5 research outputs found
Swap structures semantics for Ivlev-like modal logics
In 1988, J. Ivlev proposed some (non-normal) modal systems which are semantically characterized by four-valued non-deterministic matrices in the sense of A. Avron and I. Lev. Swap structures are multialgebras (a.k.a. hyperalgebras) of a special kind, which were introduced in 2016 by W. Carnielli and M. Coniglio in order to give a non-deterministic semantical account for several paraconsistent logics known as logics of formal inconsistency, which are not algebraizable by means of the standard techniques. Each swap structure induces naturally a non-deterministic matrix. The aim of this paper is to obtain a swap structures semantics for some Ivlev-like modal systems proposed in 2015 by M. Coniglio, L. FariƱas del Cerro and N. Peron. Completeness results will be stated by means of the notion of LindenbaumāTarski swap structures, which constitute a natural generalization to multialgebras of the concept of LindenbaumāTarski algebras
Modal logic with non-deterministic semantics: Part IāPropositional case
Dugundji proved in 1940 that most parts of standard modal systems cannot be characterized by a single finite deterministic matrix. In the eighties, Ivlev proposed a semantics of four-valued non-deterministic matrices (which he called quasi-matrices), in order to characterize a hierarchy of weak modal logics without the necessitation rule. In a previous paper, we extended some systems of Ivlevās hierarchy, also proposing weaker six-valued systems in which the (T) axiom was replaced by the deontic (D) axiom. In this paper, we propose even weaker systems, by eliminating both axioms, which are characterized by eight-valued non-deterministic matrices. In addition, we prove completeness for those new systems. It is natural to ask if a characterization by finite ordinary (deterministic) logical matrices would be possible for all those Ivlev-like systems. We will show that finite deterministic matrices do not characterize any of them
On six-valued logics of evidence and truth expanding Belnap-Dunn four-valued logic
The main aim of this paper is to introduce the logics of evidence and truth
LETK+ and LETF+ together with a sound, complete, and decidable six-valued
deterministic semantics for them. These logics extend the logics LETK and LETF-
with rules of propagation of classicality, which are inferences that express
how the classicality operator o is transmitted from less complex to more
complex sentences, and vice-versa. The six-valued semantics here proposed
extends the 4 values of Belnap-Dunn logic with 2 more values that intend to
represent (positive and negative) reliable information. A six-valued
non-deterministic semantics for LETK is obtained by means of Nmatrices based on
swap structures, and the six-valued semantics for LETK+ is then obtained by
imposing restrictions on the semantics of LETK. These restrictions correspond
exactly to the rules of propagation of classicality that extend LETK. The logic
LETF+ is obtained as the implication-free fragment of LETK+. We also show that
the 6 values of LETK+ and LETF+ define a lattice structure that extends the
lattice L4 defined by the Belnap-Dunn four-valued logic with the 2 additional
values mentioned above, intuitively interpreted as positive and negative
reliable information. Finally, we also show that LETK+ is Blok-Pigozzi
algebraizable and that its implication-free fragment LETF+ coincides with the
degree-preserving logic of the involutive Stone algebras.Comment: 38 page
19th Brazilian Logic Conference: Book of Abstracts
This is the book of abstracts of the 19th Brazilian Logic Conferences. The Brazilian Logic Conferences (EBL) is one of the most traditional logic conferences in South America. Organized by the Brazilian Logic Society (SBL), its main goal is to promote the dissemination of research in logic in a broad sense. It has been occurring since 1979, congregating logicians of different fields ā mostly philosophy, mathematics and computer science ā and with different backgrounds ā from undergraduate students to senior researchers. The meeting is an important moment for the Brazilian and South American logical community to join together and discuss recent developments of the field. The areas of logic covered in the conference spread over foundations and philosophy of science, analytic philosophy, philosophy and history of logic, mathematics, computer science, informatics, linguistics and artificial intelligence. Previous editions of the EBL have been a great success, attracting researchers from all over Latin America and elsewhere.
The 19th edition of EBL takes place from May 6-10, 2019, in the beautiful city of JoĆ£o Pessoa, at the northeast coast of Brazil. It is conjointly organized by Federal University of ParaĆba (UFPB), whose main campus is located in JoĆ£o Pessoa, Federal University of Campina Grande (UFCG), whose main campus is located in the nearby city of Campina Grande (the second-largest city in ParaĆba state) and SBL. It is sponsored by UFPB, UFCG, the Brazilian Council for Scientific and Technological Development (CNPq) and the State Ministry of Education, Science and Technology of ParaĆba. It takes place at Hotel Luxxor Nord TambaĆŗ, privileged located right in front TambaĆŗ beach, one of JoĆ£o Pessoaās most famous beaches