Appendix:Glossary of logic
This is a glossary of logic.
- The conditional part of a hypothetical proposition
- In a syllogism, the proposition that follows as a necessary consequence of the premises.
- The second half of a hypothetical proposition; Q, if the form of the proposition is "If P, then Q."
- The statement of the form "if not Q then not P", given the statement "if P then Q".
- domain of discourse
- In predicate logic, an indication of the relevant set of entities that are being dealt with by quantifiers.
- 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.
- 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".
- The act or process of inferring; the production of a proposition based on given propositions.
- A statement constructed from the negatives of the premise and conclusion of some other statement: ~p → ~q is the inverse of p → q.
- 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.
- Either of the first two propositions of a syllogism, from which the conclusion is deduced.
- 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.
- reductio ad absurdum
- The method of proving a statement by assuming the statement is false and, with that assumption, arriving at a blatant contradiction.
- A formula with no free variables.
- An inference in which one proposition (the conclusion) follows necessarily from two other propositions, known as the premises.