2002•Unpublished venueRequires access
The Sentential Calculus
Lech Polkowski
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Abstract
We begin with a discussion of the basic tool of mathematical reasoning: the sentential calculus (or, calculus of propositions, propositional calculus, propositional logic). By a proposition, sentence we mean any statement about reality of interest to us whose truth value can be established with certainty. By a truth value of a proposition, we understand either of two possible values: truth (T or 1), falsity (F or 0). A proposition p may be therefore either true or false and only one of the two possibilities actually holds for p. For instance, the statement “if today is Monday then tomorrow is Tuesday” is according to our best knowledge true while the statement of ordinary arithmetic “ 2+2 = 3” is false. In the sequel, we denote truth values with the symbols 0, 1.