1,720,974 research outputs found
A constructive sequence algebra for the calculus of indications
No full textIn this paper, we investigate some aspects of Spencer–Brown’s Calculus of Indications. Drawing from earlier work by Kauffman and Varela, we present a new categorical framework that allows to characterize the construction of infinite arithmetic expressions as sequences taking values in grossone.Fil: Gangle, Rocco. Endicott College. Center for Diagrammatic and Computational Philosophy; Estados UnidosFil: Gianluca, Caterina. Endicott College. Center for Diagrammatic and Computational Philosophy; Estados UnidosFil: Tohmé, Fernando Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentin
A Generic Figures Reconstruction of Peirce’s Existential Graphs (Alpha)
No full textWe present a category-theoretical analysis, based on the concept of generic figures, of a diagrammatic system for propositional logic (Peirce’s Existential Graphs α). The straightforward construction of a presheaf category EGα∗ 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 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.Fil: Gangle, Rocco. Endicott College; Estados UnidosFil: Caterina, Gianluca. Endicott College; Estados UnidosFil: Tohmé, Fernando Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentin
A category theory approach to the semiotics of machine learning
No full textThe successes of Machine Learning, and in particular of Deep Learning systems, have led to a reformulation of the Artificial Intelligence agenda. One of the pressing issues in the field is the extraction of knowledge out of the behavior of those systems. In this paper we propose a semiotic analysis of that behavior, based on the formal model of learners. We analyze the topos-theoretic properties that ensure the logical expressivity of the knowledge embodied by learners. Furthermore, we show that there exists an ideal universal learner, able to interpret the knowledge gained about any possible function as well as about itself, which can be monotonically approximated by networks of increasing size.Fil: Tohmé, Fernando Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: Gangle, Rocco. Endicott College. Center for Diagrammatic and Computational Philosophy; Estados UnidosFil: Caterina, Gianluca. Endicott College. Center for Diagrammatic and Computational Philosophy; Estados Unido
Abduction: A Categorical Characterization
No full textScientific knowledge is gained by the informed (on the basis of theoretic ideas and criteria) examination of data. This can be easily seen in the context of quantitative data, handled with statistical methods. Here we are interested in other forms of data analysis, although with the same goal of extracting meaningful information. The idea is that data should guide the construction of suitable models, which later may lead to the development of new theories. This kind of inference is called abduction and constitutes a central procedure called Peircean qualitative induction. In this paper we will present a category-theoretic representation of abduction based on the notion of adjunction, which highlights the fundamental fact that an abduction is the most efficient way of capturing the information obtained from a large body of evidence.Fil: Tohme, Fernando Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Matemática Bahía Blanca (i); Argentina. Universidad Nacional del Sur; ArgentinaFil: Caterina, Gianluca. Center for Diagrammatic and Computacional Philosophy; Estados UnidosFil: Gangle, Rocco. Center for Diagrammatic and Computacional Philosophy; Estados Unido
The class of states of the world as an -groupoid: identifying states of the world and hierarchies of belief
No full textA natural problem in the methodology of Economics is how to model interactions in which the decisions made by agents depend on the beliefs held about both objective aspects of the relevant situation and the beliefs ascribed to other agents. There are two ways of representing such contexts. One is by means of a hierarchy of beliefs, the other as a state of the world. These two can be seen, from a Systems-theoretical perspective, as representing streams generated by a process and its fixed points, respectively. These two representations are in fact equivalent. The finer question we address here is whether they are identical. Resorting to a type-theoretical syntax, we obtain a unified interpretation in which both entities give rise to ∞-groupoids. Voevodsky´s univalent axiom then ensures their identity in small types universes.Fil: Tohmé, Fernando Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: Gianluca, Caterina,. Endicott College; Estados UnidosFil: Gangle, Rocco. Endicott College; Estados Unido
Local and global optima in decision-making: a sheaf-theoretical analysis of the difference between classical and behavioral approaches
No full textOne of the main differences between the traditional and the behavioral approaches to decision-making is that the latter has not yet been captured in a unifying framework. This hampers in a certain way the whole research program and raises the question of whether this competing approach can provide an encompassing alternative to the classical one. We analyze this issue in light of the problem of reconstructing global choices of an agent up from the solutions found for local problems. We show that a representation based on category theory of the conditions for such reconstruction is general and robust enough to represent both the case in which problems are non-contextual and local as well as that, typical in the literature on behavioral decision-making, in which such properties do not hold. In the first case, we show how a sheaf-theoretical representation provides an abstract characterization of the global solution. In the latter case, we show how locality and contextuality generate obstructions toward the reconstruction of global solutions, yielding a possible clue for the intrinsic difference between behavioral and classical decision theory.Fil: Tohmé, Fernando Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: Gianluca, Caterina. Endicott College; Estados UnidosFil: Gangle, Rocco. Endicott College; Estados Unido
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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