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by Ricardo Caferra
Logic for Computer Science and Artificial Intelligence
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Preface
Chapter 1: Introduction
1.1. Logic, foundations of computer science, and applications of logic to computer science
1.2. On the utility of logic for computer engineers
Chapter 2: A Few Thoughts Before the Formalization
2.1. What is logic?
2.1.1. Logic and paradoxes
2.1.2. Paradoxes and set theory
2.1.2.1. The answer
2.1.3. Paradoxes in arithmetic and set theory
2.1.3.1. The halting problem
2.1.4. On formalisms and well-known notions
2.1.4.1. Some “well-known” notions that could turn out to be difficult to analyze
2.1.5. Back to the definition of logic
2.1.5.1. Some definitions of logic for all
2.1.5.2. A few more technical definitions
2.1.5.3. Theory and meta-theory (language and meta-language)
2.1.6. A few thoughts about logic and computer science
2.2. Some historic landmarks
Chapter 3: Propositional Logic
3.1. Syntax and semantics
3.1.1. Language and meta-language
3.1.2. Transformation rules for cnf and dnf
3.2. The method of semantic tableaux
3.2.1. A slightly different formalism: signed tableaux
3.3. Formal systems
3.3.1. A capital notion: the notion of proof
3.3.2. What do we learn from the way we do mathematics?
3.4. A formal system for PL (PC)
3.4.1. Some properties of formal systems
3.4.2. Another formal system for PL (PC)
3.4.3. Another formal system
3.5. The method of Davis and Putnam
3.5.1. The Davis-Putnam method and the SAT problem
3.6. Semantic trees in PL
3.7. The resolution method in PL
3.8. Problems, strategies, and statements
3.8.1. Strategies
3.9. Horn clauses
3.10. Algebraic point of view of propositional logic
Chapter 4: First-order Terms
4.1. Matching and unification
4.1.1. A motivation for searching for a matching algorithm
4.1.2. A classification of trees
4.2. First-order terms, substitutions, unification
Chapter 5: First-Order Logic (FOL) or Predicate Logic (PL1, PC1)
5.1. Syntax
5.2. Semantics
5.2.1. The notions of truth and satisfaction
5.2.2. A variant: multi-sorted structures
5.2.2.1. Expressive power, sort reduction
5.2.3. Theories and their models
5.2.3.1. How can we reason in FOL?
5.3. Semantic tableaux in FOL
5.4. Unification in the method of semantic tableaux
5.5. Toward a semi-decision procedure for FOL
5.5.1. Prenex normal form
5.5.1.1. Skolemization
5.5.2. Skolem normal form
5.6. Semantic trees in FOL
5.6.1. Skolemization and clausal form
5.7. The resolution method in FOL
5.7.1. Variables must be renamed
5.8. A decidable class: the monadic class
5.8.1. Some decidable classes
5.9. Limits: Gödel’s (first) incompleteness theorem
Chapter 6: Foundations of Logic Programming
6.1. Specifications and programming
6.2. Toward a logic programming language
6.3. Logic programming: examples
6.3.1. Acting on the execution control: cut “/”
6.3.2. Negation as failure (NAF)
6.3.2.1. Some remarks about the strategy used by LP and negation as failure
6.3.2.2. Can we simply deduce instead of using NAF?
6.4. Computability and Horn clauses
Chapter 7: Artificial Intelligence
7.1. Intelligent systems: AI
7.2. What approaches to study AI?
7.3. Toward an operational definition of intelligence
7.3.1. The imitation game proposed by Turing
7.4. Can we identify human intelligence with mechanical intelligence?
7.4.1. Chinese room argument
7.5. Some history
7.5.1. Prehistory
7.5.2. History
7.6. Some undisputed themes in AI
Chapter 8: Inference
8.1. Deductive inference
8.2. An important concept: clause subsumption
8.2.1. An important problem
8.3. Abduction
8.3.1. Discovery of explanatory theories
8.3.1.1. Required conditions
8.4. Inductive inference
8.4.1. Deductive inference
8.4.2. Inductive inference
8.4.3. Hempel’s paradox (1945)
8.5. Generalization: the generation of inductive hypotheses
8.5.1. Generalization from examples and counter examples
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
9.1.10.1. Paramodulation and demodulation
9.2. Constraints
9.3. Second Order Logic (SOL): a few notions
9.3.1. Syntax and semantics
9.3.1.1. Vocabulary
9.3.1.2. Syntax
9.3.1.3. Semantics
Chapter 10: Non-Classical Logics
10.1. Many-valued logics
10.1.1. How to reason with p-valued logics?
10.1.1.1. Semantic tableaux for p-valued logics
10.2. Inaccurate concepts: fuzzy logic
10.2.1. Inference in FL
10.2.1.1. Syntax
10.2.1.2. Semantics
10.2.2. Herbrand’s method in FL
10.2.2.1. Resolution and FL
10.3. Modal logics
10.3.1. Toward a semantics
10.3.1.1. Syntax (language of modal logic)
10.3.1.2. Semantics
10.3.2. How to reason with modal logics?
10.3.2.1. Formal systems approach
10.3.2.2. Translation approach
10.4. Some elements of temporal logic
10.4.1. Temporal operators and semantics
10.4.1.1. A famous argument
10.4.2. A temporal logic
10.4.3. How to reason with temporal logics?
10.4.3.1. The method of semantic tableaux
10.4.4. An example of a PL for linear and discrete time: PTL (or PLTL)
10.4.4.1. Syntax
10.4.4.2. Semantics
10.4.4.3. Method of semantic tableaux for PLTL (direct method)
Chapter 11: Knowledge and Logic: Some Notions
11.1. What is knowledge?
11.2. Knowledge and modal logic
11.2.1. Toward a formalization
11.2.2. Syntax
11.2.2.1. What expressive power? An example
11.2.2.2. Semantics
11.2.3. New modal operators
11.2.3.1. Syntax (extension)
11.2.3.2. Semantics (extension)
11.2.4. Application examples
11.2.4.1. Modeling the muddy children puzzle
11.2.4.2. Corresponding Kripke worlds
11.2.4.3. Properties of the (formalization chosen for the) knowledge
Chapter 12: Solutions to the Exercises
Bibliography
Index
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