A Generalization of Ordered-Pair Semantics

Abstract In this paper, we generalize the ordered-pair semantics advanced by Matthew Clemens for the Logic of Paradox ( LP ) 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 (or distinguished) 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.

Authors

• Hitoshi Omori
• Jonas R. Becker Arenhart

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