Finance

Discrete mathematics

Predicate (mathematical logic)

Pure mathematics

Mathematics

Swap (finance)

Algebra over a field

Artificial intelligence

Economics

Axiom

Programming language

Geometry

Extension (predicate logic)

Sentence

Computer science

T-norm fuzzy logics

Classical logic

Atomic sentence

Fuzzy set

Membership function

Fuzzy logic

Journal of Logic and Computation

The logics of formal inconsistency (LFIs, for short) are paraconsistent logics (i.e. logics containing contradictory but non-trivial 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 $\textbf{QLFI1}_\circ $ 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 $\textbf{QLFI1}_\circ $ with a standard equality predicate is also considered.

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