arXiv subjects

Gandolfo Vergottini

Publications and source records attributed to Gandolfo Vergottini.

2 recordsLinked to original sources

arXiv2026

A Logical 3-valued Semantics for Nondeterministic Choice

We propose a logical formalisation of computational errors in reactive, nondeterministic systems. To this aim, we introduce a new three-valued symmetric nondeterministic disjunction, designed to provide a faithful logical representation of the nondeterministic choice arising in concurrent computations. The connective is defined within the framework of nondeterministic matrices (Nmatrices) and derives from a minimal combination of Kleene's tolerant semantics and Bochvar's symmetric error persistence, thereby eliminating the residual asymmetry induced by sequential evaluation strategies such as McCarthy's logic. The resulting semantics admits genuinely nondeterministic outcomes in mixed cases involving errors, while preserving commutativity and operational symmetry.

cs.LO↗

arXiv2024

Tense logics based on posets

Not all logical systems can be captured using algebras. We see this in classical logic (formalized by Boolean algebras) and many-valued logics (like Lukasiewicz logic with MV-algebras). Even quantum mechanics, initially formalized with orthomodular lattices, benefits from a simpler approach using just partially ordered sets (posets). This paper explores how logical connectives are introduced in poset-based logics. Building on prior work by the authors, we delve deeper into "dynamic" logics where truth values can change over time. We consider time sets with a preference relation and propositions whose truth depends on time. Tense operators, introduced by J.Burgess and extended for various logics, become a valuable tool. This paper proposes several approaches to this topic, aiming to inspire a further stream of research.

math.LO↗