A New Introduction to Modal Logic

Front Cover
Psychology Press, 1996 - Mathematics - 421 pages

This long-awaited book replaces Hughes and Cresswell's two classic studies of modal logic: An Introduction to Modal Logic and A Companion to Modal Logic.
A New Introduction to Modal Logic is an entirely new work, completely re-written by the authors. They have incorporated all the new developments that have taken place since 1968 in both modal propositional logic and modal predicate logic, without sacrificing tha clarity of exposition and approachability that were essential features of their earlier works.
The book takes readers from the most basic systems of modal propositional logic right up to systems of modal predicate with identity. It covers both technical developments such as completeness and incompleteness, and finite and infinite models, and their philosophical applications, especially in the area of modal predicate logic.

 

Selected pages

Contents

The language of PC 3 Interpretation 4 Further operators
6
Some valid wff of PC 13 Basic modal notions 13 The language
17
The Systems K T and D
23
and M 33 Validity and soundness 36 The system T 41 A definition
45
The Systems S4 S5 B Triv and Ver
51
Iterated modalities 51 The system S4 53 Modalities in S4 54 Validity
60
Collapsing into PC 64 Exercises 3 68 Notes 70
70
Semantic diagrams 73 Alternatives in a diagram 80 S4 diagrams 85
85
Strict Implication
193
200 Validity in S2 and S3 201 Entailment 202 Exercises 11 205
205
Axiomatic PC 210 Natural deduction 211 Multiply modal logics 217
217
logics 224 Syntactical approaches to modality 225 Probabilistic
230
Interpretation 237 The Principle of replacement 240 Axiomatization
241
modal LPC 243 Systems of modal predicate logic 244 Theorems
250
The Completeness of Modal LPC
256
Canonical models for Modal LPC 256 Completeness in modal
262

S5diagrams 91 Exercises 4 92 Notes 93
93
Conjunctive Normal Form
94
Equivalence transformations 94 Conjunctive normal form 96 Modal
108
Maximal consistent sets of wff 113 Maximal consistent extensions 114
114
Consistent sets of wff in modal systems 116 Canonical models 117
121
Canonical Models
127
Convergence 134 The frames of canonical models 136 A noncanonical
142
the finite model property 153 Exercises 8 156 Notes 156
156
Frames and models 159 An incomplete modal system 160 KH and
164
Frames and Systems
172
Frames for T S4 B and S5 172 Irreflexiveness 176 Compactness
188
monadic modal LPC 271 Exercises 14 272 Notes 272
272
Canonical models without BF 280 Completeness 282 Incompleteness
287
Modality and Existence
289
Changing domains 289 The existence predicate 292 Axiomatization
302
Identity in LPC 312 Soundness and completeness 314 Definite
329
Contingent identity 330 Contingent identity systems 334 Quantifying
342
Firstorder modal theories 349 Multiple indexing 350 Counterpart
358
Bibliography
384
Index
398
Copyright

Other editions - View all

A New Introduction to Modal Logic
M.J. Cresswell,G.E. Hughes
Limited preview - 2012
A New Introduction to Modal Logic
M.J. Cresswell,G.E. Hughes
Limited preview - 2012
A New Introduction to Modal Logic
George Edward Hughes,M. J. Cresswell
Limited preview - 1996
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Common terms and phrases

assignment axiom axiomatic B₁ Barcan Formula called canonical model Chapter characterized class of frames conjunction contains defined definition diagram disjunction equivalent fact false falsifying finite model property finite number frame W,R Hughes and Cresswell individual variables intensional objects interpretation irreflexive K-valid L(Lp lemma Lp LLP Lp Ɔ Lẞ maximal consistent sets MCNF means modal LPC modal operators modal predicate logic modal system natural deduction non-modal normal modal system Ɔ L(p Ɔ Lp Ɔ Lq Ɔ q PC wff PC-valid player predicate logic propositional logic prove quantifier rectangle reflexive frames result S-consistent satisfies second-order logic semantics set of wff substitution-instance Suppose symbols tense logic theorem transformation rules Triv true truth-functional truth-value V-property valid value-assignment values w'Rw w₁ w₂ wff of PC x-alternative Y₁

References to this book

Bibliographic information

TitleA New Introduction to Modal Logic
AuthorsGeorge Edward Hughes, M. J. Cresswell
Editionreprint
PublisherPsychology Press, 1996
ISBN0415125995, 9780415125994
Length421 pages
Subjects › 

Mathematics / Logic
Philosophy / General
Philosophy / Logic
  
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