Partial Gaggles Applied to Logics with Restricted Structural Rules
Jon Michael Dunn · 1993
Abstract In Dunn (1991) a class of algebraic structures called ‘gaggles’ were investigated with an idea to abstracting out an algebraic structure common to a wide class of logics. But one feature, although common to many of the logics and abstracted into the notion of a gaggle, still is inessential to the main ideas. This feature is that there be a distributive lattice underlying the family of gaggle operations. This is an appropriate assumption to make for many logics, and leads to a representation theory where ‘conjunction’ (meet) is interpreted as intersection and ‘disjunction’ (join) as union.