The Trilattice of Constructive Truth Values

摘要

We introduce an abstract algebraic structure-a lattice defined on a generalized truth value space of constructive logic. For background one can refer to the idea of 'under-determined' and 'over-determined' valuation (Dunn), a 'useful four-valued logic' (Belnap), and the notion of a bilattice (Ginsberg). We consider within one general framework the notions of constructive turth and constructive falsity, as well as the notions of non-constructive truth and non-constructive falsity. All possible combinations of the basic truth values give rise to an interesting '16-valued logic.'