Abstract
This chapter focuses on the propositional calculus. Boolean algebra is very closely related to the system of elementary logic known as the propositional calculus. A disjunctive normal form for the function is a disjunction of terms, each of which is a conjunction of logical variables and their negations. Any logical function, in any number of variables, can be expressed in terms of conjunction, disjunction, and negation. In switching circuit terms, and-gates, or-gates, and inverters are sufficient to represent any logical or Boolean expression. A prime advantage of Polish notation is that in scanning a formula from right to left for prefix notation, or left to right for postfix notation, all operands are encountered before their operators. The search for well-formed formulas involves a determination of nesting of parentheses. Using a Polish notation, the determination becomes a simple numerical procedure involving a single scan of the formula. A set of axioms is a set of well-formed formulas. A rule of inference is a procedure, production, or algorithm for generating a new well-formed formula from given ones.
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