Rough Sets pp 95-120

# The Sentential Calculus

• Lech Polkowski
Part of the Advances in Soft Computing book series (AINSC, volume 15)

## 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.

## Keywords

Boolean Function Inference Rule Propositional Calculus Sequent Approach Deductive System

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