Abstract
Weak ontic necessity is the ontic necessity expressed by “should” or “ought to”. An example of it is “I should be dead by now”. A feature of this necessity is that whether it holds is irrelevant to whether its underlying proposition holds. This necessity essentially involves time. This paper presents a logic for conditional weak ontic necessity in branching time. The logic’s language includes the next instant operator, the last instant operator, and the operator for conditional weak ontic necessity. Formulas are evaluated at tuples consisting of a tree-based model, a context, a timeline, and an instant. A context is a set of ordered ontic laws determining expected timelines. When evaluating conditional weak ontic necessity, we first update the context with the antecedent, then check whether the consequent holds with respect to the updated context. We discuss some consequences of the formalization and compare it to some related work. We study the logic’s expressivity and axiomatize a special validity of it.
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Acknowledgements
I want to thank Valentin Goranko for his kind help during the development of this project. Thanks also go to the anonymous reviewers of Studia Logica. Of course, all errors are mine. This research was supported by the National Social Science Foundation of China (No. 19BZX137).
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Ju, F. A Logical Theory for Conditional Weak Ontic Necessity in Branching Time. Stud Logica (2023). https://doi.org/10.1007/s11225-023-10076-z
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DOI: https://doi.org/10.1007/s11225-023-10076-z