# implies

Logical consequence (also entailment) is one of the most fundamental concepts in logic. It is the relationship between statements that holds true when one logically “follows from” one or more others. A valid logical argument is one in which the conclusions follow from its premises, and its conclusions are consequences of its premises. The philosophical analysis of logical consequence involves asking, ‘in what sense does a conclusion follow from its premises?’ and ‘what does it mean for a conclusion to be a consequence of premises?’ All of philosophical logic can be thought of as providing accounts of the nature of logical consequence, as well as logical truth. Logical consequence is taken to be both necessary and formal with examples explicated using models and proofs. A sentence is said to be a logical consequence of a set of sentences, for a given language, if and only if, using logic alone (i.e. without regard to any interpretations of the sentences) the sentence must be true if every sentence in the set were to be true. Logicians make precise accounts of logical consequence with respect to a given language by constructing a deductive system for , or by formalizing the intended semantics for . Alfred Tarski highlighted three salient features for which any adequate characterization of logical consequence needs to account: 1) that the logical consequence relation relies on the logical form of the sentences involved, 2) that the relation is a priori, i.e. it can be determined whether or not it holds without regard to sense experience, and 3) that the relation has a modal component.