35 found
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  1. On defining the notion of complete and immediate formal grounding.Francesca Poggiolesi - 2016 - Synthese 193 (10).
    The aim of this paper is to provide a definition of the the notion of complete and immediate formal grounding through the concepts of derivability and complexity. It will be shown that this definition yields a subtle and precise analysis of the concept of grounding in several paradigmatic cases.
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  2.  77
    On constructing a logic for the notion of complete and immediate formal grounding.Francesca Poggiolesi - 2018 - Synthese 195 (3):1231-1254.
    In Poggiolesi we have introduced a rigorous definition of the notion of complete and immediate formal grounding; in the present paper our aim is to construct a logic for the notion of complete and immediate formal grounding based on that definition. Our logic will have the form of a calculus of natural deduction, will be proved to be sound and complete and will allow us to have fine-grained grounding principles.
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  3.  45
    Conceptual (and Hence Mathematical) Explanation, Conceptual Grounding and Proof.Francesca Poggiolesi & Francesco Genco - 2023 - Erkenntnis 88 (4):1481-1507.
    This paper studies the notions of conceptual grounding and conceptual explanation (which includes the notion of mathematical explanation), with an aim of clarifying the links between them. On the one hand, it analyses complex examples of these two notions that bring to the fore features that are easily overlooked otherwise. On the other hand, it provides a formal framework for modeling both conceptual grounding and conceptual explanation, based on the concept of proof. Inspiration and analogies are drawn with the recent (...)
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  4.  79
    Conceptual (and Hence Mathematical) Explanation, Conceptual Grounding and Proof.Francesca Poggiolesi & Francesco Genco - 2021 - Erkenntnis:1-27.
    This paper studies the notions of conceptual grounding and conceptual explanation (which includes the notion of mathematical explanation), with an aim of clarifying the links between them. On the one hand, it analyses complex examples of these two notions that bring to the fore features that are easily overlooked otherwise. On the other hand, it provides a formal framework for modeling both conceptual grounding and conceptual explanation, based on the concept of proof. Inspiration and analogies are drawn with the recent (...)
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  5.  60
    A cut-free simple sequent calculus for modal logic S5.Francesca Poggiolesi - 2008 - Review of Symbolic Logic 1 (1):3-15.
    In this paper, we present a simple sequent calculus for the modal propositional logic S5. We prove that this sequent calculus is theoremwise equivalent to the Hilbert-style system S5, that it is contraction-free and cut-free, and finally that it is decidable. All results are proved in a purely syntactic way.
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  6. Method of Tree-Hypersequents for Modal Propositional Logic.Francesca Poggiolesi - 2009 - In Jacek Malinowski David Makinson & Wansing Heinrich (eds.), Towards Mathematical Philosophy. Springer. pp. 31–51.
  7.  45
    Grounding rules and (hyper-)isomorphic formulas.Francesca Poggiolesi - 2020 - Australasian Journal of Logic 17 (1):70-80.
    An oft-defended claim of a close relationship between Gentzen inference rules and the meaning of the connectives they introduce and eliminate has given rise to a whole domain called proof-theoretic semantics, see Schroeder- Heister (1991); Prawitz (2006). A branch of proof-theoretic semantics, mainly developed by Dosen (2019); Dosen and Petric (2011), isolates in a precise mathematical manner formulas (of a logic L) that have the same meaning. These isomorphic formulas are defined to be those that behave identically in inferences. The (...)
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  8.  30
    A Critical Overview of the Most Recent Logics of Grounding.Francesca Poggiolesi - 2016 - In Francesca Boccuni & Andrea Sereni (eds.), Objectivity, Realism, and Proof. FilMat Studies in the Philosophy of Mathematics. Cham, Switzerland: Springer International Publishing.
    In this paper our aim is twofold: on the one hand, to present in a clear and faithful way two recent contributions to the logic of grounding, namely Correia, and Fine ; on the other hand, to argue that some of the formal principles describing the notion of grounding proposed by these logics need to be changed and improved.
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  9.  48
    Grounding principles for (relevant) implication.Francesca Poggiolesi - 2020 - Synthese 198 (8):7351-7376.
