A higher-order extension of constraint programming in disourse analysis

Variables on which constraints are imposed incrementally can be said to carry \existential" force in the following sense. Under a translation, commonly used in analyzing natural language discourse, of rst-order formulas into programs from quantiied dynamic logic, such a variable is introduced (at the level of formulas) by an existential quantiier. The present paper extends that translation to support constraints on variables introduced, as it were, by universal quantiication. The extension rests on a certain program construct) that can be interpreted (following Kleene's realizability analysis of universal-existential clauses) by closing the collection of states on which the programs act under partial functions. An alternative \reduced" interpretation of) can also be given over sets of states from dynamic logic (not unlike Concurrent Dynamic Logic). These interpretations can be related by what is essentially a reduction to disjunctive normal form, involving so-called and-or computations. A formalism for analyzing natural language discourse that has received considerable attention in certain linguistic circles is Discourse Representation Theory (DRT), due to Kamp 8] and Heim 6]. The basic idea in DRT is to capture the information a piece of discourse contributes by interpreting a natural language sentence semantically as a binary relation on so-called Discourse Representation Structures (DRS's). A DRS is a pair (D; C) consisting of a set D of discourse markers and a set C of conditions on them, formulated as rst-order formulas whose free variables are among the discourse markers. For example, the piece of discourse A man walks. He sees a house. sends (fxg; fman(x); walk(x)g) to (fx; yg; fman(x); walk(x); house(y); see(x; y)g). It follows by relational composition that () A man walks. He sees a house. are introduced in a monotonic manner, with attention to consistency and entailment. That is, a condition amounts to what is called a \constraint" in constraint programming. Thus, it is not unreasonable to describe DRT as a form of constraint programming for discourse analysis. The same description applies to an extension of DRT presented below, 1 the purpose of which is best described by illustration. Notice that the variable for 1 Readers familiar with Saraswat 14], however, should be cautioned that in the present paper, (i) quantiiers are employed to introduce variables on which constraints can then be imposed, and (ii) parallel computations arise when a process spawns multiple processes, which then proceed in a \conjunctive" fashion, with identically initialized but separate stores. This contrasts …