TALK: Understanding negation thru' the modal logicians' eyes (2020)
Channel: Joao Marcos
Date: 2020-12-17

Invited Talk @ LANMR 2020
Thirteenth Latin American Workshop on New Methods of Reasoning 2020
Logic / Languages, Algorithms, New Methods of Reasoning
Mexico City (online), Dec 2020
http://www.lanmr.unam.mx/

Abstract:
It is perhaps not so widely known as it should be that any normal modal logic may be presented in a language containing, besides a classic-like implication, a paraconsistent negation whose interpretation dualizes that of intuitionistic negation.  Taking such sort of negative modalities seriously, it is also worth noting that modal languages containing them on top of the usual language of distributive lattices may be studied that cover the main classes of Kripke models, and in some such classes no classical negation (nor deductive implications) happen to be definable.  In this talk I will review what it means for a connective to be called a negative modality, illustrate how paraconsistent and paracomplete modal negations may interact with one another, extend the approach so as to express modal connectives that allow for negation-consistency and for negation-determinedness to be recovered, and show how several logics with such languages may be presented by way of appropriate standard analytic sequent calculi.

Slides:
https://drive.google.com/file/d/12IF4dmvTaBlSsiPIvFuY18aoRDIGNQYQ/