arXiv subjects

Pietro Vigiani

Publications and source records attributed to Pietro Vigiani.

3 recordsLinked to original sources

arXiv2026

Paraclassical Logics with Two Negations

We study three paraclassical propositional logics with two negations, CLoaN, CLouN, and CLauN, obtained by pairwise combining the one-negation systems CLuN, CLaN, and CLoN. CLuN's negation is glut-tolerant and paraconsistent, CLaN's negationis gap-tolerant and paracomplete, and CLoN's negation is both paraconsistent and paracomplete. We provide sound and complete two-valued non-deterministic semantics for each of the two-negations systems. We then focus on CLauN, the system containing the primitive dual pair of CLaN and CLuN negations. In this setting, we show deductive relationships between different negations expressible in CLauN; we show two diferent ways to recapture classical logic by means of translations, locally and globally; and we show a duality results for the multiple conclusion consequence relation of the logic.

cs.LO↗

arXiv2026

Modal Extensions of Generalised Nelson Logics

Motivated by relevant epistemic logic, we extend Dunn's simple Kripke-style binary relational semantics for the semi-relevant logic RM to fit a modal extension of RM. It is shown that the modal axioms and rules that need to be added to RM to obtain a sound and complete axiomatisation of its modal extension give an axiomatisation of modal extensions of all logics in the family of generalised Nelson logics, also studied by Dunn.

cs.LO↗

arXiv2022

Relevant Reasoners in a Classical World

We develop a framework for epistemic logic that combines relevant modal logic with classical propositional logic. In our framework the agent is modeled as reasoning in accordance with a relevant modal logic while the propositional fragment of our logics is classical. In order to achieve this feature, we modify the relational semantics for relevant modal logics so that validity in a model is defined as satisfaction throughout a set of designated states that, as far as propositional connectives are concerned, behave like classical possible worlds. The main technical result of the paper is a modular completeness theorem parametrized by the relevant modal logic formalizing the agent's reasoning.

cs.LO↗