InvolvesentailsAB

InvolvesentailsAB is a term used in theoretical discussions of logic and semantics to denote a specific relation between two propositions or predicates, A and B. The relation is defined to hold when A structurally involves B and, within a given deductive framework, B entails A. It is not a standard operator in classical logics but a construct used to express a combined inclusion-entailment property for a pair (A,B).

Formally, A structurally involves B if B occurs as a subformula or subcomponent of A. B entails A if, in the chosen inference system or under the chosen model theory, every model of B is a model of A, or A is derivable from B. InvolvesentailsAB, therefore, holds for a pair (A,B) when both conditions are satisfied: B is embedded in A, and B is sufficient, under the theory, to entail A.

Because it relies on a theory-specific notion of entailment and a theory-specific notion of structural inclusion, InvolvesentailsAB is not universally defined across all logics. Researchers specify the underlying language, the construction rules that determine what counts as a subcomponent, and the exact entailment criteria used to decide when B entails A.

Applications of the concept appear in discussions of semantic composition, knowledge representation, and natural language processing, where it helps formalize cases in which a larger expression depends on a smaller one and the truth of the larger follows from the truth of the smaller within a given framework. Related topics include entailment, subformula relations, and dependency-based approaches to meaning representation.