Dynamic logic of propositional commitments

Abstract

This paper describes how the effects of acts of asserting and conceding can be captured in a new logic DMPCL. DMPCL is developed according to a strategy similar to the strategy that leads to the development of dynamic epistemic logics. Thus acts of asserting and conceding are modeled as updators of propositional commitments, and a complete set of reduction axioms is presented. This paper also describes an extension of DMPCL called DMPCL+, which deals with the effects of acts of withdrawing assertions and concessions together with the effects of acts of asserting and conceding. As may be expected, the effects of acts of withdrawing turn out to be very difficult to capture, and the completeness problem for DMPCL+ is still open. Yet the possibility of withdrawal seems to be a distinguishing characteristic common to a wide range of acts whose effects are conventional or institutional, and so the logical dynamics of withdrawal seems to be of considerable significance to the study of social interactions among rational agents. We make a brief comparison with AGM approach to belief revision and briefly discuss an application of DMPCL+ to scorekeeping for argumentation games.