    Most of the logics of grounding that have so far been proposed contain grounding axioms, or grounding rules, for the connectives of conjunction, disjunction and negation, but little attention has been dedicated to the implication connective. The present paper aims at repairing this situation by proposing adequate grounding principles for relevant implication. Because of the interaction between negation and implication, new grounding principles concerning negation will also arise.
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  10.  30
    Display calculi and other modal calculi: a comparison.Francesca Poggiolesi - 2010 - Synthese 173 (3):259-279.
    In this paper we introduce and compare four different syntactic methods for generating sequent calculi for the main systems of modal logic: the multiple sequents method, the higher-arity sequents method, the tree-hypersequents method and the display method. More precisely we show how the first three methods can all be translated in the fourth one. This result sheds new light on these generalisations of the sequent calculus and raises issues that will be examined in the last section.
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  11. From thin objects to thin concepts?Massimiliano Carrara, Ciro De Florio & Francesca Poggiolesi - 2023 - Theoria 89 (3):256-265.
    In this short paper we consider Linnebo's thin/thick dichotomy: first, we show that it does not overlap with the very common one between abstract/concrete objects; second, on the basis of some difficulties with the distinction, we propose, as a possible way out, to move from thin/thick objects to thin/thick concepts.
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  12.  37
    Grounding and Propositional Identity: A Solution to Wilhelm’s Inconsistencies.Francesca Poggiolesi - forthcoming - Logic and Logical Philosophy:1-6.
    By following a recent result of [Wilhelm, 2021], it can easily be shown that standard conditions for immediate partial grounding and relevant identity conditions for propositions are inconsistent with one another. This is an unfortunate situation for all grounding enthusiasts; however, by adopting the approach presented by Poggiolesi [2016a,b], which displays a more-fined grained use of negations, it can also be shown that consistency can be restored back.
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  13. A purely syntactic and cut-free sequent calculus for the modal logic of provability.Francesca Poggiolesi - 2009 - Review of Symbolic Logic 2 (4):593-611.
    In this paper we present a sequent calculus for the modal propositional logic GL (the logic of provability) obtained by means of the tree-hypersequent method, a method in which the metalinguistic strength of hypersequents is improved, so that we can simulate trees shapes. We prove that this sequent calculus is sound and complete with respect to the Hilbert-style system GL, that it is contraction free and cut free and that its logical and modal rules are invertible. No explicit semantic element (...)
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  14.  47
    Natural Deduction Calculi and Sequent Calculi for Counterfactual Logics.Francesca Poggiolesi - 2016 - Studia Logica 104 (5):1003-1036.
    In this paper we present labelled sequent calculi and labelled natural deduction calculi for the counterfactual logics CK + {ID, MP}. As for the sequent calculi we prove, in a semantic manner, that the cut-rule is admissible. As for the natural deduction calculi we prove, in a purely syntactic way, the normalization theorem. Finally, we demonstrate that both calculi are sound and complete with respect to Nute semantics [12] and that the natural deduction calculi can be effectively transformed into the (...)
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  15.  34
    On the importance of being analytic. The paradigmatic case of the logic of proofs.Francesca Poggiolesi - 2012 - Logique Et Analyse 55 (219):443-461.
    In the recent literature on proof theory, there seems to be a new raising topic which consists in identifying those properties that characterise a good sequent calculus. The property that has received by far the most attention is the analyticity property. In this paper we propose a new argument in support of the analyticity property. We will do it by means of the example of the logic of proofs, a logic recently introduced by Artemov [1]. Indeed a detailed proof analysis (...)
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  16.  41
    Mathematical Explanations: An Analysis Via Formal Proofs and Conceptual Complexity.Francesca Poggiolesi - forthcoming - Philosophia Mathematica:nkad023.
    This paper studies internal (or intra-)mathematical explanations, namely those proofs of mathematical theorems that seem to explain the theorem they prove. The goal of the paper is a rigorous analysis of these explanations. This will be done in two steps. First, we will show how to move from informal proofs of mathematical theorems to a formal presentation that involves proof trees, together with a decomposition of their elements; secondly we will show that those mathematical proofs that are regarded as having (...)
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  17.  21
    A Contraction-free and Cut-free Sequent Calculus for Propositional Dynamic Logic.Brian Hill & Francesca Poggiolesi - 2010 - Studia Logica 94 (1):47-72.
