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## 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.

1. Cover
2. Title Page
4. Preface
5. Chapter 1: Introduction
6. Chapter 2: A Few Thoughts Before the Formalization
1. 2.1. What is logic?
2. 2.1.2. Paradoxes and set theory
3. 2.1.3. Paradoxes in arithmetic and set theory
4. 2.1.4. On formalisms and well-known notions
5. 2.1.5. Back to the definition of logic
6. 2.1.6. A few thoughts about logic and computer science
2. 2.2. Some historic landmarks
7. Chapter 3: Propositional Logic
1. 3.1. Syntax and semantics
2. 3.2. The method of semantic tableaux
3. 3.3. Formal systems
4. 3.4. A formal system for PL (PC)
5. 3.5. The method of Davis and Putnam
6. 3.6. Semantic trees in PL
7. 3.7. The resolution method in PL
8. 3.8. Problems, strategies, and statements
9. 3.9. Horn clauses
10. 3.10. Algebraic point of view of propositional logic
8. Chapter 4: First-order Terms
1. 4.1. Matching and unification
2. 4.2. First-order terms, substitutions, unification
9. Chapter 5: First-Order Logic (FOL) or Predicate Logic (PL1, PC1)
1. 5.1. Syntax
2. 5.2. Semantics
1. 5.2.1. The notions of truth and satisfaction
2. 5.2.2. A variant: multi-sorted structures
3. 5.2.3. Theories and their models
3. 5.3. Semantic tableaux in FOL
4. 5.4. Unification in the method of semantic tableaux
5. 5.5. Toward a semi-decision procedure for FOL
1. 5.5.1. Prenex normal form
2. 5.5.2. Skolem normal form
6. 5.6. Semantic trees in FOL
7. 5.7. The resolution method in FOL
8. 5.8. A decidable class: the monadic class
9. 5.9. Limits: Gödel’s (first) incompleteness theorem
10. Chapter 6: Foundations of Logic Programming
1. 6.1. Specifications and programming
2. 6.2. Toward a logic programming language
3. 6.3. Logic programming: examples
1. 6.3.1. Acting on the execution control: cut “/”
2. 6.3.2. Negation as failure (NAF)
4. 6.4. Computability and Horn clauses
11. Chapter 7: Artificial Intelligence
1. 7.1. Intelligent systems: AI
2. 7.2. What approaches to study AI?
3. 7.3. Toward an operational definition of intelligence
4. 7.4. Can we identify human intelligence with mechanical intelligence?
5. 7.5. Some history
6. 7.6. Some undisputed themes in AI
12. Chapter 8: Inference
1. 8.1. Deductive inference
2. 8.2. An important concept: clause subsumption
3. 8.3. Abduction
1. 8.3.1. Discovery of explanatory theories
4. 8.4. Inductive inference
5. 8.5. Generalization: the generation of inductive hypotheses
13. Chapter 9: Problem Specification in Logical Languages
1. 9.1. Equality
2. 9.2. Constraints
3. 9.3. Second Order Logic (SOL): a few notions
1. 9.3.1. Syntax and semantics
14. Chapter 10: Non-Classical Logics
1. 10.1. Many-valued logics
1. 10.1.1. How to reason with p-valued logics?
2. 10.2. Inaccurate concepts: fuzzy logic
1. 10.2.1. Inference in FL
2. 10.2.2. Herbrand’s method in FL
3. 10.3. Modal logics
1. 10.3.1. Toward a semantics
2. 10.3.2. How to reason with modal logics?
4. 10.4. Some elements of temporal logic
1. 10.4.1. Temporal operators and semantics
2. 10.4.2. A temporal logic
3. 10.4.3. How to reason with temporal logics?
4. 10.4.4. An example of a PL for linear and discrete time: PTL (or PLTL)
15. Chapter 11: Knowledge and Logic: Some Notions
1. 11.1. What is knowledge?
2. 11.2. Knowledge and modal logic
1. 11.2.1. Toward a formalization
2. 11.2.2. Syntax
3. 11.2.3. New modal operators
4. 11.2.4. Application examples
16. Chapter 12: Solutions to the Exercises
17. Bibliography
18. Index