D-posets with meet function

Abstract

For any two observables on a full tribe we can always construct a two–dimensional observable. In this case the crucial role is played by pointwise multiplication of the functions of tribe. Riečan and Mundici, ([6]) studied semisimple MV–algebras enriched by an additional product operation. The abstract product operation on MV–algebra is relating with the natural pointwise multiplication of functions. The sequential product on effect algebras defined by Gudder and Geechie, ([3]) is based on the similar idea as above. In this paper the meet function as a generalization of the product is defined and the properties of D–posets with meet function are presented.