Towards a Formal Pragmatics

Gianluigi Bellin

The project of providing a logic for formal pragmatics (presented in the Dagstuhl seminar on linear logic 1999) is motivated by the need of extending the framework of logical theory to account for aspects of informal reasoning involving the illocutionary acts of assertion, obligation, etc. also in mixed contexts. A long-term aim of the project is to give "intended interpretations" of substructual logics and a coherent account of these formal system within the standard framework of logical theory. Currently, the language ILP has the usual intuitionistic connectives plus a connective -o expressing relevant causal implication; the elementary sentences are of the form |- \alpha (alpha is assertible) and O-alpha (alpha is obligatory), where alpha is a classically interpreted proposition. The main result reached so far is the characterization of mixed-contexts inferences yielding the principle: "if alpha is obligatory and from the assertion that alpha it can be causally inferred the assertion that beta, then beta is obligatory" An open problem is how to reflect classical reasoning within the system, e.g., to account for the principle "if beta is forbidden and from the assertion that alpha it can be causally inferred the assertion that beta, then alpha is forbidden"