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Erschienen in:
2013 | OriginalPaper | Buchkapitel
3. Propositional Logic
verfasst von : Shashi Mohan Srivastava
Erschienen in: A Course on Mathematical Logic
Verlag: Springer New York
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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 A∨B 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 ¬A∨A 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.