Essays on Non-Classical Logic

by Wansing, Heinrich

• ISBN13: 9789810247355
• ISBN10: 9810247354
• Format: Hardcover
• Copyright: 2001-11-01
• Publisher: WORLD SCIENTIFIC PUB CO INC

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