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  1.  66
    Iconicity and Abduction.Rocco Gangle & Gianluca Caterina - 2016 - New York, USA: Springer. Edited by Rocco Gangle.
    This book consolidates and extends the authors’ work on the connection between iconicity and abductive inference. It emphasizes a pragmatic, experimental and fallibilist view of knowledge without sacrificing formal rigor. Within this context, the book focuses particularly on scientific knowledge and its prevalent use of mathematics. To find an answer to the question “What kind of experimental activity is the scientific employment of mathematics?” the book addresses the problems involved in formalizing abductive cognition. For this, it implements the concept and (...)
  2.  17
    A Generic Figures Reconstruction of Peirce’s Existential Graphs (Alpha).Fernando Tohme, Gianluca Caterina & Rocco Gangle - 2020 - Erkenntnis 87 (2):623-656.
    We present a category-theoretical analysis, based on the concept of generic figures, of a diagrammatic system for propositional logic (Peirce’s Existential Graphs α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}). The straightforward construction of a presheaf category EGα∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal {E}}}{{\mathcal {G}}}_{\alpha ^{*}}$$\end{document} of cuts-only Existential Graphs (equivalent to the well-studied category of finite forests) provides a basis for the further construction of the category EGα\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} (...)
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  3.  57
    The sheet of indication: a diagrammatic semantics for Peirce’s EG-alpha.Gianluca Caterina & Rocco Gangle - 2015 - Synthese 192 (4):923-940.
    Following the guiding thread of Peirce’s use of diagrammatic syntax in his system of existential graphs , which depends crucially on the role of the Sheet of Assertion, we introduce the notion of Sheet of Indication as the basis for a general diagrammatic semantics applicable to a wide range of diagrams. We then show how Peirce’s EG-alpha graphs may be understood as instances of SIs and how logically coherent models of the graphs are represented in the SI semantics.
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  4.  45
    Abduction: A categorical characterization.Fernando Tohmé, Gianluca Caterina & Rocco Gangle - 2015 - Journal of Applied Logic 13 (1):78-90.
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  5.  37
    Advances in Peircean Mathematics: The Colombian School ed. by Fernando Zalamea (review).Gianluca Caterina - 2024 - Transactions of the Charles S. Peirce Society 59 (3):373-376.
    In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Advances in Peircean Mathematics: The Colombian School ed. by Fernando ZalameaGianluca CaterinaFernando Zalamea (Ed.) Advances in Peircean Mathematics: The Colombian School Berlin, Boston: De Gruyter, 2022. 212 pp. (incl. index).The volume Advances in Peircean Mathematics is an important, very much needed contribution towards a deeper understanding of the impact of Peirce's work especially in the fields of mathematics, logic, and semiotic. It fills a gap in the current (...)
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  6.  48
    Consequences of a Diagrammatic Representation of Paul Cohen's Forcing Technique Based on CS Peirce's Existential Graphs.Gianluca Caterina & Rocco Gangle - 2010 - In W. Carnielli L. Magnani (ed.), Model-Based Reasoning in Science and Technology. pp. 429--443.
  7.  28
    Native diagrammatic soundness and completeness proofs for Peirce’s Existential Graphs (Alpha).Fernando Tohmé, Rocco Gangle & Gianluca Caterina - 2022 - Synthese 200 (6).
    Peirce’s diagrammatic system of Existential Graphs (EGα)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$EG_{\alpha })$$\end{document} is a logical proof system corresponding to the Propositional Calculus (PL). Most known proofs of soundness and completeness for EGα\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$EG_{\alpha }$$\end{document} depend upon a translation of Peirce’s diagrammatic syntax into that of a suitable Frege-style system. In this paper, drawing upon standard results but using the native diagrammatic notational framework of the graphs, we present (...)
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  8.  28
    A Generic Figures Reconstruction of Peirce’s Existential Graphs.Rocco Gangle, Gianluca Caterina & Fernando Tohme - 2020 - Erkenntnis 87 (2):623-656.
    We present a category-theoretical analysis, based on the concept of generic figures, of a diagrammatic system for propositional logic ). The straightforward construction of a presheaf category \ of cuts-only Existential Graphs provides a basis for the further construction of the category \ which introduces variables in a reconstructedly generic, or label-free, mode. Morphisms in these categories represent syntactical embeddings or, equivalently but dually, extensions. Through the example of Peirce’s system, it is shown how the generic figures approach facilitates the (...)
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  9.  27
    Abductive Spaces: Modeling Concept Framework Revision with Category Theory.Rocco Gangle, Gianluca Caterina & Fernando Tohmé - 2021 - In John R. Shook & Sami Paavola (eds.), Abduction in Cognition and Action: Logical Reasoning, Scientific Inquiry, and Social Practice. Springer Verlag. pp. 49-73.
    A formal model of abductive inference is provided in which abduction is conceived as expansive and contractive movements through a topological space of theoretical and practical commitments. A pair of presheaves over the space of commitments corresponds to communities sharing commitments on the one hand and possible obstructions to commitments on the other. In this framework, abductive inference is modeled by the dynamics of redistributed communities of commitment made in response to obstructive encounters. This semantic-pragmatic model shows how elementary category (...)
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  10. Abductive Realism in Topos Theory.Rocco Gangle & Gianluca Caterina - 2016 - In Rocco Gangle & Gianluca Caterina (eds.), Iconicity and Abduction. New York, USA: Springer.
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  11. Categorical Iconicity in Peirce’s Existential Graphs.Rocco Gangle & Gianluca Caterina - 2016 - In Rocco Gangle & Gianluca Caterina (eds.), Iconicity and Abduction. New York, USA: Springer.
     
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  12. Modeling Abductive Reasoning.Rocco Gangle & Gianluca Caterina - 2016 - In Rocco Gangle & Gianluca Caterina (eds.), Iconicity and Abduction. New York, USA: Springer.
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  13. Ontology and Abduction in Badiou’s Being and Event.Rocco Gangle & Gianluca Caterina - 2016 - In Rocco Gangle & Gianluca Caterina (eds.), Iconicity and Abduction. New York, USA: Springer.
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  14. Phenomenology and Iconicity in Badiou’s Logics of Worlds.Rocco Gangle & Gianluca Caterina - 2016 - In Rocco Gangle & Gianluca Caterina (eds.), Iconicity and Abduction. New York, USA: Springer.
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  15.  32
    Iterated Admissibility Through Forcing in Strategic Belief Models.Fernando Tohmé, Gianluca Caterina & Jonathan Gangle - 2020 - Journal of Logic, Language and Information 29 (4):491-509.
    Iterated admissibility embodies a minimal criterion of rationality in interactions. The epistemic characterization of this solution has been actively investigated in recent times: it has been shown that strategies surviving \ rounds of iterated admissibility may be identified as those that are obtained under a condition called rationality and m assumption of rationality in complete lexicographic type structures. On the other hand, it has been shown that its limit condition, with an infinity assumption of rationality ), might not be satisfied (...)
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  16. The Logic of Picturing: Wittgenstein, Sellars and Peirce’s EG-beta.Fernando Tohmé, Gianluca Caterina & Rocco Gangle - 2019 - In Matthieu Fontaine, Cristina Barés-Gómez, Francisco Salguero-Lamillar, Lorenzo Magnani & Ángel Nepomuceno-Fernández (eds.), Model-Based Reasoning in Science and Technology: Inferential Models for Logic, Language, Cognition and Computation. Springer Verlag.
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