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Order-based inference in natural logic. (English) Zbl 1076.03529

Summary: 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 for 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.

MSC:

03B65 Logic of natural languages
68T50 Natural language processing
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