Semantics of non-deterministic possibility computation

Possibility computation, introduced by Chen and Wu in 2008, is a kind of computational model to deal with non-determinism, based on the axiomatic rule of possibility measures in the framework of domain theory. In this paper, we consider the case of non-determinism of possibility computation, i.e., non-deterministic and possibility computations co-exist. Both its denotational semantics, i.e., state transformer semantics, and logical semantics, i.e., predicate transformer semantics are established and their duality is verified in the framework of fuzziness. The denotational semantics is defined to be a Scott-continuous function from the input spaces to Hoare possibilistic powerdomain of output spaces. The logical semantics is given by strongly healthy fuzzy predicate transformers from fuzzy predicates on the domain of output spaces to the ones on the domain of input spaces. We prove a duality property between these two semantics by means of Sugeno integral with respect to possibility valuations. Finally, we establish the semantics of a fuzzy programming language in terms of our methods.