Bidirectional Functional Semantics for Pregroup Grammars

Pregroup grammars are a recent descendant of the original categorial grammars of Bar-Hillel [1] and Lambek [10] in which types take the form of strings of basic types and left and right adjoints, as opposed to the non-commutative functional types of categorial grammars. Whereas semantic extraction is possible in other categorial grammars through the λ-calculus, this approach will not be feasible for pregroup grammars. In this paper, we show how to build a term calculus that could be used to fill this void. This system is inspired by the λ-calculus but differs in crucial aspects: it uses function composition as its main reduction strategy instead of function application and is bidirectional, i.e. the direction arguments are applied to terms matters. We show how this term calculus is one- to-one with a proper subset of pregroup types and give multiple examples to show how this system could be used to do semantic analysis in parallel to doing grammaticality checks with pregroup grammars.

From Natural Language to RDF Graphs with Pregroups

We define an algorithm translating natural language sentences to the formal syntax of RDF, an existential conjunctive logic widely used on the Semantic Web. Our translationis based on pregroup grammars, an efficient type-logical grammatical framework with atransparent syntax-semantics interface. We introduce a restricted notion of side effects inthe semantic category of finitely generated free semimodules over {0,1} to that end.The translation gives an intensional counterpart to previous extensional models.We establish a one-to-one correspondence between extensional models and RDF models such that satisfaction is preserved. Our translation encompasses the expressivity of the target language and supports complex linguistic constructions like relative clauses and unbounded dependencies.