One must be able to say at all times - in stead of points, straight lines, and planes - tables, chairs and beer mugs. (David Hilbert) One service mathematics has rendered the human race. It has put common sense back where it belongs, on the topmost shelf next to the dusty canister labelled "discarded nonsense. " (Eric T. Bell) This book discusses reasoning with partial information. We investigate the proof theory, the model theory and some applications of reasoning with par tial information. We have as a goal a general theory for combining, in a principled way, logic formulae expressing partial information, and a logical tool for choosing among them for application and implementation purposes. We also would like to have a model theory for reasoning with partial infor mation that is a simple generalization of the usual Tarskian semantics for classical logic. We show the need to go beyond the view of logic as a geometry of static truths, and to see logic, both at the proof-theoretic and at the model-theoretic level, as a dynamics of processes. We see the dynamics of logic processes bear with classical logic, the same relation as the one existing between classical mechanics and Euclidean geometry.
Author(s): Areski Nait Abdallah
Series: Monographs in Theoretical Computer Science. An EATCS Series
Publisher: Springer
Year: 1995
Language: English
Pages: 739
Tags: Artificial Intelligence (incl. Robotics); Mathematical Logic and Formal Languages; Logics and Meanings of Programs; Programming Techniques; Programming Languages, Compilers, Interpreters; Mathematical Logic and Foundations
Front Matter....Pages I-XXV
Introduction....Pages 1-20
Partial Propositional Logic....Pages 21-55
Syntax of the Language of Partial Information Ions....Pages 56-66
Reasoning with Partial Information Ions: An Overview....Pages 67-102
Semantics of Partial Information Logic of Rank 1....Pages 103-157
Semantics of Partial Information Logic of Infinite Rank....Pages 158-171
Algebraic Properties of Partial Information Ionic Logic....Pages 172-216
Beth Tableaux for Propositional Partial Information Ionic Logic....Pages 217-262
Applications; the Statics of Logic Systems....Pages 263-304
Naive Axiomatics and Proof Theory of Propositional Partial Information Ionic Logic....Pages 305-355
Soundness of Propositional Partial Information Ionic Logic....Pages 356-365
Formal Axiomatics of Propositional Partial Information Ionic Logic....Pages 366-388
Extension and Justification Closure Approach to Partial Information Ionic Logic....Pages 389-424
Partial First-Order Logic....Pages 425-452
Syntax and Semantics of First-Order Partial Information Ions....Pages 453-465
Beth Tableaux for First-Order Partial Information Ions....Pages 466-499
Axiomatics and Proof Theory of First-Order Partial Information Ionic Logic....Pages 500-505
Partial Information Ionic Logic Programming....Pages 506-536
Syntactic and Semantic Paths; Application to Defeasible Inheritance....Pages 537-561
The Frame Problem: The Dynamics of Logic Systems....Pages 562-623
Reasoning About Actions: Projection Problem....Pages 624-680
Reasoning About Actions: Explanation Problem....Pages 681-705
Back Matter....Pages 707-718
