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# propositional calculus

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## affirming the consequent

In conditional reasoning, arguing invalidly from a hypothetical proposition of the form If p then q that, because q therefore p. For example, given the proposition If the burglars entered by the ...

## axiom

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A generally accepted and perhaps self-evident principle, maxim, or rule, based on empirical observations, logical analysis of evidence, or universal experience.

## calculus

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Subject:
Philosophy
A calculus is a formal language and rules for manipulating expressions of the language. For example, by applying algorithms to arabic numerals one can determine the values of arithmetical functions. ...

## conjunction

If p and q are statements, then the statement ‘p and q’, denoted by p ∧ q, is the conjunction of p and q. For example, if p is ‘It is raining’ and q is ‘It is Monday’, then p ∧ q is ‘It is raining ...

## constant

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Philosophy
A term in a logical calculus to which any interpretation assigns a fixed meaning, unlike a variable or schematic letter.

## De Morgan's laws

For all sets A and B (subsets of a universal set), (A∪B)′=A′∩B′ and (A∩B)′=A′∪B′. These are De Morgan's laws.

## decision problem

A computational task that for each possible input requires “true” or “false” to be output, depending on whether the input possesses a certain property. An algorithm that produces the correct decision ...

## decision procedure

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Subject:
Philosophy
A specifiable terminating procedure (algorithm) for determining whether something has a given property. In logic one focus has been on procedures for determining for a formal system whether or not ...

## deduction

The form of reasoning characteristic of logic and mathematics in which a conclusion is inferred from a set of premises that logically imply it. The term also denotes a conclusion drawn by this ...

## denying the antecedent

In conditional reasoning, arguing invalidly from a hypothetical proposition of the form If p then q that, because p is false, therefore q is false. For example, given the proposition If the burglars ...

## deontic logic

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Subject:
Philosophy
A logical calculus created by adding operators ‘Op’ (it ought to be the case that p) and ‘Pp’ (it is permissible that p) to a basic system such as the propositional calculus, together with rules of ...

## dilemma

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Subject:
Philosophy
A situation in which a difficult choice has to be made between two or more alternatives, especially ones that are equally undesirable (see also on the horns of a dilemma). The word is recorded from ...

## disjunction

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n. the separation of pairs of homologous chromosomes during meiosis or of the chromatids of a chromosome during anaphase of mitosis or meiosis. Compare nondisjunction.

## double negation

The proposition that the negation of the negation of A is equivalent to the proposition A. In English, a double negative is not always precisely a double negation. For example, in hypothesis testing ...

## duality

A property of an optimization problem. Duality relates any linear maximization problem to an equivalent minimization problem. For example, with non-negative x-variables and y-variables, the maximum ...

## equivalence

1 The logical connective combining two statements or formulas P and Q in such a way that the outcome is true if both P and Q are true or if both are false, as shown in the table. P and Q are said to ...

## exportation

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Subject:
Philosophy
An operator is exported from a place within a sentence if it is repositioned so that the whole of the rest of the sentence is within its scope. This may or may not give an equivalent sentence. ‘When ...

## George Boole

(1815–64)English mathematician and logician. Born in Lincoln and educated locally, Boole worked as a schoolmaster until he gained recognition as a mathematician, and became professor at Queen's ...

## Gottlob Frege

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Subject:
Philosophy
(1848–1925)German mathematician, logician, and philosopher who laid the foundations for modern investigations into the philosophy of logic and language.Born in Wismar (now East Germany), the son of a ...

## iff

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In logic and mathematics, if and only if. It indicates that the two sentences that it conjoins are necessary and sufficient conditions for each other. See biconditional.

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