QUASI-HEYTING ALGEBRAS - A NEW CLASS OF LATTICES

Quasi-Heyting algebras (QHAs) generalize both the Heyting algebras (HA s) of intuitionistic logic and the orthomodular lattices (OMLs) of qua ntum logic. As in HAs, negation is a Galois connection, which expresse s abandonment of the law of the excluded middle, and as in OMLs, incom patibility of propositions is expressed by departures from distributiv ity. Formulating an equational definition of QHAs leads to generalizat ions of familiar operations. QHAs are the truth-value objects of a gen eralization of toposes. So far, this development has aimed to provide foundations of logic and model theory suitable for addressing computer science problems, but they also appear applicable as formulations of the logic of some types of scientific measurement. Many properties of OMLs are likely to have generalizations to QHAs.