## propositional calculus Quick reference

### The Concise Oxford Dictionary of Linguistics (3 ed.)

... calculus Branch of mathematical logic in which propositions are treated as unanalysed wholes. E.g. let p be one proposition and q be another: by the definition of an operator &, p & q is true if and only if both p is true and q is true. Propositions are analysed in the predicate calculus...

## propositional calculus Quick reference

### A Dictionary of Philosophy (3 ed.)

... calculus The logical calculus whose expressions are letters representing sentences or propositions, and constants representing operations on those propositions, to produce others of higher complexity. The operations include conjunction , disjunction , material implication and negation (although these need not be primitive: see Sheffer’s stroke ). Propositional logic was partially anticipated by the Stoics but reached maturity only with the work of Frege , Russell , and Wittgenstein . See also logic , tautology , truth function...

##
propositional calculus
*n.*
Quick reference

### A Dictionary of Psychology (4 ed.)

... calculus n . Any formal system of symbolic logic providing a language for expressing propositions ( 1 ) and the relations between them ( and , or , not , and if…then ), without regard to the internal structure or content of the propositions, together with a set of axioms and rules of inference, enabling the process of constructing a valid argument to be reduced to a mechanical process. See also logical analysis , sentence functor , truth functor , truth table . Compare predicate calculus...

## propositional calculus Quick reference

### A Dictionary of Computer Science (7 ed.)

... calculus A system of symbolic logic , designed to study propositions . A proposition is a statement that is true or false. There are many alternative but equivalent definitions of propositional calculus, one of the more useful definitions for the computer scientist being given here. The only terms of the propositional calculus are the two symbols T and F (standing for true and false) together with variables for logical propositions, which are denoted by small letters p , q , r ,…; these symbols are basic and indivisible and are thus called ...

## propositional calculus Reference library

*Ruth Barcan Marcus*

### The Oxford Companion to Philosophy (2 ed.)

... calculus . A systematization of that part of logic concerned with operators corresponding to some uses of ‘not’, ‘or’, ‘and’, ‘If … then’, and ‘If and only if’, some of which are interdefinable. They are represented in the propositional calculus ( PC ) in one standard notation as ‘˜’, ‘∨’, ‘˙’, ‘⊃’, and ‘≡’, respectively. A class of well-formed formulae is defined for PC and a definition of proof which generates the set of theorems of PC . A desideratum is a system where the set of well-formed formulae of PC which are logical truths are...