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