Book description
Logic and its components (propositional, first-order, non-classical) play a key role in Computer Science and Artificial Intelligence. While a large amount of information exists scattered throughout various media (books, journal articles, webpages, etc.), the diffuse nature of these sources is problematic and logic as a topic benefits from a unified approach. Logic for Computer Science and Artificial Intelligence utilizes this format, surveying the tableaux, resolution, Davis and Putnam methods, logic programming, as well as for example unification and subsumption. For non-classical logics, the translation method is detailed.
Logic for Computer Science and Artificial Intelligence is the classroom-tested result of several years of teaching at Grenoble INP (Ensimag). It is conceived to allow self-instruction for a beginner with basic knowledge in Mathematics and Computer Science, but is also highly suitable for use in traditional courses. The reader is guided by clearly motivated concepts, introductions, historical remarks, side notes concerning connections with other disciplines, and numerous exercises, complete with detailed solutions, The title provides the reader with the tools needed to arrive naturally at practical implementations of the concepts and techniques discussed, allowing for the design of algorithms to solve problems.
Table of contents
- Cover
- Title Page
- Copyright
- Preface
- Chapter 1: Introduction
- Chapter 2: A Few Thoughts Before the Formalization
-
Chapter 3: Propositional Logic
- 3.1. Syntax and semantics
- 3.2. The method of semantic tableaux
- 3.3. Formal systems
- 3.4. A formal system for PL (PC)
- 3.5. The method of Davis and Putnam
- 3.6. Semantic trees in PL
- 3.7. The resolution method in PL
- 3.8. Problems, strategies, and statements
- 3.9. Horn clauses
- 3.10. Algebraic point of view of propositional logic
- Chapter 4: First-order Terms
-
Chapter 5: First-Order Logic (FOL) or Predicate Logic (PL1, PC1)
- 5.1. Syntax
- 5.2. Semantics
- 5.3. Semantic tableaux in FOL
- 5.4. Unification in the method of semantic tableaux
- 5.5. Toward a semi-decision procedure for FOL
- 5.6. Semantic trees in FOL
- 5.7. The resolution method in FOL
- 5.8. A decidable class: the monadic class
- 5.9. Limits: Gödel’s (first) incompleteness theorem
- Chapter 6: Foundations of Logic Programming
- Chapter 7: Artificial Intelligence
- Chapter 8: Inference
-
Chapter 9: Problem Specification in Logical Languages
-
9.1. Equality
- 9.1.1. When is it used?
- 9.1.2. Some questions about equality
- 9.1.3. Why is equality needed?
- 9.1.4. What is equality?
- 9.1.5. How to reason with equality?
- 9.1.6. Specification without equality
- 9.1.7. Axiomatization of equality
- 9.1.8. Adding the definition of = and using the resolution method
- 9.1.9. By adding specialized rules to the method of semantic tableaux
- 9.1.10. By adding specialized rules to resolution
- 9.2. Constraints
- 9.3. Second Order Logic (SOL): a few notions
-
9.1. Equality
-
Chapter 10: Non-Classical Logics
- 10.1. Many-valued logics
- 10.2. Inaccurate concepts: fuzzy logic
- 10.3. Modal logics
- 10.4. Some elements of temporal logic
- Chapter 11: Knowledge and Logic: Some Notions
- Chapter 12: Solutions to the Exercises
- Bibliography
- Index
Product information
- Title: Logic for Computer Science and Artificial Intelligence
- Author(s):
- Release date: August 2011
- Publisher(s): Wiley
- ISBN: 9781848213012
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