Compositionality and omniscience in situation semantics

Abstract

We have defined the syntax and semantics for the language Determiner-Free Aliass of Barwise and Perry using a compositional definition in the same style of MS. The interpretation of a sentence is defined as a constraint on situations and required to be computationally expressed. A situation is a finite collection of facts about the world. The notion of statement, the utterance of an indicative sentence, is defined as a pair of an uttering situation and a sentence. The notion of equality of meaning for statements is modeled or formalized with the concept of strong equivalence between statements. We showed that in general such semantics can suffer from the problem of omniscience. However, if we restrict ourselves to real and computable interpretations, where we avoid strict synonymity and quantification of the interpretation on the definition of equivalence, we may avoid that problem. We believe that this solution could be used both for Situation Semantics and for possible-worlds semantics, or alternatively that this would be used as a distinguishing characteristic for the former semantics. We also commented on Hintikka's formal semantics for propositional attitudes, and we noticed that his attempt to make the use of knowledge mathematically objective, always creates omniscience.