Propositional Logic

  • Shashi Mohan Srivastava
Chapter
Part of the Universitext book series (UTX)

Abstract

We now turn our attention to the fundamental notion of a logical deduction or a proof. Note that in computing the truth value of a statement in a structure one uses some rules of inference depending only on the syntactical construction of the statement. For instance, if A or B is true in a structure, then we infer that AB is true in the structure. We have also noted that statements with some specific syntactical structures are valid in all structures. For instance, a statement of the form ¬AA is true in all structures. Statements true in all structures of a language are called tautologies. So all tautologies should be theorems. Are there a convenient list of tautologies (to be called logical axioms) and a list of rules of inference such that a statement is valid if and only if it can be inferred from logical and nonlogical axioms using the rules of inference from our list? Indeed there is.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Shashi Mohan Srivastava
    • 1
  1. 1.Indian Statistical InstituteKolkataIndia

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