A 'Natural Logic' inference system using the Lambek calculus

Anna Zamansky, Nissim Francez, Yoad Winter

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)273-295
Number of pages23
JournalJournal of Logic, Language and Information
Issue number3
StatePublished - Oct 2006
Externally publishedYes


  • Inference
  • Lambek calculus
  • Natural logic
  • Normalization

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Philosophy
  • Linguistics and Language


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