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

Cambridge University Press, Apr 10, 2008 - Science
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