•  17
    Cut elimination for coherent theories in negation normal form
    Archive for Mathematical Logic 63 (3): 427-445. 2024.
    We present a cut-free sequent calculus for a class of first-order theories in negation normal form which include coherent and co-coherent theories alike. All structural rules, including cut, are admissible.
  •  51
    Intuitionistic Mereology II: Overlap and Disjointness
    Journal of Philosophical Logic 52 (4): 1197-1233. 2023.
    This paper extends the axiomatic treatment of intuitionistic mereology introduced in Maffezioli and Varzi (_Synthese, 198_(S18), 4277–4302 2021 ) by examining the behavior of constructive notions of overlap and disjointness. We consider both (i) various ways of defining such notions in terms of other intuitionistic mereological primitives, and (ii) the possibility of treating them as mereological primitives of their own.
  •  28
    The Arithmetical dictum
    with Riccardo Zanichelli
    History and Philosophy of Logic 44 (4): 373-394. 2023.
    Building on previous scholarly work on the mathematical roots of assertoric syllogistic we submit that for Aristotle, the semantic value of the copula in universal affirmative propositions is the relation of divisibility on positive integers. The adequacy of this interpretation, labeled here ‘arithmetical dictum’, is assessed both theoretically and textually with respect to the existing interpretations, especially the so-called ‘mereological dictum’.
  •  11
    I provide a mereological analysis of Zeno of Sidon’s objection that in Euclid’s Elements we need to supplement the principle that there are no common segments of straight lines and circumferences. The objection is based on the claim that such a principle is presupposed in the proof that the diameter cuts the circle in half. Against Zeno, Posidonius attempts to prove against Zeno the bisection of the circle without resorting to Zeno’s principle. I show that Posidonius’ proof is flawed as it fails…Read more
  •  68
    The article investigates what happens when philosophy meets and begins to establish connections with two formal research methods such as game theory and network science. We use citation analysis to identify, among the articles published in Synthese and Philosophy of Science between 1985 and 2021, those that cite the specialistic literature in game theory and network science. Then, we investigate the structure of the two corpora thus identified by bibliographic coupling and divide them into clust…Read more
  •  23
    Hume on the Monetary Fallacy of Monotonic Counterfactuals
    Axiomathes 32 (2): 593-606. 2022.
    I focus on the commonly shared view that Hume’s monetary theory is inconsistent. I review several attempts to solve the alleged inconsistency in Hume’s monetary theory, including the consensus interpretation according to which Hume was committed to the neutrality of money only in the long run, while he conceded that money can be non-neutral in the short run. Then, building on a monetary version of the logical fallacy of monotonic counterfactuals in the essay Of the Balance of Trade, I argue for …Read more
  •  115
    Logic in analytic philosophy: a quantitative analysis
    Synthese 198 (11): 10991-11028. 2020.
    Using quantitative methods, we investigate the role of logic in analytic philosophy from 1941 to 2010. In particular, a corpus of five journals publishing analytic philosophy is assessed and evaluated against three main criteria: the presence of logic, its role and level of technical sophistication. The analysis reveals that logic is not present at all in nearly three-quarters of the corpus, the instrumental role of logic prevails over the non-instrumental ones, and the level of technical sophis…Read more
  •  44
    Bocheński's Formalization of Summa Theologiae (Ia,75,6) Reconsidered
    History and Philosophy of Logic 41 (2): 191-198. 2020.
    I investigate Bocheński's first-order logic formalization of the argument for the incorruptibility of the human soul given by Aquinas in Summa Theologiae (Ia,75,6). I suggest a slightly different axiomatization that reflect better Aquinas' informal argument. Along the way, I also fix a mistake in Bocheński's derivation that the human soul is not corruptible per se.
  •  33
    In previous work by Baaz and Iemhoff, a Gentzen calculus for intuitionistic logic with existence predicate is presented that satisfies partial cut elimination and Craig's interpolation property; it is also conjectured that interpolation fails for the implication-free fragment. In this paper an equivalent calculus is introduced that satisfies full cut elimination and allows a direct proof of interpolation via Maehara's lemma. In this way, it is possible to obtain much simpler interpolants and to …Read more
  •  30
    Interpolation in Extensions of First-Order Logic
    with Guido Gherardi and Eugenio Orlandelli
    Studia Logica 108 (3): 619-648. 2020.
    We prove a generalization of Maehara’s lemma to show that the extensions of classical and intuitionistic first-order logic with a special type of geometric axioms, called singular geometric axioms, have Craig’s interpolation property. As a corollary, we obtain a direct proof of interpolation for (classical and intuitionistic) first-order logic with identity, as well as interpolation for several mathematical theories, including the theory of equivalence relations, (strict) partial and linear orde…Read more
  •  36
    An intuitionistic logic for preference relations
    Logic Journal of the IGPL 27 (4): 434-450. 2019.
    We investigate in intuitionistic first-order logic various principles of preference relations alternative to the standard ones based on the transitivity and completeness of weak preference. In particular, we suggest two ways in which completeness can be formulated while remaining faithful to the spirit of constructive reasoning, and we prove that the cotransitivity of the strict preference relation is a valid intuitionistic alternative to the transitivity of weak preference. Along the way, we al…Read more
  •  25
    Sequents for non-wellfounded mereology
    Logic and Logical Philosophy 25 (3): 351-369. 2016.
    The paper explores the proof theory of non-wellfounded mereology with binary fusions and provides a cut-free sequent calculus equivalent to the standard axiomatic system.
  •  133
    Intuitionistic mereology
    Synthese 198 (Suppl 18): 4277-4302. 2021.
    Two mereological theories are presented based on a primitive apartness relation along with binary relations of mereological excess and weak excess, respectively. It is shown that both theories are acceptable from the standpoint of constructive reasoning while remaining faithful to the spirit of classical mereology. The two theories are then compared and assessed with regard to their extensional import.
  •  68
    Modular Sequent Calculi for Classical Modal Logics
    Studia Logica 103 (1): 175-217. 2015.
    This paper develops sequent calculi for several classical modal logics. Utilizing a polymodal translation of the standard modal language, we are able to establish a base system for the minimal classical modal logic E from which we generate extensions in a modular manner. Our systems admit contraction and cut admissibility, and allow a systematic proof-search procedure of formal derivations
  •  192
    Anti-realist epistemic conceptions of truth imply what is called the knowability principle: All truths are possibly known. The principle can be formalized in a bimodal propositional logic, with an alethic modality ${\diamondsuit}$ and an epistemic modality ${\mathcal{K}}$, by the axiom scheme ${A \supset \diamondsuit \mathcal{K} A}$. The use of classical logic and minimal assumptions about the two modalities lead to the paradoxical conclusion that all truths are known, ${A \supset \mathcal{K} A}…Read more
  •  50
    Analytic Rules for Mereology
    Studia Logica 104 (1): 79-114. 2016.
    We present a sequent calculus for extensional mereology. It extends the classical first-order sequent calculus with identity by rules of inference corresponding to well-known mereological axioms. Structural rules, including cut, are admissible
  •  1
  •  105
    Proof theory of epistemic logic of programs
    Logic and Logical Philosophy 23 (3): 301--328. 2014.
    A combination of epistemic logic and dynamic logic of programs is presented. Although rich enough to formalize some simple game-theoretic scenarios, its axiomatization is problematic as it leads to the paradoxical conclusion that agents are omniscient. A cut-free labelled Gentzen-style proof system is then introduced where knowledge and action, as well as their combinations, are formulated as rules of inference, rather than axioms. This provides a logical framework for reasoning about games in a…Read more