Forthcoming Papers

2001 Journal of Logic and Computation  
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" valuations (Dunn), a "useful four-valued logic" (Belnap), and the notion of a bilattice (Ginsberg). We consider within one general framework the notions of constructive truth and constructive falsity, as well as the notions of non-constructive truth and nonconstructive falsity. All possible
more » ... ombinations of the basic truth values give rise to an interesting "16 valued logic". It appears that these 16 truth values constitute what we call a trilattice -a natural mathematical structure with three partial orderings that represent respectively an increase in information, truth and constructivity. The presentation of the paper is essentially conceptual: the stress is laid on introducing new concepts and structures as well as on their general interpretation.
doi:10.1093/logcom/11.5.755 fatcat:6sp2os6ulfhmfkfvxczfheyl4a