arXiv subjects

Raffaele Mascella

Publications and source records attributed to Raffaele Mascella.

3 recordsLinked to original sources

arXiv2025

Considerations on Everett J. Nelson's connexive logic

This work explores Everett John Nelson's connexive logic, outlined in his PhD thesis and partially summarized in his 1930 paper \emph{Intensional Relations}, which is obtained by extending the system $\mathsf{NL}$ (reconstructed by E. Mares and F. Paoli) with a weak conjunction elimination rule explicitly assumed in the former but not in the latter. After a preliminary analysis of Nelson's philosophical ideas, we provide an algebraic-relational semantics for his logic and we investigate possible extensions thereof which are able to cope with Nelson's ideas with much more accuracy than the original system. For example, we will inquire into extensions whose algebraic-relational models are endowed with irreflexive incompatibility relations, or determine a ``weakly'' transitive entailment. Such an investigation will allow us to establish relationships between some of the trademarks of Nelson's thought and concepts of prominent importance for connexive logic, as e.g. Kapsner's strong connexivity and superconnexivity, as well as between the algebraic-relational semantics of Nelsonian logics and ordered structures that have gained great attention over the past years, namely partially ordered involutive residuate groupoids and (non-orthomodular) orthoposets.

math.LO↗

arXiv2024

A logical perspective on intending to keep a true secret

Logical investigations of the notion of secrecy are typically concentrated on tools for deducing whether private information is well hidden from unauthorized, direct, or indirect access attempts. This paper proposes a multi-agent, normal multi-modal logic to capture salient features of secrecy's intentions. Specifically, we focus on the intentions, beliefs, and knowledge of secret keepers and, more generally, of all the actors involved in secret-keeping scenarios. In particular, we investigate intentions underlying the keeping of a true secret, namely a secret concerning information known (and so true) by the secret keeper. The resulting characterization of intending to keep a true secret provides valuable insights into conditions ensuring or undermining secrecy depending on agents' attitudes and links between secrets and their surrounding context. We present the proposed logical system's soundness, completeness, and decidability results. Furthermore, we outline some theorems with potential applications to several fields, e.g., computer science and the social sciences.

math.LO↗

arXiv2023

On Contextuality and Unsharp Quantum Logic

In this paper we provide a preliminary investigation of subclasses of bounded posets with antitone involution which are "pastings" of their maximal Kleene sub-lattices. Specifically, we introduce super-paraorthomodular lattices, namely paraothomodular lattices whose order determines, and it is fully determined by, the order of their maximal Kleene sub-algebras. It will turn out that the (spectral) paraorthomodular lattice of effects over a separable Hilbert space can be considered as a prominent example of such. Therefore, it arguably provides an algebraic/order theoretical rendering of complementarity phenomena between unsharp observables. A number of examples, properties and characterization theorems for structures we deal with will be outlined. For example, we prove a forbidden configuration theorem and we investigate the notion of commutativity for modular pseudo-Kleene lattices, examples of which are (spectral) paraorthomodular lattices of effects over finite-dimensional Hilbert spaces. Finally, we show that structures introduced in this paper yield paraconsistent partial referential matrices, the latter being generalizations of J. Czelakowski's partial referential matrices. As a consequence, a link between some classes of posets with antitone involution and algebras of partial "unsharp" propositions is established.

math.LO↗