The logic book /
Bergman, Merrie.
The logic book / Merrie Bergman, James Moor and Jack Nelson. - Second edition. - United States McGraw Hill 1990 - xii, 529 pages : illustrations + solutions to selected exercises.
Includes bibligraphies and index.
Basic notions of logic --
Background --
Why study logic? --
Sentences, truth-values, and arguments --
Deductive validity and soundness --
Inductive arguments --
Logical consistency, truth, falsity, and equivalence --
Special cases of validity --
Sentential logic : symbolization and syntax --
Symbolization and truth-functional connectives --
Syntax complex symbolizations --
Non-truth-functional connectives --
The syntax of SL --
Sentential logic : semantics --
Truth-value assignments and truth-tables for sentences --
Truth-functional truth, falsity, and indeterminacy --
Truth-functional equivalence --
Truth-functional consistency --
Truth-functional entailment and truth-functional validity --
Truth-functional properties and truth-functional consistency --
Sentential logic : truth-trees --
The truth-tree method --
Truth-tree rules for sentences containing --
Rules for sentences containing and more complex truth-trees --
Using truth-trees to test for truth-functional truth, falsity, and indeterminacy --
Truth-functional equivalence --
Truth-functional entailment and truth-functional validity --
Sentential logic : derivations --The derivation system SD --
Basic concepts of SD --
Strategies for constructing derivations in SD --
The derivation system SD1 --
Sentential logic : metatheory --
Mathematical induction --
Truth-functional completeness --
The soundness of SD and SD1 --
The completeness of SD and SD1 --
Predicate logic : symbolization and syntax --
The limitations of SL --
Predicates, individual constants, and quantity terms of English --
Introduction to PL --Quantifiers introduced --
The formal syntax of PL --
A, E, I, O, U and O sentences --
Symbolization techniques --
Multiple quantifiers with overlapping scope --
Identity, definite descriptions, properties of relations, and functions --
Predicate logic : semantics --
Informal semantics for PL --
Quantificational truth, falsehood, and indeterminacy --
Quantificational equivalence and consistency --
Quantificational entailment and validity --
Truth-functional expansions --
Semantics for predicate logic with identity and functors --
Formal semantics of PL and PLE --
Predicate logic : truth-trees --
Expanding the rules for truth-trees --
Truth-trees and quantificational consistency --
Truth-trees and other semantic properties --
Fine-tuning the tree method --
Trees for PLE --
Fine-tuning the tree method for PLE --
Predicate logic : derivations --
The derivation system PD --
Using derivations to establish syntactic properties of pd --
The derivation system PD1 --
The derivation system PDE --
Predicate logic : metatheory --
Semantic preliminaries for PL --
Semantic preliminaries for PLE --
The soundness of PD and PDE --
The completeness of PD, PD1, and PDE --
The soundness of the tree method --
The completeness of the tree method.
0079095240
Logic.
BC 135 / .B435
The logic book / Merrie Bergman, James Moor and Jack Nelson. - Second edition. - United States McGraw Hill 1990 - xii, 529 pages : illustrations + solutions to selected exercises.
Includes bibligraphies and index.
Basic notions of logic --
Background --
Why study logic? --
Sentences, truth-values, and arguments --
Deductive validity and soundness --
Inductive arguments --
Logical consistency, truth, falsity, and equivalence --
Special cases of validity --
Sentential logic : symbolization and syntax --
Symbolization and truth-functional connectives --
Syntax complex symbolizations --
Non-truth-functional connectives --
The syntax of SL --
Sentential logic : semantics --
Truth-value assignments and truth-tables for sentences --
Truth-functional truth, falsity, and indeterminacy --
Truth-functional equivalence --
Truth-functional consistency --
Truth-functional entailment and truth-functional validity --
Truth-functional properties and truth-functional consistency --
Sentential logic : truth-trees --
The truth-tree method --
Truth-tree rules for sentences containing --
Rules for sentences containing and more complex truth-trees --
Using truth-trees to test for truth-functional truth, falsity, and indeterminacy --
Truth-functional equivalence --
Truth-functional entailment and truth-functional validity --
Sentential logic : derivations --The derivation system SD --
Basic concepts of SD --
Strategies for constructing derivations in SD --
The derivation system SD1 --
Sentential logic : metatheory --
Mathematical induction --
Truth-functional completeness --
The soundness of SD and SD1 --
The completeness of SD and SD1 --
Predicate logic : symbolization and syntax --
The limitations of SL --
Predicates, individual constants, and quantity terms of English --
Introduction to PL --Quantifiers introduced --
The formal syntax of PL --
A, E, I, O, U and O sentences --
Symbolization techniques --
Multiple quantifiers with overlapping scope --
Identity, definite descriptions, properties of relations, and functions --
Predicate logic : semantics --
Informal semantics for PL --
Quantificational truth, falsehood, and indeterminacy --
Quantificational equivalence and consistency --
Quantificational entailment and validity --
Truth-functional expansions --
Semantics for predicate logic with identity and functors --
Formal semantics of PL and PLE --
Predicate logic : truth-trees --
Expanding the rules for truth-trees --
Truth-trees and quantificational consistency --
Truth-trees and other semantic properties --
Fine-tuning the tree method --
Trees for PLE --
Fine-tuning the tree method for PLE --
Predicate logic : derivations --
The derivation system PD --
Using derivations to establish syntactic properties of pd --
The derivation system PD1 --
The derivation system PDE --
Predicate logic : metatheory --
Semantic preliminaries for PL --
Semantic preliminaries for PLE --
The soundness of PD and PDE --
The completeness of PD, PD1, and PDE --
The soundness of the tree method --
The completeness of the tree method.
0079095240
Logic.
BC 135 / .B435