Logic for conditional strong historical necessity in branching time and analyses of an argument for future determinism

In this paper, we present a logic for conditional strong historical necessity in branching time and apply it to analyze a nontheological version of Lavenham's argument for future determinism. Strong historical necessity is motivated from a linguistical perspective, and an example of it is ``If I had not gotten away, I must have been dead''. The approach of the logic is as follows. The agent accepts ontic rules concerning how the world evolves over time. She takes some rules as indefeasible, which determine acceptable timelines. When evaluating a sentence with conditional strong historical necessity, we introduce its antecedent as an indefeasible ontic rule and then check whether its consequent holds for all acceptable timelines. The argument is not sound by the logic.