Economical Discourse Representation Theory

First-order logic (FOL) is undecidable — that is, no algorithm exists that can decide whether a formula of FOL is valid or not. However, there are various fragments of FOL that are known to be decidable. FO, the two-variable fragment of FOL, is one of such languages [1,2]. FO is a first-order language where formulas have maximally two variables, no function symbols, but possibly do have equality. FO has the finite model property [1], which means that if a formula of FO is satisfiable, it is satisfiable in a finite model. In this paper we propose a controlled fragment of Discourse Representation Theory (DRT, [3]) with a semantics formalised on the basis of the two-variable fragment with equality. DRT encapsulates the idea of text interpretation that “one and the same structure serves simultaneously as content and context” [4], where content refers to the semantic interpretation of sentences already processed, and context serves in aiding the interpretation of anaphoric expressions (such as pronouns) in subsequent sentences. However, providing a two-variable natural language fragment is, in itself, not a new idea. In fact, the framework presented here is very much inspired by Ian Pratt-Hartmann’s language E2V [5]. But as Pratt-Hartmann himself notes, E2V is “certainly not proposed as a practically useful controlled language”. Our aim is to try to find out how useful a controlled language based on the two-variable fragment actually can be, mostly from a computational linguistic point of view. We will do this by: