A logical theory for strong and weak ontic necessities in branching time

Abstract: Ontic necessities are those modalities universally quantifying over domains of ontic possibilities, whose existence'' is independent of our knowledge. An ontic necessity, called the weak ontic necessity, causes interesting questions. An example for it isI should be dead by now''. A feature of this necessity is whether it holds at a state has nothing to do with whether its prejacent holds at the state. Is there a weak epistemic necessity expressed by should''? Is there a strong ontic necessity expressed bymust''? How do we make sense of the strong and weak ontic necessities formally? In this paper, we do the following work. Firstly, we recognize strong/weak ontic/epistemic necessities and give our general ideas about them. Secondly, we present a complete logical theory for the strong and weak ontic necessities in branching time. This theory is based on the following approach. The weak ontic necessity quantifies over a domain of expected timelines, determined by the agent's system of ontic rules. The strong ontic necessity quantifies over a domain of accepted timelines, determined by undefeatable ontic rules.