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Introduction to Non-Classical Logic [Mīkstie vāki]

4.17/5 (155 ratings by Goodreads)
(University of Queensland)
  • Formāts: Paperback / softback, 264 pages, height x width x depth: 229x153x17 mm, weight: 420 g, Worked examples or Exercises
  • Izdošanas datums: 22-Feb-2001
  • Izdevniecība: Cambridge University Press
  • ISBN-10: 052179434X
  • ISBN-13: 9780521794343
Citas grāmatas par šo tēmu:
  • Mīkstie vāki
  • Cena: 22,19 €
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  • Formāts: Paperback / softback, 264 pages, height x width x depth: 229x153x17 mm, weight: 420 g, Worked examples or Exercises
  • Izdošanas datums: 22-Feb-2001
  • Izdevniecība: Cambridge University Press
  • ISBN-10: 052179434X
  • ISBN-13: 9780521794343
Citas grāmatas par šo tēmu:
This book is an introduction to non-classical propositional logics. It brings together for the first time in a textbook a range of topics in logic, many of them of relatively recent origin, including modal, conditional, intuitionist, many-valued, paraconsistent, relevant and fuzzy logics. The material is unified by the underlying theme of world-semantics. All of the topics are explained clearly and accessibly, using devices such as tableaux proofs, and their relation to current philosophical issues and debates is discussed. Students with a basic understanding of classical logic will find this an invaluable introduction to an area that has become of central importance in both logic and philosophy, but which, until now, could be studied only through the research literature. It will interest those studying logic, those who need to know about non-classical logics because of their philosophical importance, and, more widely, readers working in mathematics and computer science.

Recenzijas

'For anyone who wants to explore the non-classical systems, this is the only book of its kind and could not be more highly recommended.' The Times Higher Education Supplement

Papildus informācija

This is the first introductory textbook on non-classical propositional logics.
Preface xiii
Mathematical prolegomenon xvii
Set-theoretic notation xvii
Proof by induction xix
Classical logic and the material conditional
1(19)
Introduction
1(1)
The syntax of the object language
2(1)
Semantic validity
3(1)
Tableaux
4(4)
Counter-models
8(1)
Conditionals
9(1)
The material conditional
10(1)
Subjunctive and counterfactual conditionals
11(2)
More counter-examples
13(1)
Arguments for ⊃
14(1)
*Proofs of theorems
15(2)
History
17(1)
Further reading
17(1)
Problems
18(2)
Basic modal logic
20(18)
Introduction
20(1)
Necessity and possibility
20(1)
Modal semantics
21(3)
Modal tableaux
24(4)
Possible worlds: representation
28(1)
Modal realism
29(1)
Modal actualism
30(1)
Meinongianism
31(2)
*Proofs of theorems
33(2)
History
35(1)
Further reading
36(1)
Problems
36(2)
Normal modal logics
38(20)
Introduction
38(1)
Semantics for normal modal logics
38(2)
Tableaux for normal modal logics
40(4)
Infinite tableaux
44(3)
S5
47(1)
Which system represents necessity?
48(4)
*Proofs of theorems
52(2)
History
54(1)
Further reading
54(1)
Problems
55(3)
Non-normal worlds; strict conditionals
58(16)
Introduction
58(1)
Non-normal worlds
58(2)
Tableaux for non-normal modal logics
60(2)
The properties of non-normal logics
62(1)
Strict conditionals
63(1)
The paradoxes of strict implication
64(1)
... and their problems
65(2)
The explosion of contradictions
67(1)
Lewis' argument for explosion
68(1)
*Proofs of theorems
69(2)
History
71(1)
Further reading
72(1)
Problems
72(2)
Conditional logics
74(25)
Introduction
74(1)
Some more problematic inferences
74(3)
Conditional semantics
77(1)
Tableaux for C
78(2)
Extensions of C
80(3)
Similarity spheres
83(5)
C1 and C2
88(3)
Further philosophical reflections
91(2)
*Proofs of theorems
93(2)
History
95(1)
Further reading
96(1)
Problems
96(3)
Intuitionist logic
99(18)
Introduction
99(1)
Intuitionism: the rationale
99(2)
Possible-world semantics for intuitionism
101(3)
Tableaux for intuitionist logic
104(4)
The foundations of intuitionism
108(2)
The intuitionist conditional
110(1)
*Proofs of theorems
111(3)
History
114(1)
Further reading
114(1)
Problems
115(2)
Many-valued logics
117(22)
Introduction
117(1)
Many-valued logic: the general structure
117(2)
The 3-valued logics of Kleene and Łukasiewicz
119(3)
LP and RM3
122(1)
Many-valued logics and conditionals
123(2)
Truth-value gluts: inconsistent laws
125(2)
Truth-value gluts: paradoxes of self-reference
127(1)
Truth-value gaps: denotation failure
128(2)
Truth-value gaps: future contingents
130(1)
Supervaluations, modality and many-valued logic
131(3)
*Proofs of theorems
134(2)
History
136(1)
Further reading
137(1)
Problems
137(2)
First degree entailment
139(23)
Introduction
139(1)
The semantics of FDE
139(2)
Tableaux for FDE
141(3)
FDE and many-valued logics
144(3)
The Routley star
147(4)
Paraconsistency and the disjunctive syllogism
151(1)
*Proofs of theorems
152(7)
History
159(1)
Further reading
159(1)
Problems
160(2)
Basic relevant logic
162(20)
Introduction
162(1)
Adding →
162(1)
Tableaux for K4
163(2)
Non-normal worlds again
165(2)
Tableaux for N4
167(1)
Star again
168(3)
Impossible worlds and relevant logic
171(3)
*Proofs of theorems
174(5)
History
179(1)
Further reading
179(1)
Problems
179(3)
Mainstream relevant logics
182(29)
Introduction
182(1)
The logic B
182(2)
Tableaux for B
184(4)
Extensions of B
188(5)
The system R
193(4)
The ternary relation
197(1)
Ceteris paribus enthymemes
198(4)
*Proofs of theorems
202(3)
History
205(1)
Further reading
206(1)
Problems
207(4)
Fuzzy logic
211(18)
Introduction
211(1)
Sorites paradoxes
211(1)
... and responses to them
212(2)
The continuum-valued logic Ł
214(4)
Axioms for Łx
218(3)
Conditionals in Ł
221(1)
Fuzzy relevant logic
222(3)
History
225(1)
Further reading
226(1)
Problems
226(3)
Conclusion: an historical perspective
229(2)
References 231(6)
Index of names 237(2)
Index of subjects 239