This paper describes an implemented parser-interpreter which is intended as an abstract formal model of part of the process of sentence comprehension. It is illustrated here for Phrase Structure Grammars with a translation into a familiar type of logical form, although the general principles are intended to apply to any grammatical theory sharing certain basic assumptions, which are discussed in the paper. The procedure allows for incremental semantic interpretation as a sentence is parsed, and provides a principled explanation for some familiar observations concerning properties of deeply recursive constructions.