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A formalization of the Protagoras court paradox in a temporal logic of epistemic and normative reasons

A formalization of the Protagoras court paradox in a temporal logic of epistemic and normative... We combine linear temporal logic (with both past and future modalities) with a deontic version of justification logic to provide a framework for reasoning about time and epistemic and normative reasons. In addition to temporal modalities, the resulting logic contains two kinds of justification assertions: epistemic justification assertions and deontic justification assertions. The former presents justification for the agent’s knowledge and the latter gives reasons for why a proposition is obligatory. We present two kinds of semantics for the logic: one based on Fitting models and the other based on neighborhood models. The use of neighborhood semantics enables us to define the dual of deontic justification assertions properly, which corresponds to a notion of permission in deontic logic. We then establish the soundness and completeness of an axiom system of the logic with respect to these semantics. Further, we formalize the Protagoras versus Euathlus paradox in this logic and present a precise analysis of the paradox, and also briefly discuss Leibniz’s solution. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Artificial Intelligence and Law Springer Journals

A formalization of the Protagoras court paradox in a temporal logic of epistemic and normative reasons

Ghari, Meghdad
Artificial Intelligence and Law , Volume OnlineFirst – Mar 16, 2023
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43 pages

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Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
ISSN
0924-8463
eISSN
1572-8382
DOI
10.1007/s10506-023-09351-0
Publisher site
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Abstract

We combine linear temporal logic (with both past and future modalities) with a deontic version of justification logic to provide a framework for reasoning about time and epistemic and normative reasons. In addition to temporal modalities, the resulting logic contains two kinds of justification assertions: epistemic justification assertions and deontic justification assertions. The former presents justification for the agent’s knowledge and the latter gives reasons for why a proposition is obligatory. We present two kinds of semantics for the logic: one based on Fitting models and the other based on neighborhood models. The use of neighborhood semantics enables us to define the dual of deontic justification assertions properly, which corresponds to a notion of permission in deontic logic. We then establish the soundness and completeness of an axiom system of the logic with respect to these semantics. Further, we formalize the Protagoras versus Euathlus paradox in this logic and present a precise analysis of the paradox, and also briefly discuss Leibniz’s solution.

Journal

Artificial Intelligence and Law – Springer Journals

Published: Mar 16, 2023

Keywords: Justification logic; Deontic logic; Temporal logic; Normative reason; Interpreted system; Protagoras paradox

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