An Introduction to Non-Classical Logic: From If to Is

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Cambridge University Press, Apr 10, 2008 - Science
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This revised and considerably expanded 2nd edition brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and their relation to current philosophical issues and debates are discussed. Students with a basic understanding of classical logic will find this book an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will also interest people working in mathematics and computer science who wish to know about the area.
 

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Contents

3 Normal Modal Logics
36
restricted class of interpretations in our case those appropriate for
38
4 Nonnormal Modal Logics Strict
64
5 Conditional Logics
82
6 Intuitionist Logic
103
7 Manyvalued Logics
120
8 First Degree Entailment
142
A false ie untrue Define a relational interpretation p by
160
14 Constant Domain Modal Logics
308
15 Variable Domain Modal Logics
329
16 Necessary Identity in Modal Logic
349
Proof
363
17 Contingent Identity in
367
a Q i
380
18 Nonnormal Modal Logics
384
Imatrix
397

9 Logics with Gaps Gluts
163
10 Relevant Logics
188
C13 If a e N a E a
199
In the Completeness Theorem we have to check that the
216
11 Fuzzy Logics
221
For an account of the variety of fuzzy logics and
239
Manyvalued
241
11a42 As we saw in chapter 8 FDE can be
245
12 Classical Firstorder Logic
263
A HHB means A H B and B H A
271
13 Free Logics
290
1347 It has been suggested by some that sentences in
295
19 Conditional Logics
399
20 Intuitionist Logic
421
not be true Choose any constant c with entry number
448
21 Manyvalued Logics
456
D
463
2169 One final example Some have argued that paradoxical sentences
465
22 First Degree Entailment
476
23 Logics with Gaps
504
24 Relevant Logics
535
25 Fuzzy Logics
564
2545 Finally before we turn to identity I note that
572

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About the author (2008)

Graham Priest is Boyce Gibson Professor of Philosophy, University of Melbourne. His most recent publications include Towards Non-Being (2005) and Doubt Truth to be a Liar (2006).

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