Kripke completeness of predicate modal logics
Date
2024
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Abstract
Kripke semantics is well-known for predicate and propositional modal logic. While the study of Kripke semantics has produced numerous completeness results for propositional modal logics, there are substantially fewer examples of Kripke complete predicate modal logics. This is dually attributable to inadequacies of predicate Kripke semantics as well as to the inherent technical difficulties that accompany domains in semantics of predicate logic. There is presently little literature in the area of Kripke completeness for predicate modal logics, which motivates a comprehensive survey of existing results, recent innovations as well as an investigation into what insights are required to produce more general results. The study of canonicity - the property of a modal logic where it is validated by its canonical frame - has led to wide coverage of Kripke completeness results in propositional modal logic. Canonicity, however, does not always persist for predicate extensions of propositional modal logics. We survey a number of propositional and predicate modal logics, both canonical and non-canonical, demonstrating techniques which show Kripke completeness for these logics, and discuss the extent to which the canonical model technique is useful to this end.
Description
A research report submitted in fulfilment of the requirements for the degree of Master of Science to the Faculty of Science, School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, 2023
Keywords
Kripke semantics, Canonicity