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Deductive Logic in Natural Language

Autor Douglas Cannon
en Limba Engleză Paperback – 13 noi 2002
This text offers an innovative approach to the teaching of logic, which is rigorous but entirely non-symbolic. By introducing students to deductive inferences in natural language, the book breaks new ground pedagogically. Cannon focuses on such topics as using a tableaux technique to assess inconsistency; using generative grammar; employing logical analyses of sentences; and dealing with quantifier expressions and syllogisms. An appendix covers truth-functional logic.
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Specificații

ISBN-13: 9781551114453
ISBN-10: 1551114453
Pagini: 302
Dimensiuni: 178 x 229 x 16 mm
Greutate: 0.54 kg
Editura: BROADVIEW PR
Colecția Broadview Press
Locul publicării:Peterborough, Canada

Recenzii

This text offers an innovative approach to the teaching of logic, which is rigorous but entirely non-symbolic. By introducing students to deductive inferences in natural language, the book breaks new ground pedagogically. Cannon focuses on such topics as using a tableaux technique to assess inconsistency; using generative grammar; employing logical analyses of sentences; and dealing with quantifier expressions and syllogisms. An appendix covers truth-functional logic.

Cuprins

Preface
Acknowledgments
Abbreviations
I. Fundamentals
  1. Propositions and sentences—the basic units of logic and language
  2. Truth and (declarative) sentences
  3. Consistency and sets of sentences
  4. Validity and arguments
    Exercises
II. Stories and Situations
  1. Reference and truth
  2. Meaning and truth
  3. Might have beens
  4. Truth with respect to a situation
    Exercises
III. Establishing Inconsistency with Tableaux
  1. Obvious inconsistency
  2. Semantic tableaux: dividing and conquering
  3. Efficiencies in tableaux
  4. A tableau that closes
    Exercises
IV. Extending the Tableau Technique
  1. Counter sets and validity
  2. Resolving reference
  3. Additional constructions
  4. When can a sentence be checked?
    Exercises
V. Generative Grammar
  1. What we mean by a grammar
  2. Phrase-structure grammars; Phrase-markers
  3. Transformations
  4. Syntactic ambiguity
    Exercises
VI. Logical Analysis of Complex Sentences
  1. “If s,” “And’s,” or “But’s”: Conjunctions and sentence connectives
  2. Rule-governed sentence connectives in tableaux
  3. Transformations in logical analysis; Grouping
  4. The reach of rules; Negated conditionals
  5. Tableaux constructed by rules
    Exercises
VII. Logical Analysis of Simple Sentences: Identity and Other Relations
  1. Designators and predicates
  2. Properties and relations; Types of relations
  3. The peculiar relation of identity
  4. Tableau rules for identity
    Exercises
VIII. Logical Analysis of Simple Sentences: One-Word Quantifiers
  1. Quantifiers in general
  2. The simplest quantifiers: “everyone,” “someone,” and “no one”
  3. Tableau rules for the simplest quantifiers
  4. The simplest quantifiers in tableaux
  5. “Anyone,” quantifier scope, and anaphoric pronouns
    Exercises
IX. Quantifier Expressions and Syllogisms
  1. The universal quantifier
  2. Relative pronouns, and the existential and nihilistic quantifiers
  3. Tableaux for syllogisms and other arguments
  4. “Anyone” and logical equivalence
  5. Things, times, and places
    Exercises
Appendix: Truth-Functional Logic
  1. Review: Tableau rules for sentence connectives
  2. Three levels of symbolization
  3. Symbolic languages for algebra
  4. Truth-functions and their computational tables
  5. Truth tables and calculating truth-values
  6. Constructing an arbitrary function; Normal form
    Exercises
For Reading and Reference
Index