# Historical/temporal necessities/possibilities, and a logical theory of them in branching time

arXiv: https://arxiv.org/abs/2208.11922 · HTML: https://mlsanity.com/paper/2208.11922/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 25 Aug 2022.

## Abstract (arXiv)

In this paper, we do three kinds of work. First, we recognize four notions of necessity and two notions of possibility related to time flow, namely strong/weak historical/temporal necessities, as well as historical/temporal possibilities, which are motivated more from a linguistic perspective than from a philosophical one. Strong/weak historical necessities and historical possibility typically concern the possible futures of the present world, and strong/weak temporal necessities and temporal possibility concern possible timelines of alternatives of the present world. Second, we provide our approach to the six notions and present a logical theory of them in branching time. Our approach to the six notions is as follows. The agent has a system of ontic rules that determine expected timelines. She treats some ontic rules as undefeatable, determining accepted timelines. The domains of strong/weak historical necessities, respectively, consist of accepted and expected timelines passing through the present moment, and historical possibility is the dual of strong historical necessity. The domains of strong/weak temporal necessities, respectively, consist of accepted and expected timelines, and temporal possibility is the dual of strong temporal necessity. The logical theory has six operators: a last-moment operator, a next-moment operator, and four operators for the four notions of necessity. Formulas' evaluation contexts consist of a tree-like model representing a time flow, a context representing the agent's system of ontic rules, a timeline, and an instant. Third, we offer an axiomatic system for the logical theory and show its soundness and completeness.