The Logic of Partial Information

1. Front Matter

   Pages I-XXV

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2. Introduction

   • Areski Nait Abdallah

   Pages 1-20

3. Partial Propositional Logic

   • Areski Nait Abdallah

   Pages 21-55

4. Syntax of the Language of Partial Information Ions

   • Areski Nait Abdallah

   Pages 56-66

5. Reasoning with Partial Information Ions: An Overview

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   Pages 67-102

6. Semantics of Partial Information Logic of Rank 1

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   Pages 103-157

7. Semantics of Partial Information Logic of Infinite Rank

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   Pages 158-171

8. Algebraic Properties of Partial Information Ionic Logic

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   Pages 172-216

9. Beth Tableaux for Propositional Partial Information Ionic Logic

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   Pages 217-262

10. Applications; the Statics of Logic Systems

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    Pages 263-304

11. Naive Axiomatics and Proof Theory of Propositional Partial Information Ionic Logic

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    Pages 305-355

12. Soundness of Propositional Partial Information Ionic Logic

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    Pages 356-365

13. Formal Axiomatics of Propositional Partial Information Ionic Logic

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    Pages 366-388

14. Extension and Justification Closure Approach to Partial Information Ionic Logic

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    Pages 389-424

15. Partial First-Order Logic

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    Pages 425-452

16. Syntax and Semantics of First-Order Partial Information Ions

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    Pages 453-465

17. Beth Tableaux for First-Order Partial Information Ions

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    Pages 466-499

18. Axiomatics and Proof Theory of First-Order Partial Information Ionic Logic

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    Pages 500-505

19. Partial Information Ionic Logic Programming

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    Pages 506-536

20. Syntactic and Semantic Paths; Application to Defeasible Inheritance

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    Pages 537-561

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.

• Artificical Intelligence
• Künstliche Intelligenz
• Logik
• Programmiersprachen
• Programming Languages
• Reasoning
• Semantik
• algorithms
• logic
• nonmonotonic reasoning
• semantics
• uncertainty

• Middlesex College, Department of Computer Science, University of Western Ontario, London, Canada

  Areski Nait Abdallah

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