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.