Automatic Synthesis of Semantics for Context-free Grammars

We are investigating the mechanical transformation of an unambiguous context-free grammar (CFG) into a deenite-clause grammar (DCG) using a nite set of examples, each of which is a pair hs; mi, where s is a sentence belonging to the language deened by the CFG and m is a semantic representation (meaning) of s. The resulting DCG would be such that it can be executed (by the interpreter of a logic programming language) to compute the semantics for every sentence of the original DCG. Three important assumptions underlie our approach: (i) the semantic representation language is the simply typed-calculus; (ii) the semantic representation of a sentence can be obtained from the semantic representations of its parts (compositionality); and (iii) the structure of the semantic representation determines its meaning (intensionality). The basic technique involves an enumeration of parse trees for sentences of increasing size; and, for each parse tree, a set of equations over (typed) function variables that represent the meanings of the constituent subtrees is formulated and solved by means of a higher-order uniication procedure. The solutions for these function variables serve to augment the original grammar in order to derive the nal DCG. A technique called partial execution is used to convert, where possible, the generated higher-order DCG into a rst-order DCG, to facilitate eecient bidirectional execution. In the appendix, we provide detailed illustration of the use of such a system for storing and retrieving information contained in natural language sentences. Based on our experimentation, we conclude that an improved version of this system will facilitate rapid prototyping of natural language front-ends for various applications.