Logic Glossary

Affirming the consequent — An invalid argument form: “If p then q / q // p’

Argument – a series of declarative statements, one of which (the conclusion), is intended to be supported by the others (the premises).

Biconditional statement (biconditional)  — A statement having a triple bar as its main operator (read, if and only if)

Commutativity —  A valid rule of inference that provides for the rearrangement of conjunctions and disjunctions

Compound statement — A statement that contains at least one simple statement as a component

Conclusion – (1) the statement in an argument that the premises are claimed to support or imply; (2) a statement in an argument supported by premises.

Conjunct — The component in a conjunctive statement on either side of the main operator

Conjunction —  (1) A statement having a dot as its main operator (2) a valid rule of inference: “p / q // p and q’

Conjunctive statement (conjunction) — A statement having a dot as its main operator

Connectives Symbols — used to connect or negate propositions in propositional logic

Consistent statements — Statements for which there is at least one line on their truth tables in which all of them are true

Constructive dilemma — A valid argument form/rule of inference: “If p then q, and if r then s / p  or  r // q or s’

Contingent statement — A statement that is neither necessarily true nor necessarily false

Corresponding conditional — The conditional statement having the conjunction of an argument’s premises as its antecedent and the conclusion as its consequent

Denying the antecedent — An invalid argument form: “If p then q / not p // not q’

Destructive dilemma — A valid argument form/rule of inference: “If p then q, and if r then s / not q or not s // not p or not r’

Disjunct — The component in a disjunctive statement on either side of the main operator

Disjunctive statement (disjunction) — A statement having a wedge as its main operator

Disjunctive syllogism (1) — A syllogism having a disjunctive statement for one or both of its premises (2) a valid argument form/rule of inference: “p or q / not p // q’

Enthymeme – an argument with hidden premises

Fallacy – an argument that appears to be deductive or inductive, but which is based on mistaken rules of inference.  (These may, of course, be widely accepted.)

False – a sentence that incorrectly describes the way things are is false.

Inconsistent statements — Statements such that there is no line on their truth tables in which all of them are true

Logical Form (of a proposition) – the basic structure of a statement in which only the operators are prominent.

Logical Form (of an argument) – the basic structure of an argument in which only the operators are prominent.

Logically equivalent statements  — (1) Statements that necessarily have the same truth value (2) statements having the same truth value on each line under their main operators

Logically false statement — A statement that is necessarily false, a self-contradictory statement

Main operator — The operator (connective) in a compound statement that governs the largest component(s) in the statement

Material equivalence — (1) The relation expressed by a truth-functional biconditional (2) a valid rule of inference that allows an equivalence statement to be replaced by a conjunctive statement or a disjunctive statement

Material implication — (1) The relation expressed by a truth-functional conditional (2) a valid rule of inference that allows an implication sign to be replaced by a disjunction sign if and only if the antecedent is negated

Necessary condition — The condition represented by the consequent in a conditional statement

Negation — A statement having a tilde as its main operator

Non-sequitur – a statement , intended as a conclusion, that does not actually follow logically from the statements that are alleged to support it.

Operators – (1) symbols used to connect simple propositions in propositional logic; (2) the truth-functional parts of a proposition.

Premise – a statement in an argument offered as a reason supporting a conclusion.

Proposition – a statement represented in its logical form.

Propositional logic — A kind of logic in which the fundamental components are whole statements or propositions

Self-contradictory statement — A statement that is necessarily false, a logically false statement

Simple statement — A statement that does not contain any other statement as a component

Sound Argument – an argument that is valid and has all true premises.

Standard Form (of an argument) – an argument, laid out as a series of steps, in which the supporting reasons (premises) occur first and the defended statement (conclusion) last.

Statement – a sentence capable of being either true or false.

Statement form — An arrangement of statement variables and operators such that the uniform substitution of statements in place of the variables results in a statement

Statement variable — A lowercase letter, such as p or q, that can represent any statement

Substitution instance — An argument or statement that has the same form as a given argument form or statement form of an argument form

Sufficient condition — The condition represented by the antecedent in a conditional statement

Tautologous statement — A statement that is necessarily true a logically true statement

True – a sentence that correctly describes the way things are is true.

Truth function — A compound proposition whose truth value is completely determined by the truth values of its components

Truth table — An arrangement of truth values that shows in every possible case how the truth value of a compound proposition is determined by the truth values of its simple components

Valid Argument – an argument in which the conclusion cannot be false when its premises are true.

Well-formed formula (WFF) — A syntactically correct arrangement of symbols

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