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zpravodaj ČSKI - duben 2019 [ pdf ]
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datum: 24.4.2019 v 16:00
název: The poset of all logics
přednášející: Tommaso Moraschini (UI)
místo konání: UI, 2.patro, místnost č.318

souhrn: A notion of interpretability between arbitrary propositional logics is introduced, and shown to be a preorder on the class of all logics. Accordingly, we refer to its associated poset as to the “poset of all logics”. In this talk we shall explore the structure of this poset. In particular, we observe that that it has infima of arbitrarily large sets, but even finite suprema may fail to exist. This should not come as a surprise, since the universe of the poset of all logics is indeed a proper class. The formalism of interpretability is subsequently exploited to introduce the notion of a Leibniz class of logics, and we refer to the complete lattice of Leibniz class as to the Leibniz hierarchy. This order-theoretic perspective allows us to address in mathematical terms the following foundational question: do the classes traditionally associated to the Leibniz hierarchy (e.g. that of protoalgebraic logics) capture “fundamental” concepts?