Modal Semantics without Possible Worlds: A Study of Hierarchical Non-deterministic Many-valued Semantics
Final Report Abstract
The project aimed at investigating many-valued non-deterministic and hierarchical semantics for normal and non-normal modal logics. The starting point was work by John Kearns and Yuri Ivlev who had already done research on this topic in the 1980s, but who were ignored by a large part of the logicians of their time. This ignorance was probably due to the fact that a systematic account of non-deterministic semantics was not given until Arnon Avron and others in the early 21st century. Accordingly, the work of Kearns and Ivlev was rediscovered only in 2014 by the applicant and in parallel by a group of researchers led by Marcelo Coniglio, resulting in independently published research articles. As a result of the project „Modal Semantics without Possible Worlds“, a new relational semantics for various normal and non-normal modal logics stands, significantly different from Kripke’s semantics for modal logics, in which the notion of modality of formulas stands as a new semantic entity independent of „truth“ and „falsity“ in possible worlds. The investigation here was as general as possible, in that it did not specify which modality (alethic, epistemic, doxastic, temporal, etc.) was being investigated. Instead, the properties of concrete modal operators emerge in interaction with rules and axioms. This has the advantage that properties intrinsic to Kripke semantics, while available, need not necessarily appear in the semantics for modal logic, so that the resulting semantics can be conceived more generally as Kripke’s possible world semantics.
Publications
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Modal Logics or: How I stopped worrying about possible worlds, Bochum- Lodz Workshop, OnlineTalk, 2021
Daniel Skurt
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Non-deterministic Semantics and Modal Logics without possible worlds, DGPhil 25, Online Talk, 2021
Daniel Skurt
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On Ivlev semantics for modality, Smirnoff Readings 20, Online Talk, 2021
Daniel Skurt
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Untruth, falsity and non-deterministic semantics, ISMVL 51, Online Talk, 2021.
Daniel Skurt
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Untruth, falsity and non-deterministic semantics. 2021 IEEE 51st International Symposium on Multiple-Valued Logic (ISMVL), 74-80. IEEE.
Omori, Hitoshi & Skurt, Daniel
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The smallest modal system (and extensions), AiML 2022, Rennes
Daniel Skurt
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The smallest modal system and its extensions, 1st Workshop on Non-deterministic Semantics for Modal Logics, Bochum, 2022
Daniel Skurt
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The smallest modal system and its extensions, Logica 2022, Teplá, 2022
Daniel Skurt
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There is no “i” in modal logic, Colloquium Logic and Epistemology, Bochum, 2022
Daniel Skurt
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RNmatrices for Modal Logics, Logic and Metaphysics Workshop, CUNY, New York, 2023
Daniel Skurt
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On Ivlev’s Semantics for Modality. Synthese Library, 243-275. Springer International Publishing.
Omori, Hitoshi & Skurt, Daniel
