Contents Introduction - logic and logical form What is the subject matter of logic? Logical inference and logical form Logical words A brief history of logic Modern logic 1. Propositional logic 1.1 Conjunction, negation, disjunction What does propositional logic do? Propositions and truth values Atomic and compound sentences Conjunction Negation Disjunction Exercises 1.2 Conditional and biconditional Conditional Biconditional A systematic way to symbolize natural language sentences Exercises 1.3 Truth tables Syntax of propositional logic Semantics of propositional logic. Truth tables Exercises 1.4 Indirect proof Exercises 1.5 Truth-value analysis Exercises 1.6 Logical inference and logical equivalence Logical inference Logical equivalence Exercises 1.7 Quick test of logical inference Exercises 1.8 Natural deduction Inference schemes Equivalence schemes Indirect proof and conditional proof Exercises 1.9 Logical transformations Disjunctive normal form Conjunctive normal form Exercises 2. Traditional logic 2.1 Categorical sentences Subject, predicate, extension of a term Types of categorical sentences Alternative ways to form a categorical sentence Exercises 2.2 Square of opposition. Exercises 2.3 Immediate inferences Conversion Obversion Contraposition Exercises 2.4 Syllogisms What is a syllogism? Figure and mood Valid syllogisms Exercises 2.5 Syllogistic rules Distribution Rules Exercises 2.6 Venn diagrams Exercises 3. Predicate logic 3.1 General and singular terms Exercises 3.2 Variables and quantifiers Variables, open sentences, existential quantifier Universal quantifier. Symbolizing categorical sentences Universe of discourse Exercises 3.3 The advantages of predicate logic Differences between traditional and predicate logic Advantages of predicate over traditional logic Sentences that traditional logic is unable to symbolize Exercises 3.4 Syntax and semantics of predicate logic Syntax of predicate logic Semantics of predicate logic 3.5 Proof procedure The relationship between the quantifiers Universal and existential instantiation The proof procedure Properties of relations Exercises 3.6 Identity The sign of identity Definite descriptions Exercises 3.7 Logical transformations in predicate logic Rules of passage Prenex form Exercises 4. Non-classical logics 4.1 Modal logic Modal operators Syntax of modal logic Semantics of modal logic Different kinds of necessity and possibility Counterfactual conditionals and disposition terms Exercises 4.2 Three-valued logic The principle of bivalence and the law of excluded middle The three-valued logics of Lukasiewicz and Kleene Other reasons for using three-valued logic The three-valued logic of Bochvar Problems in three-valued logic Exercises 5. Appendix 5.1 Completeness of Predicate Logic Concepts and notations Proof procedure Consistency and determinacy of structures Principle of substitutability of equivalents Correctness Existential instantiation does not compromise the proof procedure Validity of used schemes and subproofs with assumptions Alternative formulation of correctness and completeness Some notations, concepts, and propositions from set theory Completeness theorem Bibliography Solutions

Logic

Introduction - logic and logical form What does logic do? Logical inference and logical form Logical words A brief history of logic Modern logic 1. Propositional logic 1.1 Conjunction, negation, disjunction What does propositional logic do? Propositions and truth values Atomic and compound sentences Conjunction Negation Disjunction Exercises 1.2 Conditional and biconditional Conditional Biconditional A systematic way to symbolize natural language sentences Exercises 1.3 Truth tables Syntax of propositional logic Semantics of propositional logic. Truth tables Exercises 1.4 Indirect proof Exercises 1.5 Truth-value analysis Exercises 1.6 Logical inference and logical equivalence Logical inference Logical equivalence Exercises 1.7 Quick test of logical inference Exercises 1.8 Natural deduction Inference schemes Equivalence schemes Indirect proof and conditional proof Exercises 1.9 Logical transformations Disjunctive normal form Conjunctive normal form Exercises 2. Traditional logic 2.1 Categorical sentences Subject, predicate, extension of а term Тypes of categorical sentences Alternative ways to form a categorical sentence Exercises 2.2 Square of opposition Exercises 2.3 Immediate inferences Conversion Obversion Contraposition Exercises 2.4 Syllogisms What is a syllogism? Figure and mood Valid syllogisms Exercises 2.5 Syllogistic rules Distribution Rules Exercises 2.6 Venn diagrams Exercises 3. Predicate logic 3.1 General and singular terms Exercises 3.2 Variables and quantifiers Variables, open sentences, existential quantifier Universal quantifier. Symbolizing categorical sentences Universe of discourse Exercises 3.3 The advantages of predicate logic Differences between traditional and predicate logic Advantages of predicate over traditional logic Sentences that traditional logic is unable to symbolize Exercises 3.4 Syntax and semantics of predicate logic Syntax of predicate logic Semantics of predicate logic 3.5 Proof procedure The relationship between the quantifiers Universal and existential instantiation The proof procedure Properties of relations Exercises 3.6 Identity The sign of identity Definite descriptions Exercises 3.7 Logical transformations in predicate logic Rules of passage Prenex form Exercises 4. Non-classical logics 4.1 Modal logic Modal operators Syntax of modal logic Semantics of modal logic Different kinds of necessity and possibility Counterfactual conditionals and disposition terms Exercises 4.2 Three-valued logic The principle of bivalence and the law of excluded middle The three-valued logics of Lukasiewicz and Kleene Other reasons for using three-valued logic The three-valued logic of Bochvar Problems in three-valued logic Exercises 5. Appendix 5.1 Completeness of Predicate Logic Concepts and notations Proof procedure Consistency and determinacy of structures Principle of substitutability of equivalents Correctness Existential instantiation does not compromise the proof procedure Validity of used schemes and subproofs with assumptions Alternative formulation of correctness and completeness Some notations, concepts, and propositions from set theory Completeness theorem Bibliography Solutions

author: Evgeni Latinov
e-mail: e_latinov@abv.bg

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