Deductive Logic in Natural Language

Douglas Cannon is a professor in the Department of Philosophy at the University of Puget Sound.

Preface
Acknowledgments
Abbreviations

I. Fundamentals



Propositions and sentences—the basic units of logic and language
Truth and (declarative) sentences
Consistency and sets of sentences
Validity and arguments
Exercises

II. Stories and Situations



Reference and truth
Meaning and truth
Might have beens
Truth with respect to a situation
Exercises

III. Establishing Inconsistency with Tableaux



Obvious inconsistency
Semantic tableaux: dividing and conquering
Efficiencies in tableaux
A tableau that closes
Exercises

IV. Extending the Tableau Technique



Counter sets and validity
Resolving reference
Additional constructions
When can a sentence be checked?
Exercises

V. Generative Grammar



What we mean by a grammar

Phrase-structure grammars; Phrase-markers

Transformations

Syntactic ambiguity
Exercises

VI. Logical Analysis of Complex Sentences



“If s,” “And’s,” or “But’s”: Conjunctions and sentence connectives
Rule-governed sentence connectives in tableaux
Transformations in logical analysis; Grouping
The reach of rules; Negated conditionals
Tableaux constructed by rules
Exercises

VII. Logical Analysis of Simple Sentences: Identity and Other Relations



Designators and predicates

Properties and relations; Types of relations

The peculiar relation of identity

Tableau rules for identity
Exercises

VIII. Logical Analysis of Simple Sentences: One-Word Quantifiers



Quantifiers in general
The simplest quantifiers: “everyone,” “someone,” and “no one”
Tableau rules for the simplest quantifiers
The simplest quantifiers in tableaux
“Anyone,” quantifier scope, and anaphoric pronouns
Exercises

IX. Quantifier Expressions and Syllogisms



The universal quantifier
Relative pronouns, and the existential and nihilistic quantifiers
Tableaux for syllogisms and other arguments
“Anyone” and logical equivalence
Things, times, and places
Exercises

Appendix: Truth-Functional Logic



Review: Tableau rules for sentence connectives
Three levels of symbolization
Symbolic languages for algebra
Truth-functions and their computational tables
Truth tables and calculating truth-values
Constructing an arbitrary function; Normal form
Exercises

For Reading and Reference

Index