A Logical Theory for Conditional Weak Ontic Necessity Based on Context Update

Weak ontic necessity is the ontic necessity expressed by should/ought to in English. An example of it is I should be dead by now. A feature of this necessity is that whether it holds at the present world is irrelevant to whether its prejacent holds at the present world. In this paper, by combining premise semantics and update semantics for conditionals, we present a logical theory for conditional weak ontic necessity based on context update. A context is a set of ordered defaults, determining expected possible states of the present world. Sentences are evaluated with respect to contexts. When evaluating the conditional weak ontic necessity with respect to a context, we first update the context with the antecedent, then check whether the consequent holds with respect to the updated context. We compare this theory to some related works. The logic's expressivity is studied.

Automated summary

This paper presents a logical theory for conditional weak ontic necessity based on context update. By combining premise semantics and update semantics, the theory evaluates the weak necessity in a specific context to determine the possible states of the present world.