implicatio

Implicatio is a Latin noun meaning an entanglement or folding in, and in philosophical and logical contexts it denotes a relation of entailment, consequence, or implication between propositions. In English-language scholarship the term is usually translated as "implication," and it is distinguished from causal relations, definitions, or equivalence.

Historically, implicatio appears in medieval Latin scholastic logic as part of discussions on inferential validity and deductive reasoning. Scholastics analyzed how certain premises imply a conclusion within syllogistic and disputational frameworks. With the rise of modern formal logic, the term began to be associated more specifically with the inferential relation captured by the logical connective often written as p → q, and its interpretation evolved alongside developments in proof theory and semantics.

In contemporary usage, implicatio commonly refers to the logical connective "if p then q." In mathematics and computer science, it denotes a connective whose truth is defined by a precise truth-functional or deductive criterion, most commonly the material implication in classical logic. A typical example is: if it is raining (p), then the street is wet (q). The implication is considered true whenever p is false or q is true, or both, in the standard truth-table interpretation. The term can be confused with linguistic implicature, which concerns conveyed meaning beyond explicit content rather than formal entailment.