Continuation semantics for the Lambek-Grishin calculus

Categorial grammars in the tradition of Lambek [18, 19] are asymmetric: sequent statements are of the form Γ ⇒ A, where the succedent is a single formula A, the antecedent a structured configuration of formulas A1, . . . , An. The absence of structural context in the succedent makes the analysis of a number of phenomena in natural language semantics problematic. A case in point is scope construal: the different possibilities to build an interpretation for sentences containing generalized quantifiers and related expressions. In this paper, we explore a symmetric version of categorial grammar, based on work by Grishin [15]. In addition to the Lambek product, left and right division, we consider a dual family of type-forming operations: coproduct, left and right difference. Communication between the two families is established by means of structurepreserving distributivity principles. We call the resulting system LG. We present a Curry-Howard interpretation for LG(/, \, , ) deriva...

• Type: Journal
• Year: 2010
• Where: IANDC
• Authors: Raffaella Bernardi, Michael Moortgat
• Keywords: Categorial Grammars, Grammars, IANDC 2010, Natural Language