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} (...) \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal {E}}}{{\mathcal {G}}}_\alpha $$\end{document} 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 formal investigation of relations between syntax and semantics in such diagrammatic systems. (shrink)

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 (...) by any state in the epistemic structure, if the class of types is complete and the types are continuous. In this paper we analyze the problem in a different framework. We redefine the notion of type as well as the epistemic notion of assumption. These new definitions are sufficient for the characterization of iterated admissibility as the class of strategies that indeed satisfy \. One of the key methodological innovations in our approach involves defining a new notion of generic types and employing these in conjunction with Cohen’s technique of forcing. (shrink)

What role does language play in the process of building worldviews? To address this question, in the first section of this paper we will clarify what we mean by worldviews and how they differ, in our perspective, from cosmovisions. In a nutshell, we define worldviews as the biological interpretations agents create of the world around them and cosmovision the more general cultural-based reflections on it. After presenting our definition for worldview, we will also present the multi-shaped viewpoint that frames our (...) analysis, adopting three concepts that can help us explain how agents construct and develop their worldviews: saliences, pregnances, and abduction. While the notions of saliences and pregnances will explain how agents recognize anomalies in their worldview, the concept of abduction will help us discuss how they can learn to approach, explain, and use these anomalies to get new skills and abilities. This other point will lead us to discuss the role of language in this process, which will be describe as an artifact that permits the agent to use abduction to “normalize” and exploit anomalies, being now the ultimate artifact to build, develop, and update their worldviews. (shrink)

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 (...) formal investigation of relations between syntax and semantics in such diagrammatic systems. (shrink)

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 (...) formal investigation of relations between syntax and semantics in such diagrammatic systems. (shrink)