On the Interpretation of Denotational Semantics

The denotational approach to the semantics of programming languages views program meanings as elements of domains, abstract partially ordered structures that form the basis of a mathematical theory of computation. This paper discusses how the interpretation of these structures as models of information in computation has evolved into the interactive view of domains represented by game semantics. As a unifying motif of these developments, we propose the interpretation of program meanings as fulfillments of intentions suggested by Heyting's phenomenological meaning explanation of intuitionistic logical constants, recently carried on by van Atten and Tieszen. We will also make an attempt to interpret this idea in the light of a pragmatic view of computation as communication, connecting it to the foundation of game semantics for programming languages and looking at this pragmatic turn as a source of new intentionalities.