From English to Logic: Context-Free Computation of 'Conventional' Logical Translation

We describe an approach to parsing and logical translation that was inspired by Gazdar's work on context-free grammar for English. Each grammar rule consists of a syntactic part that specifies an acceptable fragment of a parse tree, and a semantic part that specifies how the logical formulas corresponding to the constituents of the fragment are to be combined to yield the formula for the fragment. However, we have sought to reformulate Gazdar's semantic rules so as to obtain more or less 'conventional' logical translations of English sentences, avoiding the interpretation of NPs as property sets and the use of intensional functors other than certain propositional operators. The reformulated semantic rules often turn out to be slightly simpler than Gazdar's. Moreover, by using a semantically ambiguous logical syntax for the preliminary translations, we can account for quantifier and coordinator scope ambiguities in syntactically unambiguous sentences without recourse to multiple semantic rules, and are able to separate the disambiguation process from the operation of the parser-translator. We have implemented simple recursive descent and left-corner parsers to demonstrate the practicality of our approach.