures and Hintikka's Model Sets", "Solutions to Exercises", "Bibliography", "Index of Authors", "Index of Subjects", "List of Symbols and Important Rules".

En introduktion til modal logik.… (plus d'informations)