arXiv subjects

Marcelo Coniglio

Publications and source records attributed to Marcelo Coniglio.

4 recordsLinked to original sources

arXiv2026

On Many-logic modal structures and information-based logics

This paper proposes an approach to information-based logics using many-logic modal structures (MLMS). These structures can express accessibility relations between worlds with different underlying logics by anchoring them to a base lattice, which contains the semantics of each logic as a down-complete sublattice. MLMS are suitable for representing connections between information states (i.e., configurations of databases) and the evolution of information states over time. We will illustrate the application of MLMS by means of the six-valued logic of evidence and truth LET+K , related to the lattice L6, and some four-, three-, and two-valued logics related to down-complete sublattices of L6. These logics are capable of representing paracomplete, paraconsistent, and classical contexts with six-, four-, three-, and two-valued scenarios.

math.LO↗

arXiv2023

A new decision method for Intuitionistic Logic by 3-valued non-deterministic truth-tables (pre-print version)

Kurt G\"odel proved that it is not possible to characterize Intuitionistic Propositional Logic (IPL) by means of finite and deterministic truth-tables. After extending the same result with respect to non-deterministic matrices, we provide a semantical characterization of IPL by means of a 3-valued non-deterministic matrix with a restricted set of valuations. This structure allows to define an algorithm to delete unsound rows from the non-deterministic truth-tables generated for each formula, which constitutes a new and very simple decision procedure for IPL. This method can be seen as truth-tables in a broader sense, and a way to overcome G\"odel's limiting result.

math.LO↗

arXiv2023

Normal proofs and tableaux for the Font-Rius tetravalent modal logic

Tetravalent modal logic (T ML) was introduced by Font and Rius in 2000; and it is an expansion of the Belnap-Dunn four{valued logic FOUR, a logical system that is well{known for the many applications it has been found in several fields. Besides, T ML is the logic that preserve degrees of truth with respect to Monteiro's tetravalent modal algebras. Among other things, Font and Rius showed that T ML has a strongly adequate sequent system, but unfortunately this system does not enjoy the cut-elimination property. However, in [16], it was presented a sequent system for T ML with the cut{elimination property. Besides, in this same work, it was also presented a sound and complete natural deduction system for this logic. In the present work, we continue with the study of T ML under a proof-theoretic perspective. In first place, we show that the natural deduction system given in [16] admits a normalization theorem. In second place, taking advantage of the contrapositive implication for the tetravalent modal algebras introduced in [17], we define a decidable tableau system adequate to check validity in the logic T ML. Finally, we provide a sound and complete tableau system for T ML in the original language.These two tableau systems constitute new (proof-theoretic) decision procedures for checking validity in the variety of tetravalent modal algebras.

math.LO↗

arXiv2014

Logics of formal inconsistency arising from systems of fuzzy logic

This paper proposes the meeting of fuzzy logic with paraconsistency in a very precise and foundational way. Specifically, in this paper we introduce expansions of the fuzzy logic MTL by means of primitive operators for consistency and inconsistency in the style of the so-called Logics of Formal Inconsistency (LFIs). The main novelty of the present approach is the definition of postulates for this type of operators over MTL-algebras, leading to the definition and axiomatization of a family of logics, expansions of MTL, whose degree-preserving counterpart are paraconsistent and moreover LFIs.

math.LO↗