BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Tadeusz Litak (Friedrich-Alexander-University of Erlangen-Nürnber g) DTSTART:20210212T170000Z DTEND:20210212T190000Z DTSTAMP:20260423T021227Z UID:NCLogic/7 DESCRIPTION:Title: Lewis meets Brouwer\, or perhaps Heyting\nby Tadeusz Litak (Friedrich- Alexander-University of Erlangen-Nürnberg) as part of Nonclassical Logic Webinar\n\n\nAbstract\nThis talk is an introduction to what one might call the Heyting-Lewis calculus of strict implication over the intuitionistic propositional base\; the names "constructive strict implication" or "Brouw er-Lewis implication/calculus" have also been used. The corresponding clas s of algebras can be seen as the fusion of Heyting algebras and weak Heyti ng algebras (Celani and Jansana) over the shared bounded lattice reduct. ( Super)intuitionistic modal logics with unary box are a limiting case\, but in the intuitionistic setting there are many examples where strict implic ation is not reducible to box. Its variants arise\, e.g.\, in the context of preservativity in Heyting Arithmetic (where it was first invented by Vi sser)\, in the inhabitation logic of simple type theory extended with Hask ell-style arrows\, and in a generalization of Intuitionistic Epistemic Log ic of Artemov and Protopopescu. The move to the intuitionistic propositio nal base also throws interesting light on the complex fate of Lewis' origi nal systems. The Heyting-Lewis calculus enjoys a natural Kripke semantics (first studied by Iemhoff and coauthors)\, which also allows defining an a ppropriate notion of descriptive frame and Esakia-style dualities. Further more\, one can follow the Wolter-Zakharyaschev idea of generalizing the G ödel-McKinsey-Tarski translation\, reducing the metatheory of Heyting-Lew is logics to suitable bimodal logics over the classical propositional base \, obtaining a suitable variant of the Blok-Esakia theorem\, and (re)provi ng many correspondence\, completeness\, decidability and fmp results in an uniform way. However\, it seems that ultimately one will have to drop one of the axioms\, losing the natural Kripke semantics. In the final part of the talk\, I am going to discuss alternative semantics for the weakened s ystem and its position in the broader landscape of intuitionistic logics w ith an additional implication-like connective. This talk involves joint wo rk with Albert Visser (Utrecht University)\, Jim de Groot and Dirk Pattins on (ANU)\, Igor Sedlar and the Prague group\, and Miriam Polzer (Google).\ n LOCATION:https://researchseminars.org/talk/NCLogic/7/ END:VEVENT END:VCALENDAR