AIC Seminar Series

According to the classical consistency presupposition, contradictions have an explosive disposition: Whenever they are present in a theory, anything goes, and no sensible reasoning can thus take place. A logic is paraconsistent if it disallows such presupposition, and allows instead for some inconsistent yet non-trivial theories to make perfect sense. The Logics of Formal Inconsistency, LFIs, form a particularly expressive class of paraconsistent logics in which the metatheoretical notion of consistency can be internalized at the object-language level. As a consequence, the LFIs are able to recapture consistent reasoning by the addition of appropriate consistency assumptions. So, for instance, while typical classical rules such as disjunctive syllogism (from A and (not-A)-or-B, infer B) are bound to fail in a paraconsistent logic (because A and (not-A) could both be true for some A, independently of B), they can be recovered by an LFI if the set of premises is enlarged by the presumption that we are reasoning in a consistent environment (in this case, by the addition of (consistent-A) as an extra hypothesis of the rule).

Our talk will provide an introduction to the class of LFIs, as well as an illustration of how rich this class is, in that it naturally subsumes most logics originating from both the Brazilian and the Polish schools of paraconsistency and is characterized by the same kind of derivability adjustment theorem that gives foundation to the logics originating from the Belgian school of paraconsistency.

JOÃO MARCOS is a logician and holds a PhD in Mathematics from the TU-Lisbon (Portugal) and a PhD in Philosophy from the State University of Campinas (Brazil). He is currently a member of the Group for Logic, Language, Information, Theory and Applications (LoLITA), an Associate Professor at the Department of Informatics and Applied Mathematics (DIMAp) of UFRN (Brazil), and collaborates with the Security and Quantum Information Group (SQIG) / IT (Portugal). His main topics of investigation center around non-classical logics (paraconsistent, many-valued, modal, intuitionistic), formal semantics (possible-translations semantics, possible-worlds semantics, society semantics), abstract logic, and the philosophy of logic.

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