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Logic Journal of IGPL 2003 11(4):385-416; doi:10.1093/jigpal/11.4.385
© 2003 by Oxford University Press
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Original Article

Order-Based Inference in Natural Logic

Yaroslav Fyodorov1, Yoad Winter2 and Nissim Francez3

1 Computer Science Faculty, Technion - IIT, Haifa, Israel. E-mail: yaroslav{at}cs.technion.ac.il 2 Computer Science Faculty, Technion - IIT, Haifa, Israel. E-mail: winter{at}cs.technion.ac.il 3 Computer Science Faculty, Technion - IIT, Haifa, Israel. E-mail: francez{at}cs.technion.ac.il

This paper develops a version of Natural Logic – an inference system that works directly on natural language syntactic representations, with no intermediate translation to logical formulae. Following work by Sánchez, we develop a small fragment that computes semantic order relations between derivation trees in Categorial Grammar. The proposed system has the following new characteristics: (i) It uses orderings between derivation trees as purely syntactic units, derivable by a formal calculus. (ii) The system is extended for conjunctive phenomena like coordination and relative clauses. This allows a simple account of non-monotonic expressions that are reducible to conjunctions of monotonic ones. (iii) A decision procedure for provability is developed for a fragment of Natural Logic.

Key Words: inference, monotonicity, natural logic, order, semantics

Received 15 January 2001.


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