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9789810247355

Essays on Non-Classical Logic

by
  • ISBN13:

    9789810247355

  • ISBN10:

    9810247354

  • Format: Hardcover
  • Copyright: 2001-11-01
  • Publisher: WORLD SCIENTIFIC PUB CO INC
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Summary

Covers a broad range of up to date issues in non-classical logic that are of interest not only to philosophical and mathematical logicians but also to computer scientists and researchers in artificial intelligence.

Table of Contents

Fine Grained Theories of Time
1(36)
Patrick Blackburn
Priorean Tense Logic
3(4)
Referential Tense Logic
7(10)
A First Look at Allen's System
17(6)
A Sorted Interval-Based Language
23(7)
Concluding Remarks
30(7)
Revision Sequences and Computers With an Infinite Amount of Time
37(24)
Benedikt Lowe
Introduction
37(2)
The Gupta-Belnap Systems
39(6)
Revision Sequences
39(3)
The Systems S# and S*
42(3)
Infinite Time Turing Machines
45(4)
Revision Sequences Modeled by Infinite Time Turing Machines
49(6)
The Limit Rule and Other Applications
55(1)
Aftermath
56(5)
On Frege's Nightmare: A Combination of Intuitionistic, Free and Paraconsistent Logics
61(30)
Shahid Rahman
Aims of This Paper
62(1)
The Dialogical Approach to Free Logic
63(14)
Dialogical Free Logic With and Without tertium non datur
63(5)
Winning Strategies and Dialogical Tableaux for DFL
68(5)
Many Quantifiers and Sorts of Objects --- The System DFLn and DFL ⟨n⟩
73(2)
Combining DFLI and DFLC
75(2)
Inconsistent Objects
77(8)
Paraconsistency
77(2)
The Dialogical Approach to Paraconsistent Logic and Frege's Nightmare
79(6)
Conclusions
85(6)
Truthmakers, Entailment and Necessity
91(20)
Stephen Read
Truthmakers
92(2)
Entailment
94(3)
Necessity
97(3)
Reductionism
100(2)
Proofs
102(5)
Conclusion
107(4)
Global Definability in Basic Modal Logic
111(26)
Maarten de Rijke
Holger Sturm
Introduction
111(2)
Basic Concepts
113(1)
Local Definability
114(3)
Global Definability
117(5)
Hansoul's Theorem
122(5)
Universal Classes
127(3)
Concluding Remarks
130(7)
Ackermann's Implication for Typefree Logic
137(28)
Klaus Robering
Ackermann's Typefree Logic
137(12)
Deductive and Combinatorial Completeness
137(2)
A Deductive Interpretation of Implication
139(1)
The Positive Fragments of Ackermann's Systems
140(4)
The Two Deducibility Relation of Σ+
144(5)
A Hierarchy of Deductive Systems
149(9)
The Base Calculus K0
151(2)
The Calculus K1
153(2)
The Full Hierarchy
155(3)
Algebraic Semantics
158(7)
Ackermann Structures
158(2)
The Canonical Ackermann Lattice
160(5)
Why Dialogical Logic?
165(22)
Helge Ruckert
Introduction
165(6)
Pluralism Concerning Logics and Logical Methodology
166(1)
Dialogical Logic: A Short Outline
167(4)
Prejudices Against Dialogical Logic
171(2)
`Dialogical Logic is a Constructivistic Logic'
171(1)
`Dialogical Logic is Limited to Classical and Intuitionistic Logic'
172(1)
`Dialogical Logic Complicates Things Unnecessarily'
172(1)
Advantages of Dialogical Logic
173(9)
The Distinction between General and Formal Truth
173(2)
The Distinction between the Level of Games and the Level of Strategies
175(2)
The Distinction between the Particle Rules and the Structural Rules
177(5)
Concluding Remarks
182(5)
Semantics for Constructive Negations
187(32)
Yaroslav Shramko
Preliminaries. A Hierarchy of Negations
187(2)
Introduction. ``Kripk-Approach'' to Semantic Analysis
189(1)
Formal Definitions of Constructive Negation and Informal Understanding of Negation in Intuitionism
190(2)
State-Descriptions as a Method of Semantic Analysis. A Model for Positive Logic
192(3)
Intuitionistic State-Descriptions. Models for Negation
195(10)
The System M
200(1)
The System I
200(2)
The System D
202(1)
The System E
203(1)
The System C
204(1)
Propositional Constants
204(1)
Soundness
205(1)
Completeness
206(7)
Generalizations
213(6)
Recent Trends in Paraconsistent Logic
219(28)
Max Urchs
Philosophical and Historical Background
220(3)
A Few Historical Remarks
220(1)
The Principle of Contradiction
221(2)
Harnessing Paraconsistency
223(5)
Mathematics
223(1)
Automated Reasoning
224(2)
Belief Revision
226(1)
Philosophy and Methodology
227(1)
Main Tendencies in Paraconsistent Logic
228(19)
Da Costa's Systems
228(1)
Many-Valued and Relevant Logic
229(2)
Inconsistency Adaptive Logic
231(1)
Non-Adjunctive Systems
232(7)
Other Approaches
239(1)
Will There be a Unification?
240(7)
Obligations, Authorities, and History Dependence
247(10)
Heinrich Wansing
Introduction
247(1)
Identification of Obligations
248(3)
Authorities and Addressees of Norms
251(3)
History Dependence
254(3)
Bibliography 257(2)
Index 259

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