Modalities over Action, I. Model Theory

This paper analyzes a language for actions and the deontic modalities over actions — i.e., the modalities permitted, forbidden and obligatory. The work is based on: (1) an action language that allows the representation of concurrent and repetitive events; (2) a deontic language that allows the representation of “free choice permissions”; (3) a proof procedure that admits a logic programming style of computation; and (4) a facility for nonmonotonic inference based on negation-as-failure. Applications of the language to several problems of common sense reasoning are also discussed. In particular, by imposing a “causal assumption” on the deontic modalities, we obtain an interesting solution to the frame problem and the ramification problem. This first part of the paper includes a model theory, and a sequel will include a proof theory, with soundness and completeness results for various fragments of the language.