Substructural Routes to Variable Inclusion (with A. Borzi), Journal of Logic, Language and Information (2026) [Open Access]
Uniform Weak Kleene Logics (with A. Borzi), Australasian Journal of Logic (2026) [Open Access]
The Algebra of Analytic Containment (with F. Paoli and D. Szmuc), Journal of Logic, Language and Information (2026) [online][preprint]
Non-deterministic Semantics for logics of Analytic Implication (with D. Szmuc), Erkenntnis, (2025) [online][preprint]
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-reflexive Logics (with J. S. Toranzo Calderón), in: Teijeiro P. and Barrio E., eds., Metainferences in Substructural Logics, Springer (2026)
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.
Variable and Content Inclusion in Modal Logic (with G. Rosella, A. Borzi, D. Szmuc) [submitted]
This paper investigates the application of two-address semantics to modal logic: a framework that employs bi-dimensional valuations to capture truth-conditional and topical dimensions of a proposition, in accordance with a two-component view of propositional content. This framework has proven successful in characterizing content inclusion logics in the (non-modal) propositional setting—namely, systems based on the joint preservation of truth and subject matter—but its extension to modal languages remains largely unexplored. We define two-address valuations—which maintain classical Kripke semantics and interpret the topics of modal formulas into a suitable semilattice—to advance two types of content and variable inclusion modal logics: one with topic-transparent modalities, yielding systems characterized by plain variable inclusion, and another with topic-transformative modalities, enforcing a depth-sensitive form of variable inclusion.
Varieties of De Morgan bisemilattices (with F. Paoli, D. Szmuc and A. Borzi) [submitted][arXiv]
De Morgan bisemilattices are expansions of distributive bisemilattices by an involution satisfying De Morgan properties. They have attracted interest both as algebraic models of analytic containment logics, and as a case study for a certain generalisation of the Płonka sum construction (De Morgan- Płonka sums). In this paper, we provide a complete description of the lattice of subvarieties of the variety DMBL of De Morgan bisemilattices. For each subvariety in the lattice, we identify a finite set of finite generators, a characterisation of the De Morgan-Płonka representations of its members, and a syntactic description of its valid identities. In many cases, we also give an axiomatisation relative to DMBL.
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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