A binary sentential connective frequently seen in relevant logics and logics of strict implication such that relevant or strict implication acts as the residuum of fusion. In substructural logics, fusion is often treated as a counterpart to the comma separating formulae in a set of assumptions, e.g., a cedent. In many relevant logics, is definable as , which is equivalent to or, alternatively, is introduced by the axiom scheme residuation.
In some contexts, fusion is treated as an intensional conjunction of and so that captures a notion of compossibility, compatibility, or cotenability of the two formulae. That neither formula entails the falsehood of its companion suggests a reading of as indicating the compatibility of and . In logics of strict implication, fusion is often taken as a primitive notion, and a strict implication can be defined as , that is, ‘ is not compossible with the negation of ’. In presentations of strict implication with a possibility operator , can be perspicuously defined as .
Fusion is dual to a related connective of fission, which itself is sometimes interpreted as an intensional disjunction.