Building the Framework

TL;DR: The grammar currently covers the basic aspects of predication, quanti cation, tense and aspect, and pronominal anaphora, including both quanti ers and inde nites, and generates all possible interpretations of an ambiguous sentence.

Abstract: ion. Thus, the outermost part of the expression in (14.1b) represents the abstraction h hutt-time,ui ! N, . . . , hexploits,u 3 i ! R 2 i .hire(X 1 ,X 2 ,T) j . . . . Roughly speaking, this rst part of the interpretation says that the content of the sentence Smith hired Jones is obtained by nding in context values for the parameters N,X 1 ,X 2 ,R 1 ,R 2 ,T and S, i.e., by applying the simultaneous abstraction in (14.1b) to an assignment whose domain includes the indices hutt-time,ui,hdo,u 1 i, hexploits,u 1 i,hdescr-sit,u 2 i, hrt,u 2 i, hdo,u 3 i, and hexploits,u 3 i. Inside the box representing a simultaneous abstraction is a box of the form ( jj ), which represents a restricted proposition. We are assuming the notion of proposition used in Situation Theory, according to which what can be true or false are statements of the form A holds at situation S. (Such propositions are also called austinian propositions.) A restricted proposition is an expression that denotes a proposition if all the conditions on the right of the vertical double line are satis ed (i.e., if it is true that the object denoted by X 1 is named \Smith"); unde ned otherwise. The grammar currently covers the basic aspects of predication, quanti cation, tense and aspect, and pronominal anaphora, including both quanti ers and inde nites. The grammar generates all possible interpretations of an ambiguous sentence. All possible interpretations of an anaphoric expression are generated by keeping track of the discourse referents introduced