University of Salamanca (Spain) and Arché (Philosophical research centre for logic, language, metaphysics and epistemology), University of St Andrews (Scotland)
Abstract: The famous Polish logician Łukasiewicz introduced two different analyses of modal notions by means of many-valued logics: a group of linearly ordered systems Ł3, ..., Łn, ..., Łω and the 4-valued modal logic Ł. Unfortunately, both the first group of systems and the logic Ł validate the so-called Łukasiewicz type (modal) paradoxes. The aim of this talk is threefold: (1) to present some paracomplete and paraconsistent 4-valued logics developed in the recent literature (Belnap-Dunn Semantics for the Variants of BN4 and E4 which contain Routley and Meyer's logic B); (2) to strengthen those systems by means of truth-functional modal operators according to both aforementioned Łukasiewizc's approaches to modal notions; (3) to endow the resulting 4-valued modal logics with a Belnap-Dunn type semantics and present an outline for the soundness and completeness results. Interestingly, the 4-valued modal systems so defined happen to lack some or all of the Łukasiewicz type paradoxes.
Universidad Tecnológica de la Mixteca (Mexico)
Abstract: Genuine Paraconsistent logics were defined in 2016 by Béziau et al, including only three logical conectives, namely, negation disjunction and conjunction. This is a restricted notion of paraconsistency, particularly, a logic is genuine paraconsistent if it rejects the laws φ, ¬φ ⊢ ψ and ⊢ ¬(φ ∧ ¬φ). Afterwards in 2017 Hernández-Tello et al, provide implications for some of these logics. In this work we expand the study of all three-valued genuine paraconsistent logics, providing a twist-structures characterization for a big family of them in a modular way.
IRISA/Department of Electrical Engineering and Computer Science, University of Rennes (France)
Abstract: We consider infinite relational structures that have an automata-based presentation, known as automatic structures, introduced independently by Hodgson, Khoussainov and Nerode, and Blumensath and Grädel. We recall the seminal result that such structures have a decidable first-order (FO) theory, while their monadic second-order (MSO) theory is undecidable in general. As a contribution, we introduce a remarkable strict subclass of automatic structures, called regular automatic trees, and show that their MSO theory is decidable as long as the second-order quantifiers ranges over full branches of the trees only; this logic is called chain-MSO. The proof extends the one for FO logic over automatic structures. Thus automata constructions exist which offers convenient tools to analyse perfect-recall games with arbitrary epistemic linear-time omega-regular winning conditions.