First-order swap structures semantics for some logics of formal inconsistency

Autor(es)

Coniglio, Marcelo E. ^{[1, 2]} ; Figallo-Orellano, Aldo ^{[2, 3]} ; Golzio, Ana C. ^[4]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Inst Philosophy & Humanities, BR-13083896 Campinas, SP - Brazil

^[2] Univ Estadual Campinas, Ctr Log Epistemol & Hist Sci, BR-13083896 Campinas, SP - Brazil

^[3] Univ Nacl Sur, Dept Matemat, Bahia Blanca, Buenos Aires - Argentina

^[4] Sao Paulo State Univ, Fac Philosophy & Sci, Marilia Campus, BR-17525900 Sao Paulo, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF LOGIC AND COMPUTATION; v. 30, n. 6, p. 1257-1290, SEP 2020.
• Citações Web of Science: 0

Resumo

The logics of formal inconsistency (LFIs, for short) are paraconsistent logics (i.e. logics containing contradictory but nontrivial theories) having a consistency connective which allows to recover the ex falso quodlibet principle in a controlled way. The aim of this paper is considering a novel semantical approach to first-order LFIs based on Tarskian structures defined over swap structures, a special class of multialgebras. The proposed semantical framework generalizes previous approaches to quantified LFIs presented in the literature. The case of QmbC, the simpler quantified LFI expanding classical logic, will be analyzed in detail. An axiomatic extension of QmbC called QLFI1(o), is also studied, which is equivalent to the quantified version of da Costa and D'Ottaviano 3-valued logic J3. The semantical structures for this logic turn out to be Tarkian structures based on twist structures. The expansion of QmbC and QLFI1(o) with a standard equality predicate is also considered. (AU)

• Processo FAPESP: 16/21928-0 - Semânticas não-determinísticas para as lógicas da inconsistência formal
• Beneficiário: Aldo Figallo Orellano
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 19/08442-9 - Big Data, dinâmicas sociais e línguas naturais
• Beneficiário: Ana Cláudia de Jesus Golzio
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado