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

Cambridge University Press, Apr 10, 2008 - Science - 242 pages
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 4 Nonnormal Modal Logics Strict 64 5 Conditional Logics 82 6 Intuitionist Logic 103 7 Manyvalued Logics 120 8 First Degree Entailment 142 Note that vwA 1 iff vwA 0 iff 152 9 Logics with Gaps Gluts 163
 16 Necessary Identity in Modal Logic 349 17 Contingent Identity in 367 Ancients the Evening Star The latter for example could have 368 The countermodel determined by the tableau may be depicted as 371 18 Nonnormal Modal Logics 384 188 History 397 19 Conditional Logics 399 1929 Variable domain C VC is obtained by modifying CC 402

 10 Relevant Logics 188 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 Since p holds at w Op holds at wo 250 12 Classical Firstorder Logic 263 A HI B means A h B and B 271 13 Free Logics 290 1347 It has been suggested by some that sentences in 295 14 Constant Domain Modal Logics 308 1436 The countermodel determined by the tableau can be depicted 313 15 Variable Domain Modal Logics 329
 20 Intuitionist Logic 421 not be true Choose any constant c with entry number 448 21 Manyvalued Logics 456 e d 463 2169 One ﬁnal example Some have argued that paradoxical sentences 465 22 First Degree Entailment 476 2233 Here is another to show that VxPxVxPx D Qx 480 23 Logics with Gaps 504 24 Relevant Logics 535 2423 Validity is defined in terms of truth preservation at 536 25 Fuzzy Logics 564 2545 Finally before we turn to identity I note that 572