    In this paper we present a sequent calculus for propositional dynamic logic built using an enriched version of the tree-hypersequent method and including an infinitary rule for the iteration operator. We prove that this sequent calculus is theoremwise equivalent to the corresponding Hilbert-style system, and that it is contraction-free and cut-free. All results are proved in a purely syntactic way.
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  18.  36
    Grounding rules for (relevant) implication.Francesca Poggiolesi - 2020 - Journal of Applied Non-Classical Logics 31 (1):26-55.
    In Poggiolesi [. Grounding principles for implication. Synthese, 1–28], a definition of the notion of grounding in the background of a relevant framework has been introduced; this...
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  19. Reflecting the semantic features of S5 at the syntactic level.Francesca Poggiolesi - 2010 - In Marcello D'Agostino, Federico Laudisa, Giulio Giorello, Telmo Pievani & Corrado Sinigaglia (eds.), New Essays in Logic and Philosophy of Science. College Publications. pp. 13--25.
     
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  20.  83
    Grounding, Quantifiers, and Paradoxes.Francesco A. Genco, Francesca Poggiolesi & Lorenzo Rossi - 2021 - Journal of Philosophical Logic 50 (6):1417-1448.
    The notion of grounding is usually conceived as an objective and explanatory relation. It connects two relata if one—the ground—determines or explains the other—the consequence. In the contemporary literature on grounding, much effort has been devoted to logically characterize the formal aspects of grounding, but a major hard problem remains: defining suitable grounding principles for universal and existential formulae. Indeed, several grounding principles for quantified formulae have been proposed, but all of them are exposed to paradoxes in some very natural (...)
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  21.  64
    From Single Agent to Multi-Agent via Hypersequents.Francesca Poggiolesi - 2013 - Logica Universalis 7 (2):147-166.
    In this paper we present a sequent calculus for the multi-agent system S5 m . First, we introduce a particularly simple alternative Kripke semantics for the system S5 m . Then, we construct a hypersequent calculus for S5 m that reflects at the syntactic level this alternative interpretation. We prove that this hypersequent calculus is theoremwise equivalent to the Hilbert-style system S5 m , that it is contraction-free and cut-free, and finally that it is decidable. All results are proved in (...)
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  22.  17
    Modal Truths from an Analytic-Synthetic Kantian Distinction.Francesca Poggiolesi - unknown
    In the article of 1965 Are logical truths analytic? Hintikka deals with the problem of establishing whether the logical truths of first-order logic areanalytic or synthetic. In order to provide an answer to this issue, Hintikka firstly distinguishes two different notions of analyticity, and then he showsthat the sentences of first-order logic are analytic in one sense, but synthetic in another. This interesting result clearly illustrates the non-triviality of thequestion. In this paper we aim at answering the question Are modal (...)
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  23.  24
    Towards a generalization of the logic of grounding.Francesca Poggiolesi & Nissim Francez - 2021 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 36 (1):5-24.
    The main goal of this paper is to provide a ground-analysis of two classical connectives that have so far been ignored in the literature, namely the exclusive disjunction, and the ternary disjunction. Such ground-analysis not only serves to extend the applicability of the logic of grounding but also leads to a generalization of Poggiolesi (2016)’s definition of the notion of complete and immediate grounding.
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  24. Analytic logic of proofs.Francesca Poggiolesi & Brian Hill - forthcoming - Annals of Pure and Applied Logic.
     
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  25.  33
    An Analytic Calculus for the Intuitionistic Logic of Proofs.Brian Hill & Francesca Poggiolesi - 2019 - Notre Dame Journal of Formal Logic 60 (3):353-393.
    The goal of this article is to take a step toward the resolution of the problem of finding an analytic sequent calculus for the logic of proofs. For this, we focus on the system Ilp, the intuitionistic version of the logic of proofs. First we present the sequent calculus Gilp that is sound and complete with respect to the system Ilp; we prove that Gilp is cut-free and contraction-free, but it still does not enjoy the subformula property. Then, we enrich (...)
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  26. A New Definition of the Došen's Principle.Francesca Poggiolesi - 2008 - In Michal Peliš (ed.), The Logica Yearbook 2007. Filosofia. pp. 133--142.
