Scope Dominance with Generalized Quantifiers
Languages: From Formal to Natural
Natural logic for textual inference
RTE '07 Proceedings of the ACL-PASCAL Workshop on Textual Entailment and Paraphrasing
Proceedings of the 17th Amsterdam colloquium conference on Logic, language and meaning
An analytic tableau system for natural logic
Proceedings of the 17th Amsterdam colloquium conference on Logic, language and meaning
The Soundness of Internalized Polarity Marking
Studia Logica
Inclusion and Exclusion in Natural Language
Studia Logica
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This paper develops an inference system for natural language within the `Natural Logic' paradigm as advocated by van Benthem (1997), Sánchez (1991) and others. The system that we propose is based on the Lambek calculus and works directly on the Curry-Howard counterparts for syntactic representations of natural language, with no intermediate translation to logical formulae. The Lambek-based system we propose extends the system by Fyodorov et~al. (2003), which is based on the Ajdukiewicz/Bar-Hillel (AB) calculus Bar Hillel, (1964). This enables the system to deal with new kinds of inferences, involving relative clauses, non-constituent coordination, and meaning postulates that involve complex expressions. Basing the system on the Lambek calculus leads to problems with non-normalized proof terms, which are treated by using normalization axioms.