arXiv subjects

Martin Figallo

Publications and source records attributed to Martin Figallo.

3 recordsLinked to original sources

arXiv2024

Paraconsistent Belief Revision: A Replacement-Enriched LFI for Epistemic Entrenchment

We further develop the formal foundations of Paraconsistent Belief Revision (PBR) by introducing Logics of Formal Inconsistency (LFIs) specifically designed to support the development of epistemic entrenchment-based models for belief change. The interpretation of formal consistency -- and, more broadly, of paraconsistency -- in terms of the epistemic attitudes adopted by rational agents and of these agents reasoning with potentially contradictory yet non-trivial epistemic states, respectively, is already well-established within the literature on PBR based on LFIs. However, previous approaches faced a key limitation: the absence of replacement in most LFIs prevented the construction of entrenchment-based operations. We address this gap by first revisiting and systematizing core properties essential for such modeling, formalizing them within Cbr, a previously introduced logic whose foundational properties we now examine and develop in depth. Building on this, we introduce RCbr, a replacement-enriched, self-extensional extension of Cbr, which makes it possible -- within an LFI-based framework -- to formally define epistemic entrenchment and to construct entrenchment-based belief revision mechanisms. This development enables a fully constructive approach to Belief Revision in paraconsistent settings, further advancing the theoretical treatment of LFIs and paraconsistency within the broader landscape of epistemic states and belief dynamics.

cs.LO↗

arXiv2018

Some model-theoretic results on the 3-valued paraconsistent first-order logic QCiore

In this paper the 3-valued paraconsistent first-order logic QCiore is studied from the point of view of Model Theory. The semantics for QCiore is given by partial structures, which are first-order structures in which each n-ary predicate R is interpreted as a triple of paiwise disjoint sets of n-uples representing, respectively, the set of tuples which actually belong to R, the set of tuples which actually do not belong to R, and the set of tuples whose status is dubious or contradictory. Partial structures were proposed in 1986 by I. Mikenberg, N. da Costa and R. Chuaqui for the theory of quasi-truth (or pragmatic truth). In 2014, partial structures were studied by M. Coniglio and L. Silvestrini for a 3-valued paraconsistent first-order logic called LPT1, whose 3-valued propositional fragment is equivalent to da Costa-D'Otaviano's logic J3. This approach is adapted in this paper to QCiore, and some important results of classical Model Theory such as Robinson's joint consistency theorem, amalgamation and interpolation are obtained. Although we focus on QCiore, this framework can be adapted to other 3-valued first-order logics.

math.LO↗

arXiv2013

Free algebras in varieties of Hilbert algebras with supremum generated by finite chains

Hilbert algebras with supremum, i.e., Hilbert algebras where the associated order is a join-semilattice were first considered by A.V. Figallo, G. Ramon and S. Saad in [11], and independently by S. Celani and D. Montangie in [7]. On the other hand, L. Monteiro introduced the notion of n-valued Hilbert algebras (see [12]). In this work, we investigate the class of n-valued Hilbert algebras with supremum, denoted Hn, i.e., n-valued Hilbert algebras where the associated order is a join-semilattice. The varieties Hn are generated by finite chains. The free Hn-algebra Freen+1(r) with r generators is studied. In particular, we determine an upper bound to the cardinal of the finitely generated free algebra Freen+1(r).

math.LO↗