Fourteenth Latin American Workshop on New Methods of Reasoning

(LANMR 2022)

Logic / Languages, Algorithms, New Methods of Reasoning

Invited Speakers

June 16th, 20 hrs. CET (13 hrs. Mexico city time)
Sandra María López Velasco

University of Salamanca (Spain) and Arché (Philosophical research centre for logic, language, metaphysics and epistemology), University of St Andrews (Scotland)

Title: “Defining modal expansions for some 4-valued logics by means of a Łukasiewiczian analysis of modal notions"

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.

June 17th, 17:35 hrs. CET (10:35 hrs. Mexico city time)
Verónica Borja Macías

Universidad Tecnológica de la Mixteca (Mexico)

Title: “Twist-structures for genuine paraconsistent logics"

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.

June 17th, 20 hrs. CET (13 hrs. Mexico city time)
Sophie Pinchinat

IRISA/Department of Electrical Engineering and Computer Science, University of Rennes (France)

Title: “Model checking over infinite structures: Automatic Structures and Regular Automatic Trees"

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.