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Summary
This title explains how to use the English language with logical responsibility, how to define and use formal language, and how to reason correctly. Specific issues include propositional and predicate logic, logic networks, logic programming, proof of correctness, semantics, syntax, and theorems of Herbrand and Kalman.
Table of Contents
| Preliminaries of "Naive" Mathematical Logic | |
| PART I. Propositional Logic | |
| The Formal Language of Propositional Logic | |
| The Formal Language Lo of Propositional Logic Using Parentheses | |
| The Formal Language Lo of Propositional Logic without Parentheses (Polish Notation) | |
| The Truth Structure on Lo in Semantic Version | |
| Boolean Interpretations of the Language Lo | |
| Semantic Deduction | |
| The Semantic Lindenbaum Algebra of Lo | |
| The Truth Structure of Lo in the Syntactic Version | |
| The System of Hilbert H: Axioms, Inference, Theorems | |
| Metatheorems | |
| The Syntactic Lindenbaum Algebra of Lo. Normal Formulas | |
| Connections between the Truth Structures on Lo in Semantic and Syntactic Versions | |
| All Theorems Are Tautologies (Soundness of Prepositional Logic) | |
| All Tautologies Are Theorems (Completeness of Propositional Logic) | |
| Another Proof of the Completeness Metatheorem | |
| Other Syntactic Versions of the Truth Structure on Lo | |
| The Systems L and M; Their Equivalence to the System H | |
| Some Remarks about the Independence of Axioms | |
| The System C of Lukasiewicz and Tarski | |
| Elements of Fuzzy Propositional Logic | |
| Some Elementary Notions about Fuzzy Sets | |
| The Language of Fuzzy Propositional Logic | |
| The Semantic Truth Structure of Fuzzy Propositional Logic | |
| Elements of Fuzzy Propositional Logic in Syntactic Version | |
| Applications of Propostional Logic in Computer Science | |
| Recall about Lindenbaum Algebra of the Language Lo | |
| Some Connections of Lo with Programming Languages | |
| Karnaugh Maps | |
| Switching Networks | |
| Logical Networks | |
| Exercises for Part I | |
| PART II. Predicate Logic | |
| Introductory Considerations | |
| The Formal Language of Predicate Logic | |
| The Formal Alphabet of Predicate Logic; Formal Words | |
| Terms and Formulas | |
| The Semantic Truth Structure on the Language L of Predicate Logic | |
| The Notion of Interpretation of the Language L | |
| Semantic Deduction in Predicate Logic | |
| The Syntactic Truth Structure on the Language L of Predicate Logic | |
| Axioms, Theorems | |
| Some Remarkable Metatheorems | |
| Completeness of Predicate Logic | |
| Elements of Fuzzy Predicate Logic | |
| The Language of Fuzzy Predicate Logic | |
| The Semantic Truth Structure of Fuzzy Predicate Logic | |
| The Syntactic Truth Structure of Fuzzy Predicate Logic | |
| Further Applications of Logic in Computer Science | |
| Elements of the Theory of Resolution | |
| Elements of Logical Foundations of Prolog | |
| Elements of Approximate Reasoning for Expert Systems Design | |
| Exercises for Part II | |
| A. Boolean Algebras | |
| B. MV-Algebras | |
| C. General Considerations about Fuzzy Sets | |
| Index | |
| References |
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