Logic

✍ Scribed by Salmon W.C.

• Publisher: Prentice-Hall
• Year: 1973
• Tongue: English
• Leaves: 157
• Series: Foundations of Philosophy
• Edition: 2ed
• Category: Library

✦ Synopsis

This volume contains a revised and updated version of the authors Ph.D. dissertation and is focused on proof methods and theorem proving for conditional and preferential logics. Conditional logics are extensions of classical logic by means of a conditional operator, usually denoted as =>. Conditional logics have a long history and recently they have found application in several areas of AI, including belief revision and update, the representation of causal inferences in action planning and the formalization of hypothetical queries in deductive databases. Conditional logics have also been applied in order to formalize nonmonotonic reasoning. The study of the relations between conditional logics and nonmonotonic reasoning has led to the seminal work by Kraus, Lehmann and Magidor, who have introduced the so-called KLM framework. According to this framework, a defeasible knowledge base is represented by a finite set of conditional assertions of the form A |~ B, whose intuitive reading is ""typically (normally), the A's are B's"". The operator |~ is nonmonotonic in the sense that A |~ B does not imply A and C |~ B. The logics of the KLM framework, also known as preferential logics, allow to infer new conditional assertion from a given knowledge base. In spite of their significance, very few deductive mechanisms have been developed for conditional and preferential logics. In this book, the author tries to (partially) fill the existing gap by introducing proof methods (sequent and tableau calculi) for conditional and preferential logics, as well as theorem provers obtained by implementing the proposed calculi. IOS Press is an international science, technical and medical publisher of high-quality books for academics, scientists, and professionals in all fields. Some of the areas we publish in: -Biomedicine -Oncology -Artificial intelligence -Databases and information systems -Maritime engineering -Nanotechnology -Geoengineering -All aspects of physics -E-governance -E-commerce -The knowledge economy -Urban studies -Arms control -Understanding and responding to terrorism -Medical informatics -Computer Sciences

✦ Table of Contents

Title ......Page 1
Copyright ......Page 2
Dedication ......Page 3
Contents ......Page 4
Preface ......Page 6
Argument ......Page 8
Inference ......Page 14
Discovery and Justification ......Page 17
Deductive and Inductive Arguments ......Page 20
Validity ......Page 25
Conditional Statements ......Page 29
Conditional Arguments ......Page 31
Reductio ad Absurdum ......Page 37
The Dilemma ......Page 39
Truth Tables and Validity ......Page 41
Logical Equivalences ......Page 49
Tautologies ......Page 52
Categorical Statements ......Page 54
Categorical Syllogisms ......Page 57
Venn Diagrams and Class Logic ......Page 66
The Logic of Relations ......Page 77
Quantifiers: the Fallacy of "Every" and "All" ......Page 81
Deductive Logic ......Page 86
Inductive Correctness ......Page 88
Induction by Enumeration ......Page 90
Insufficient Statistics ......Page 91
Biased Statistics ......Page 92
Statistical Syllogism ......Page 94
Argument from Authority ......Page 98
Argument against the Man ......Page 101
Analogy ......Page 104
Causal Arguments and Causal Fallacies ......Page 107
Hypotheses ......Page 112
Use and Mention ......Page 125
Definitions ......Page 129
Analytic, Synthetic, and Contradictory Statements ......Page 136
Contraries and Contradictories ......Page 140
Ambiguity and Equivocation ......Page 142
FOR FURTHER READING ......Page 145
ARGUMENT FORMS (CORRECT AND FALLACIOUS) ......Page 147
INDEX ......Page 149