Aspecto-Temporal Meanings Analysed by Combinatory Logic

Abstract

What is the meaning of language expressions and how to compute or calculate it? In this paper, we give an answer to this question by analysing the meanings of aspects and tenses in natural languages inside the formal model of an grammar of applicative, cognitive and enunciative operations (GRACE) (Descles and Ro in Math Sci Hum 194:39---70, 2011), using the applicative formalism, functional types of categorial grammars and combinatory logic (CL) (Curry and Feys in Combinatory Logic. North-Holland Publishing, Amsterdam, 1958). In the enunciative theory (Benveniste in Problemes de linguistique generale, 1, 2. Gallimard, Paris, 1974; Culioli in Formalisation et operations de reperage, tome 2. Ophrys, Paris, 1999; Descles in Une articulation entre syntaxe et semantique cognitive: la grammaire applicative et cognitive, memoires de la societe de linguistique de Paris, nouvelle serie, tome XX, l'architecture des theories, les modules et leurs interfaces. Peeters, Louvain, 2011) and following (Bally in Linguistique generale et linguistique francaise. Berne, Franke, 1965), an utterance can be decomposed into two components: a modus and a dictum (or a proposition). In GRACE, the modus is a complex operator applied to a proposition (a dictum) and is generated from more elementary operators of the categories of tense, aspect, and modality. The dictum is a proposition generated by a predicative relation. In this way, we can attribute a semantic meaning to different grammatical aspecto-temporal operators. The applicative expressions of CL can be easily translated into a functional programming language such as HASKELL or CAML (Ro in Les referentiels et operateurs aspecto-temporels: definitions, formalisation logique et informatique. PhD thesis, Universite de Paris-Sorbonne, Paris, 2012).