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  27.  14
    Are the Validities of Modal Logic Analytic? Or Analyticity Again, through Information, Proof, Modal Logic and Hintikka.Francesca Poggiolesi - 2015 - Philosophia Scientiae 19:221-243.
    Dans la philosophie de Hintikka la notion d'analyticité occupe une place particulière ; plus précisément, le philosophe finnois distingue deux notions d'analyticité : l'une qui est basée sur la notion d'information, l'autre sur la notion de preuve. Alors que ces deux notions ont été largement utilisées pour étudier la logique propositionnelle et la logique du premier ordre, aucun travail n'a été développé pour la logique modale. Cet article se propose de combler cette lacune et ainsi d'examiner l'analyticité des validités de (...)
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  28.  17
    Are the Validities of Modal Logic Analytic? Or Analyticity Again, through Information, Proof, Modal Logic and Hintikka.Francesca Poggiolesi - 2015 - Philosophia Scientiae 19:221-243.
    Dans la philosophie de Hintikka la notion d'analyticité occupe une place particulière (e.g., [Hintikka 1973], [Hintikka 2007]) ; plus précisément, le philosophe finnois distingue deux notions d'analyticité : l'une qui est basée sur la notion d'information, l'autre sur la notion de preuve. Alors que ces deux notions ont été largement utilisées pour étudier la logique propositionnelle et la logique du premier ordre, aucun travail n'a été développé pour la logique modale. Cet article se propose de combler cette lacune et ainsi (...)
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  29.  37
    Common knowledge: finite calculus with syntactic cut-elimination procedure.Francesca Poggiolesi & Brian Hill - 2015 - Logique Et Analyse 58 (230):279-306.
    In this paper we present a finitary sequent calculus for the S5 multi-modal system with common knowledge. The sequent calculus is based on indexed hypersequents which are standard hypersequents refined with indices that serve to show the multi-agent feature of the system S5. The calculus has a non-analytic right introduction rule. We prove that the calculus is contraction- and weakening-free, that (almost all) its logical rules are invertible, and finally that it enjoys a syntactic cut-elimination procedure. Moreover, the use of (...)
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  30.  15
    Dynamic in Logic.Francesca Poggiolesi - unknown
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  31.  13
    Three Different Solutions to the Knower Paradox.Francesca Poggiolesi - 2007 - Annali Del Dipartimento di Filosofia 13:147-164.
    In this paper I shall present three solutions to the Knower Paradox which, despite important points in common, differ in several respects. The first solution, proposed by C. A. Anderson [1] is a hierarchical solution, developed in the framework of first-order arithmetic. However I will try toshow that this solution is based on an incorrect argument. The second solution, inspired by a book of R.M. Smullyan [14], is developed in the framework of modal logic and it is based on the (...)
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  32.  18
    Book review of “Gentzen's Centenary”. [REVIEW]Francesca Poggiolesi - 2017 - History and Philosophy of Logic 38 (3):297-298.
    Gerhard Gentzen, one of the greatest logicians and most brilliant and deep investigators of the nature of proof, would have been 100 years old on 24 November 2009. A conference in Leeds and a works...
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  33.  26
    Can Başkent, Perspectives on Interrogative Models of Inquiry, Springer, 2016. [REVIEW]Francesca Poggiolesi - 2016 - Logic and Logical Philosophy 25 (4):555-560.
    Book Reviews: Can Başkent, Perspectives on Interrogative Models of Inquiry, Logic, Argumentation & Reasoning, Volume 8, Springer, 2016, vii + 197 pages, ISBN: 978-3-319-20761-2, 978-3-319-20762-9. DOI: 10.1007/978-3-319-20762-9.
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  34.  12
    Review of: One Hundred Years of Intuitionism (1907-2007). [REVIEW]Francesca Poggiolesi - unknown
    The book has the simple structure of a tree: the first part, the roots, is dedicated to Brouwer himself, the founding father of Intuitionism; the second part, the trunk, is dedicated to those who influenced, developed and dialogued with Brouwer and his theories; the third part, the branches, is dedicated to the most recent applications and developments of Intuitionism.
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  35.  19
    Review of: Proof Analysis. A contribution to Hilbert's last problem. [REVIEW]Francesca Poggiolesi - unknown
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