Abstract
Abstract The aim of this paper is to develop an algebraic and logical study of certain paraconsistent systems, from the family of the logics of formal inconsistency (LFIs), which are definable from the degree-preserving companions of logics of distributive involutive residuated lattices ($\textrm {dIRL}$s) with a consistency operator, the latter including as particular cases, Nelson logic ($\textsf {NL}$), involutive monoidal t-norm based logic ($\textsf {IMTL}$) or nilpotent minimum ($\textsf {NM}$) logic. To this end, we first algebraically study enriched dIRLs with suitable consistency operators. In fact, we consider three classes of consistency operators, leading respectively to three subquasivarieties of such expanded residuated lattices. We characterize the simple and subdirectly irreducible members of these quasivarieties, and we extend Sendlewski’s representation results for the case of Nelson lattices with consistency operators. Finally, we define and axiomatize the logics of three quasivarieties of $ \textrm {dIRL}$s and their corresponding degree-preserving companions that belong to the family of LFIs.
Highlights
The aim of this paper is to develop an algebraic and logical study of paraconsistent systems definable from the degree-preserving companions of logics of distributive involutive residuated lattices with a consistency operator
Moving from max- to maxB-consistency operators allows us to improve the results shown in Theorem 3.8 and Theorem 3.10 and, as anticipated, to characterize all subdirectly irreducible dIRLmc B algebras
In this paper we have been concerned with introducing logics of formal inconsistency (LFIs) upon the class of substructural logics having subvarieties of distributive involutive residuated lattices (dIRLs) as algebraic semantics
Summary
The aim of this paper is to develop an algebraic and logical study of paraconsistent systems definable from the degree-preserving companions of logics of distributive involutive residuated lattices (dIRLs) with a consistency operator. The initial motivation comes from different considerations relating paraconsistency and Nelson’s constructive logic with strong negation. In the 1950’s, constructive logic with strong negation, nowadays commonly known under the name of Nelson logic (even called N3), was formulated by Nelson and Markov as a result of
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
