A Generalization of Ordered-Pair Semantics

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In Sujata Ghosh & Thomas Icard, Logic, Rationality, and Interaction: 8th International Workshop, Lori 2021, Xi’an, China, October 16–18, 2021, Proceedings. Springer Verlag. pp. 149-157 (2021)
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Abstract

In this paper, we generalize the ordered-pair semantics advanced by Matthew Clemens for the Logic of Paradox to n-tuple semantics, for each fixed n. Moreover, we show that the resulting semantics can accommodate not only LP, but also classical logic as well as strong Kleene logic depending on the set of designated values that one chooses. Building on the technical observations, we offer intuitively plausible readings for the semantics, and we also discuss some weaknesses of the original intuitive reading advanced by Clemens.

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10.1007/978-3-030-88708-7_12

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Jonas R. B. Arenhart
Universidade Federal de Santa Catarina
Hitoshi Omori

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