A Semantic Analysis of a Logic for Pragmatics with Assertions, Obligations, and Causal Implication

Article type: Research Article

Authors: Ranalter, Kurt

Affiliations: Department of Computer Science Queen Mary, University of London Mile End Road, E1 4NS London, England. E-mail: [email protected]

Note: [] Address for correspondence: Department of Computer Science, Queen Mary, University of London, Mile End Road, E1 4NS London, England

Abstract: One of the aims of a logic for pragmatics is to provide a logical framework that formalizes reasoning about speech acts. In this paper we investigate the semantics of a fragment of the logic for pragmatics proposed by Bellin and Dalla Pozza in "A pragmatic interpretation of substructural logics" (Feferman Festschrift, ASL Lecture Notes in Logic 15, 2002). The logic deals with acts of assertion and acts of obligation, and it incorporates a rule that relates acts of obligation to acts of assertion via a notion of causal implication. As our main result we show that the logic is sound and complete with respect to a class of algebraic, Kripke, and categorical models.

Keywords: Speech act theory, proof theory, provability semantics, categorical logic and type theory

Journal: Fundamenta Informaticae, vol. 84, no. 3-4, pp. 443-470, 2008