Natural language syntax and first-order inference
Artificial Intelligence
Theoretical Computer Science
Dynamic Logic
A Two-Variable Fragment of English
Journal of Logic, Language and Information
Natural Logic for Natural Language
Logic, Language, and Computation
Proceedings of the 17th Amsterdam colloquium conference on Logic, language and meaning
Logics for two fragments beyond the syllogistic boundary
Fields of logic and computation
The expressive power of restricted fragments of english
LACL'05 Proceedings of the 5th international conference on Logical Aspects of Computational Linguistics
A System of Relational Syllogistic Incorporating Full Boolean Reasoning
Journal of Logic, Language and Information
Journal of Logic, Language and Information
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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.