A NEW INTRODUCTION TO MODAL LOGIC A NEW INTRODUCTI

文件名称: A NEW INTRODUCTION TO MODAL LOGIC

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详细说明： A NEW INTRODUCTION TO MODAL LOGIC Preface ix Part One: Basic Modal Propositional Logic 1 The Basic Notions 3 The language of PC C) Interpretation D) Further operators F) Interpretation of A , D and s G) Validity (8) Testing for validity: (i) the truth-ta ble method A0) Testing for validity: (ii) the Reductio method A1) Some valid wff of PC A3) Basic modal notions A3) The language of propositional modal logic A6) Validity in propositional modal logic A7) Exercises — 1 B1) Notes B2) 2 The Systems K, T and D 23 Systems of modal logic B3) The system K B4) Proofs of theorems B6) L and M C3) Validity and soundness C6) The system T D1) A definition of validity for T D3) The system D D3) A note on derived rules D5) Consistency D6) Constant wff D7) Exercises — 2 D8) Notes D9) 3 The Systems S4, S5, B, Triv and Ver 51 Iterated modalities E1) The system S4 E3) Modalities in S4 E4) Validity for S4 E6) The system S5 E8) Modalities in S5 E9) Validity for S5 F0) The Brouwerian system F2) Validity for B F3) Some other systems F4) Collapsing into PC F4) Exercises — 3 F8) Notes G0) 4 Testing for validity 72 Semantic diagrams G3) Alternatives in a diagram (80) S4 diagrams (85) S5-diagrams (91) Exercises — 4 (92) Notes (93) 5 Conjunctive Normal Form 94 Equivalence transformations (94) Conjunctive normal form (96) Modal functions and modal degree (97) S5 reduction theorem (98) MCNF theorem A01) Testing formulae in MCNF A03) The completeness of S5 A05) A decision procedure for S5-validity A08) Triv and Ver again A08) Exercises — 5 A10) Notes A10) 6 Completeness 111 Maximal consistent sets of wff A13) Maximal consistent extensions A14) Consistent sets of wff in modal systems A16) Canonical models A17) The completeness of K, T, B, S4 and S5 A19) Triv and Ver again A21) Exercises — 6 A22) Notes A23) Part Two: Normal Modal Systems 7 Canonical Models 127 Temporal interpretations of modal logic A27) Ending time A31) Convergence A34) The frames of canonical models A36) A non-canonical system A39) Exercises — 7 A41) Notes A42) 8 Finite Models 145 The finite model property A45) Establishing the finite model property A45) The completeness of KW A50) Decidability A52) Systems without the finite model property A53) Exercises — 8 A56) Notes A56) 9 Incompleteness 159 Frames and models A59) An incomplete modal system A60) KH and KW A64) Completeness and the finite model property A65) General frames A66) What might we understand by incompleteness? A68) Exercises — 9 A69) Notes A70) 10 Frames and Systems 172 Frames for T, S4, B and S5 A72) Irreflexiveness A76) Compactness A77) S4.3.1 A79) First-order definability A81) Second-order logic A88) Exercises — 10 A89) Notes A90) 11 Strict Implication 193 Historical preamble A93) The 'paradoxes of implication' A94) Material and strict implication A95) The 'Lewis' systems A97) The system SI A98) Lemmon's basis for SI A99) The system S2 B00) The system S3 B00) Validity in S2 and S3 B01) Entailment B02) Exercises — 11 B05) Notes B06) 12 Glimpses Beyond 210 Axiomatic PC B10) Natural deduction B11) Multiply modal logics B17) The expressive power of multi-modal logics B19) Propositional symbols B20) Dynamic logic B20) Neighbourhood semantics B21) Intermediate logics B24) 'Syntactical' approaches to modality B25) Probabilistic semantics B27) Algebraic semantics B29) Exercises — 12 B29) Notes B30) Part Three: Modal Predicate Logic 13 The Lower Predicate Calculus 235 Primitive symbols and formation rules of non-modal LPC B35) Interpretation B37) The Principle of replacement B40) Axiomatization B41) Some theorems of LPC B42) Modal LPC B43) Semantics for modal LPC B43) Systems of modal predicate logic B44) Theorems of modal LPC B44) Validity and soundness B47) De re and de dicto B50) Exercises — 13 B54) Notes B55) 14 The Completeness of Modal LPC 256 Canonical models for Modal LPC B56) Completeness in modal LPC B62) Incompleteness B65) Other incompleteness results B70) The monadic modal LPC B71) Exercises — 14 B72) Notes B72) 15 Expanding Domains 274 Validity without the Barcan Formula B74) Undefined formulae B77) Canonical models without BF B80) Completeness B82) Incompleteness without the Barcan Formula B83) LPC + S4.4 (S4.9) B83) Exercises — 15 B87) Notes B87) 16 Modality and Existence 289 Changing domains B89) The existence predicate B92) Axiomatization of systems with an existence predicate B93) Completeness for existence predicates B96) Incompleteness C02) Expanding languages C02) Possibilist quantification revisited C03) Kripke-style systems C04) Completeness of Kripke-style systems C06) Exercises — 16 C09) Notes C10) 17 Identity and Descriptions 312 Identity in LPC C12) Soundness and completeness C14) Definite descriptions C18) Descriptions and scope C23) Individual constants and function symbols C27) Exercises — 17 C28) Notes C29) 18 Intensional Objects 330 Contingent identity C30) Contingent identity systems C34) Quantifying over all intensional objects C35) Intensional objects and descriptions C42) Intensional predicates C44) Exercises — 18 C47) Notes C48) 19 Further Issues 349 First-order modal theories C49) Multiple indexing C50) Counterpart theory C53) Counterparts or intensional objects? C57) Notes C58) Axioms, Rules and Systems 359 Axioms for normal systems C59) Some normal systems C61) Non- normal systems C63) Modal predicate logic C65) Table I: Normal Modal Systems C67) Table II: Non-normal Modal Systems C68) Solutions to Selected Exercises 369 Bibliography 384 Index 398 ...展开收缩

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