Appendix:Glossary of logic

This is a glossary of logic.

Contents: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

A

antecedent

The conditional part of a hypothetical proposition

C

conclusion

In a syllogism, the proposition that follows as a necessary consequence of the premises.

consequent

The second half of a hypothetical proposition; Q, if the form of the proposition is "If P, then Q."

contraposition

The statement of the form "if not Q then not P", given the statement "if P then Q".

D

domain of discourse

In predicate logic, an indication of the relevant set of entities that are being dealt with by quantifiers.

F

formula

A syntactic expression of a proposition, built up from quantifiers, logical connectives, variables, relation and operation symbols, and, depending on the type of logic, possibly other operators such as modal, temporal, deontic or epistemic ones.

I

implication

The connective in propositional calculus that, when joining two predicates A and B in that order, has the meaning "if A is true, then B is true".

inference

The act or process of inferring; the production of a proposition based on given propositions.

inverse

A statement constructed from the negatives of the premise and conclusion of some other statement: ~p → ~q is the inverse of p → q.

M

material implication

An implication as defined in classical propositional logic, leading to the truth of paradoxes of implication such as Q → (P → P), to be read as "any proposition whatsoever is a sufficient condition for a true proposition".

modus ponens

A valid form of argument in which the antecedent of a conditional proposition is affirmed, thereby entailing the affirmation of the consequent.

P

premise

Either of the first two propositions of a syllogism, from which the conclusion is deduced.

proposition

The content of an assertion that may be taken as being true or false and is considered abstractly without reference to the linguistic sentence that constitutes the assertion.

R

reductio ad absurdum

The method of proving a statement by assuming the statement is false and, with that assumption, arriving at a blatant contradiction.

S

sentence

A formula with no free variables.

syllogism

An inference in which one proposition (the conclusion) follows necessarily from two other propositions, known as the premises.

See also

• Category:Logic
• Appendix:Glossary of fallacies