A logical theory for conditional weak ontic necessity based on context update

TL;DR

This paper develops a complete logical framework for understanding conditional weak ontic necessity, using context update mechanisms to evaluate 'should' statements based on defaults and possible world states.

Contribution

It introduces a novel logical theory that combines premise and update semantics to analyze conditional weak ontic necessity through context updates.

Findings

The logic is proven to be complete.

The framework effectively models 'should' statements in context.

It integrates premise semantics with update semantics for conditionals.

Abstract

Weak ontic necessity is the ontic necessity expressed by ``should'' or ``ought to'' in English. An example of it is ``I should be dead by now''. A feature of this necessity is whether it holds does not have anything to do with whether its prejacent holds. In this paper, 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. The logic is complete. Our theory combines premise semantics and update semantics for conditionals.