deducible

Deducible is an adjective meaning capable of being deduced or inferred. In formal logic and philosophy, deducibility is the relation by which a statement can be derived from a given set of premises through a valid sequence of inferences. A statement is deducible from a theory if there exists a formal proof whose last line asserts that statement; in semantic terms, a statement is a logical consequence of the theory if it is true in every model of the theory.

Deducibility is often distinguished from similar notions such as provability (syntactic derivability) and entailment (semantic consequence). In everyday usage, deducible describes information or conclusions that can be logically inferred from known facts, for example, "From the data, the pattern is deducible."

In common English, the term most frequently used in financial and legal contexts is deductible rather than deducible. "Deductible" refers to the amount, such as in insurance or taxes, that must be paid before coverage or tax relief applies. Using deducible in these contexts is often considered a nonstandard or erroneous form.

Etymology: derived from Latin deducere, to lead down, from which deduced, deduction, and deduction-related terms arise.

See also: deduction, entailment, provability.