9780195080292

Modern Logic A Text in Elementary Symbolic Logic

by
  • ISBN13:

    9780195080292

  • ISBN10:

    0195080297

  • Format: Paperback
  • Copyright: 1/20/1994
  • Publisher: Oxford University Press

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Summary

Filling the need for an accessible, carefully structured introductory text in symbolic logic, Modern Logic has many features designed to improve students' comprehension of the subject, including a proof system that is the same as the award-winning computer program MacLogic, and a specialappendix that shows how to use MacLogic as a teaching aid. There are graded exercises at the end of each chapter--more than 900 in all--with selected answers at the end of the book. Unlike competing texts, Modern Logic gives equal weight to semantics and proof theory and explains their relationship,and develops in detail techniques for symbolizing natural language in first-order logic. After a general introduction featuring the notion of logical form, the book offers sections on classical sentential logic, monadic predicate logic, and full first-order logic with identity. A concluding sectiondeals with extensions of and alternatives to classical logic, including modal logic, intuitionistic logic, and fuzzy logic. For students of philosophy, mathematics, computer science, or linguistics, Modern Logic provides a thorough understanding of basic concepts and a sound basis for more advancedwork.

Author Biography


Graeme Forbes is Professor of Philosophy at the University of Colorado at Boulder. He is the author of Attitude Problems (Oxford, 2006), Languages of Possibility (1989), and The Metaphysics of Modality (Oxford, 1985). He has held research fellowships at New College, Oxford, and Edinburgh University, and has taught at the University of California at Santa Barbara and at Riverside.

Table of Contents

Part I Classical Sentential Logic
What Is Logic?
3(9)
Arguments
3(2)
Logical form and validity
5(3)
Complications
8(2)
A note to the reader
10(1)
Summary
11(1)
First Steps in Symbolization
12(33)
The sentential connectives
12(2)
Negations, conjunctions and disjunctions
14(6)
Conditionals and biconditionals
20(7)
Symbolizing entire arguments
27(8)
The syntax of the formal language
35(5)
Quotation, selective and otherwise
40(4)
Summary
44(1)
Semantics for Sentential Logic
45(41)
Truth-functions
45(8)
Classifying formulae
53(5)
Testing for validity by exhaustive search
58(4)
Testing for validity by constructing interpretations
62(6)
Testing for validity by with semantic tableaux
68(4)
Properties of semantic consequence
72(2)
Expressive completeness
74(7)
Non-truth-functional connectives
81(4)
Summary
85(1)
Natural Deduction in Sentential Logic
86(63)
The concept of proof
86(2)
Rules for conjunction and the conditional
88(12)
Sequents and theorems
100(2)
Rules for negation
102(7)
Rules for disjunction
109(8)
The biconditional
117(2)
Heuristics
119(1)
Sequent and Theorem Introduction
120(8)
Alternative formats for proofs
128(5)
Systems equivalent to NK
133(7)
Semantic and deductive consequence compared
140(4)
Summary
144(5)
Part II Monadic Predicate Logic
Prediction and Quantification in English
149(21)
A different type of argument
149(3)
Further steps in symbolization: the existential quantifier
152(6)
More symbolizations: the universal quantifier
158(7)
The syntax of LMPL
165(4)
Summary
169(1)
Validity and Provability in Monadic Predicate Logic
170(49)
Semantics for the quantifiers
170(10)
Constructing counterexamples
180(5)
Deductive consequence: quantifiers in NK
185(10)
The rule of Existential Elimination
195(9)
Extensions of sequent introduction
204(3)
Decision procedures
207(4)
Tableaux for monadic predicate logic
211(3)
Alternative formats
214(2)
Summary
216(3)
Part III First-Order Logic with Identity
Advanced Symbolizations
219(31)
N-place predicates
219(12)
Identity, number and descriptions
231(10)
The syntax of LFOL
241(2)
Ambiguity
243(6)
Summary
249(1)
Validity and Provability in First-Order Logic with Identity
250(45)
Interpretations in LFOL
250(7)
Demonstrating invalidity
257(6)
Proofs in NK
263(6)
Rules for identity in NK
269(6)
Properties of binary relations
275(7)
Alternative formats
282(1)
Semantic consequence, deductive consequence and decidability
283(3)
Some limitations of first-order logic
286(5)
Summary
291(4)
Part IV Extensions and Alternatives to Classical Logic
Modal Logic
295(38)
Modal operators
295(1)
A definition of semantic consequence for sentential modal logic
296(5)
The canonical translation
301(5)
Natural deduction in S5
306(7)
First-order modal logic: S5 semantics
313(8)
First-order modal logic: natural deduction
321(11)
Summary
332(1)
Intuitionistic Logic
333(16)
The motivation for intuitionistic logic
333(5)
Semantic consequence in intuitionistic sentential logic
338(6)
Intuitionistic monadic predicate logic
344(5)
Fuzzy Logic
349(9)
Sorites paradoxes
349(2)
Degrees of truth
351(1)
Fuzzy semantics for LFOL
352(4)
Resolution of the paradoxes
356(2)
Appendix: Using MacLogic 358(2)
Solutions to Selected Exercises 360(31)
Bibliography 391(2)
Index 393

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