PP-2016-04: A bimodal perspective on possibility semantics

PP-2016-04: van Benthem, Johan and Bezhanishvili, Nick and Holliday, Wesley H. (2016) A bimodal perspective on possibility semantics. [Report]

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In this paper we develop a bimodal perspective on possibility semantics, a framework allowing partiality of states that provides an alternative modeling for classical propositional and modal logics [Humberstone,1981, Holliday, 2015a]. In particular, we define a full and faithful translation of the basic modal logic K over possibility models into a bimodal logic of partial functions over partial orders, and we show how to modulate this analysis by varying across logics and model classes that have independent topological motivations. This relates the two realms under comparison both semantically and syntactically at the
level of derivations. Moreover, our analysis clarifies the interplay between the complexity of translations
and axiomatizations of the corresponding logics: adding axioms to the target bimodal logic simplifies translations, or vice versa, complex translations can simplify frame conditions. We also investigate a transfer of first-order correspondence theory between possibility semantics and its bimodal counterpart. Finally, we discuss the conceptual trade-off between giving translations and giving new semantics for logical systems, and we identify a number of further research directions to which our analysis gives rise.

Item Type: Report
Report Nr: PP-2016-04
Series Name: Prepublication (PP) Series
Year: 2016
Uncontrolled Keywords: classical modal logic, intuitionistic modal logic, possibility semantics, embeddings into bimodal logic, topological logics
Subjects: Logic
Depositing User: Nick Bezhanishvili
Date Deposited: 12 Oct 2016 14:37
Last Modified: 12 Oct 2016 14:37
URI: https://eprints.illc.uva.nl/id/eprint/540

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