Preliminaries of "Naive" Mathematical Logic |
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PART I. Propositional Logic |
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The Formal Language of Propositional Logic |
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The Formal Language Lo of Propositional Logic Using Parentheses |
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The Formal Language Lo of Propositional Logic without Parentheses (Polish Notation) |
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The Truth Structure on Lo in Semantic Version |
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Boolean Interpretations of the Language Lo |
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Semantic Deduction |
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The Semantic Lindenbaum Algebra of Lo |
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The Truth Structure of Lo in the Syntactic Version |
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The System of Hilbert H: Axioms, Inference, Theorems |
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Metatheorems |
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The Syntactic Lindenbaum Algebra of Lo. Normal Formulas |
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Connections between the Truth Structures on Lo in Semantic and Syntactic Versions |
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All Theorems Are Tautologies (Soundness of Prepositional Logic) |
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All Tautologies Are Theorems (Completeness of Propositional Logic) |
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Another Proof of the Completeness Metatheorem |
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Other Syntactic Versions of the Truth Structure on Lo |
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The Systems L and M; Their Equivalence to the System H |
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Some Remarks about the Independence of Axioms |
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The System C of Lukasiewicz and Tarski |
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Elements of Fuzzy Propositional Logic |
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Some Elementary Notions about Fuzzy Sets |
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The Language of Fuzzy Propositional Logic |
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The Semantic Truth Structure of Fuzzy Propositional Logic |
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Elements of Fuzzy Propositional Logic in Syntactic Version |
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Applications of Propostional Logic in Computer Science |
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Recall about Lindenbaum Algebra of the Language Lo |
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Some Connections of Lo with Programming Languages |
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Karnaugh Maps |
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Switching Networks |
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Logical Networks |
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Exercises for Part I |
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PART II. Predicate Logic |
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Introductory Considerations |
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The Formal Language of Predicate Logic |
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The Formal Alphabet of Predicate Logic; Formal Words |
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Terms and Formulas |
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The Semantic Truth Structure on the Language L of Predicate Logic |
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The Notion of Interpretation of the Language L |
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Semantic Deduction in Predicate Logic |
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The Syntactic Truth Structure on the Language L of Predicate Logic |
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Axioms, Theorems |
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Some Remarkable Metatheorems |
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Completeness of Predicate Logic |
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Elements of Fuzzy Predicate Logic |
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The Language of Fuzzy Predicate Logic |
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The Semantic Truth Structure of Fuzzy Predicate Logic |
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The Syntactic Truth Structure of Fuzzy Predicate Logic |
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Further Applications of Logic in Computer Science |
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Elements of the Theory of Resolution |
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Elements of Logical Foundations of Prolog |
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Elements of Approximate Reasoning for Expert Systems Design |
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Exercises for Part II |
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A. Boolean Algebras |
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B. MV-Algebras |
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C. General Considerations about Fuzzy Sets |
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Index |
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References |
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