Abstract
By a fragment of a natural language we mean a subset of that language equipped with semantics which translate its sentences into some formal system such as first-order logic. The familiar concepts of satisfiability and entailment can be defined for any such fragment in a natural way. The question therefore arises, for any given fragment of a natural language, as to the computational complexity of determining satisfiability and entailment within that fragment. We present a series of fragments of English for which the satisfiability problem is polynomial, NP-complete, EXPTIME-complete, NEXPTIME-complete and undecidable. Thus, this paper represents a case study in how to approach the problem of determining the logical complexity of various natural language constructions. In addition, we draw some general conclusions about the relationship between natural language and formal logic.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
