Abstract

By a fragment of a natural language we mean a subset of thatlanguage equipped with semantics which translate its sentences intosome formal system such as first-order logic. The familiar conceptsof satisfiability and entailment can be defined for anysuch fragment in a natural way. The question therefore arises, for anygiven fragment of a natural language, as to the computational complexityof determining satisfiability and entailment within that fragment. Wepresent a series of fragments of English for which the satisfiabilityproblem is polynomial, NP-complete, EXPTIME-complete,NEXPTIME-complete and undecidable. Thus, this paper represents a casestudy in how to approach the problem of determining the logicalcomplexity of various natural language constructions. In addition, wedraw some general conclusions about the relationship between naturallanguage and formal logic.