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Item type:Publication, Extending computational trinitarianismComputational trinitarianism is the view that a single notion of computation has three different manifestations: in logic as proofs, in typed-calculus as programs, and in category theory as morphisms. This idea has traditionally been closely associated with intuitionistic logic but here we argue that the connection is not exclusive. We provide a logician friendly, self-contained introduction to this topic by presenting the trinities for linear, affine, and relevant logic. The ground we set for that goal is then used to show how to obtain paraconsistent trinities by including the De Morgan negation. ©The author © Oxford University Press. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Inconsistent sets and how to compute themThe idea of a paraconsistent computability theory has been proposed as a way to work effectively with inconsistent sets of numbers. The viability of such a theory, though—the very coherence of the idea of an ‘inconsistent recursive relation’—has been called into doubt, most recently in (Choi, Synthese 200(5):418, 2022). In this paper we remove some doubt, by setting out a simple model of (naïve) set theory in LP, showing how to compute inconsistent sets in terms of extensions and antiextensions, and establishing further representability results. This suggests a way that a longstanding and apparently impossible-to-answer question—how can inconsistency be computed?—can be answered. ©The author ©Springer. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Gates and circuits via Dunn semanticsComputer hardware is heavily reliant on classical logic, but could we use some non-classical logic instead? In this paper I suggest an alternative model of implementation of logic gates in electronics. In particular, I propose a model that takes descriptions of logical connectives through means of Dunn semantics and implements them as logic gates by using a double current system: one for truth and one for falsity, instead of the classical use of a single current for both values. The outcome of this proposal should pave the way to new models of non-classical and even contra-classical computation based on paraconsistent, paracomplete and paranormal logics. © The author © Oxford University Press.