On a Generalization of all Strong Kleene Generalizations of Classical Logic (with P. Cobreros, I. Grábalos, J. S. Toranzo Calderón, J. Viñeta), Studia Logica (2025) [Open Access]
Non-deterministic Semantics for logics of Analytic Implication (with D. Szmuc), Erkenntnis, (2025) [online][preprint]
Uniform Weak Kleene Logics (with A. Borzi), Australasian Journal of Logic (forthcoming) [preprint]
Substructural Routes to Variable Inclusion (with A. Borzi), Journal of Logic, Language and Information (forthcoming) [preprint]
Non-reflexive Logics (with J. S. Toranzo Calderón), in: Teijeiro P. and Barrio E., eds., Metainferences in Substructural Logics, Springer (2026)
The Algebra of Analytic Containment (with F. Paoli and D. Szmuc) [submitted]
We explore certain algebraic structures that naturally emerge within the framework of logics of synonymy, analytic containment, and hyperintensionality. In particular, we argue that Angell’s logic AC, one of the earliest and most successful attempts to analyse the properties of logical constants with a topic-transformative character, can be better understood through a direct algebraic study of De Morgan bisemilattices. Inter alia, we show that a certain 9-element algebra introduced by Ferguson generates De Morgan bisemilattices as a quasivariety, making it the most adequate semantics for AC, as opposed to other 7-element and 16-element algebras considered in the literature.
Compatibility and Implication from a Non-Classical Perspective (with A. Iacona) [submitted]
This paper draws attention to some key logical relations between two distinct and independently intelligible notions, compatibility and implication. We identify a set of inference rules that express properties of compatibility, and show how some crucial principles concerning conditionals can be derived from these rules on the assumption that implication is definable in terms of compatibility. As will emerge, and this is the main point of the paper, the logical relations considered are to a large extent neutral as to the background logic, for they hold in a significantly wide range of non-classical systems.
Contradictions are Meaningless (with A. Borzi and D. Szmuc) [submitted]
This article investigates the thesis—famously associated with Wittgenstein—that contradictions and tautologies are meaningless or about nothing, together with the assumption that such expressions behave infectiously, transmitting their lack of significance to any compound in which they occur. Taking logical validity to be modeled as content inclusion, understood as encompassing both truth preservation and subject-matter preservation, we proceed by examining alethic structures alongside topical structures whose operations provide a topical mereology well suited to our aims. Building on this, we introduce and characterize as a case study the fragment of Classical logic which reflects this version of content inclusion.
The Dark Side of a Structural Logic (with A. Borzi)
Some authors developed a two-sided conception of what a logic is, distinguishing between its positive and its negative sides, the former being the set of its valid inferences, the latter being the set of its valid anti-inferences (corresponding to unsatisfiable inferences). In this work we consider a more general account of what could be the negative part of a logic, which includes the former as a particular instance. Building on this idea, we dualize the general construction developed by Szmuc (2023), showing that for every Tarskian logic, we can construct a logic that shares exactly its negative part.
De Finetti goes Viral (with M. Rubin)
In this work, our objective is to investigate the logic and the probability logic of the De Finetti's conditional when matched with the Weak Kleene operators. Moreover, we argue that this pairing offers a more natural alternative than others extensively explored in the literature, namely the Strong Kleene and Quasi-connectives.
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