Diagrams, Iconicity, and Abductive Discovery

Peer reviewe

Explicaciones Geométrico-Diagramáticas en Física desde una Perspectiva Inferencial

El primer objetivo de este artículo es mostrar que explicaciones genuinamente geométricas/matemáticas e intrínsecamente diagramáticas de fenómenos físicos no solo son posibles en la práctica científica, sino que además comportan un potencial epistémico que sus contrapartes simbólico-verbales carecen. Como ejemplo representativo utilizaremos la metodología geométrica de John Wheeler (1963) para calcular cantidades físicas en una reacción nuclear. Como segundo objetivo pretendemos analizar, desde un marco inferencial, la garantía epistémica de este tipo de explicaciones en términos de dependencia sintáctica y semántica del contenido lo inferido en las premisas, lo cual denominaremos criterio de validez inferencial (CVI)

Les figures lul·lianes: la seva naturalesa i la seva funció com a raonament diagramàtic

Aquest article analitza les figures de l’Art lul·liana i la seva interpretació a partir de models matemàtics. Es clarifiquen alguns aspectes de l’ús de la teoria dels grafs, que en aquest cas s’amplia a la dels hipergrafs i els reticles, aquests darrers relacionats amb la Figura Elemental. En canvi, no s’aborda ni el cas dels arbres ni el de les figures del Llibre de contemplació, que seran objecte de treballs posteriors. Finalment, les figures de l’Art es presenten com un exemple del que, en la moderna ciència, la tecnologia o l’administració d’empreses, s’anomena raonament diagramàtic.This article discusses the figures of Llull’s Art and their interpretation in the light of mathematical models. Some points are cleared up concerning the use of graph theory, which is now also extended into that of hipergraphs and lattices, this last in connection with the Elemental Figure. Trees and the figures of the Book of Contemplation are not included, since they will be treated in forthcoming articles. Finally, the figures of the Art are presented as an example of what in modern science, technology and business administration is called diagrammatic reasoning

La visualización en la astrofísica como aproximación a la innovación teórica

En este trabajo se desarrolla la investigación para la implementación de una interfaz-interactiva; teniendo como base teórica el razonamiento cualitativo. Para lograrlo, se utilizan técnicas de diseño y visualización de la información, así como ingeniería de software. Lo anterior se realiza con el propósito de demostrar la diferencia entre brillo aparente vs real (caso de estudio). El razonamiento cualitativo fue propuesto por el Dr. Kenneth D. Forbus en 1996, éste hace énfasis en el razonamiento causal puesto que representa una característica del humano para analizar los fenómenos físicos; lo cual permite comprender sus implicaciones al relacionarlas con las variables asociadas al: espacio, tiempo y cantidad. A su vez, el razonamiento causal puede ser utilizado como herramienta para visualizar fenómenos científicos. Con el fin de otorgar el crédito a la hipótesis del comportamiento observado o postulado. Por lo que es una herramienta idónea para generar: explicaciones, mediciones, interpretaciones, planificación de experimentos y por extensión, la comprensión y el aprendizaje. El caso de estudio implica la simulación de un proceso físico basado en su ecuación matemática (de tercer grado de libertad). Aquí es donde se encuentra la aportación al campo de la visualización con la apertura de un punto de intersección, entre el diseño de interfaces interactivas y la simulación por computadora de procesos físicos. La ecuación del fenómeno relaciona el orden de magnitud de brillantez con la distancia de las estrellas. Uno de los objetivos de este trabajo es: generar conocimiento que permita explorar nuestras capacidades de percepción visual. Lo anterior implica que se requiera de representación y presentación de datos o conceptos comúnmente abstractos o complejos en información.Coordinación de Posgrado de Ciencias y Artes para el Diseño

Cognitive Conditions of Diagrammatic Reasoning

Forthcoming in Semiotica (ISSN: 0037-1998), published by Walter de Gruyter & Co.In the first part of this paper, I delineate Peirce's general concept of diagrammatic reasoning from other usages of the term that focus either on diagrammatic systems as developed in logic and AI or on reasoning with mental models. The main function of Peirce's form of diagrammatic reasoning is to facilitate individual or social thinking processes in situations that are too complex to be coped with exclusively by internal cognitive means. I provide a diagrammatic definition of diagrammatic reasoning that emphasizes the construction of, and experimentation with, external representations based on the rules and conventions of a chosen representation system. The second part starts with a summary of empirical research regarding cognitive effects of working with diagrams and a critique of approaches that use 'mental models' to explain those effects. The main focus of this section is, however, to elaborate the idea that diagrammatic reasoning should be conceptualized as a case of 'distributed cognition.' Using the mathematics lesson described by Plato in his Meno, I analyze those cognitive conditions of diagrammatic reasoning that are relevant in this case

Representando o processo criativo da prova nos Grafos Existenciais

Os Grafos Existenciais (GEs) de Charles S. Peirce são reconhecidos como o primeiro sistema lógico heterogêneo completo e correto equivalente à lógica predicativa de primeira ordem. Por sistema lógico heterogêneo entende-se aquele que combina uma sintaxe sentencial e diagramática. Neste artigo propomos a tese de que sistemas formais heterogêneos podem ser mais eficientes na investigação de estratégias de derivação e análise de hipóteses na prova, em razão dos elementos visuais presentes na linguagem diagramática. Como método de estudo sugere-se uma comparação do cálculo de dedução natural como os sistemas Alfa e Beta dos GEs, para a demonstração de alguns teoremas da lógica proposicional e de predicados. Justificamos a escolha em razão de ambos os métodos serem similares na composição de regras de inferências e nos propósitos por parte de seus autores (Peirce e Gentzen). Abstract The Charles S. Peirce's Existential Graphs (EGs) are recognized as the first complete and sound heterogeneous logical system equivalent to first order predicate logic. By heterogeneous logical system we mean one which combines a sentential and diagrammatical syntax. I propose in this paper the thesis that heterogeneous formal systems can be more effective inquiring strategies of derivation and in the analysis of assumptions in proofs, because of the visual aspects present in the diagrammatical language. As a method of study I suggest the comparison between the natural deduction calculus and the Alpha and Beta's systems of the EGs for demonstration of some theorems in the propositional and predicate logic. This choice is justified by the similarities found in the composition of rules of inference and purpose of the authors (Peirce and Gentzen) in both methods.Recebido em novembro de 2014 Aprovado em março de 201

Formalizing graphical notations

The thesis describes research into graphical notations for software engineering, with a principal interest in ways of formalizing them. The research seeks to provide a theoretical basis that will help in designing both notations and the software tools that process them. The work starts from a survey of literature on notation, followed by a review of techniques for formal description and for computational handling of notations. The survey concentrates on collecting views of the benefits and the problems attending notation use in software development; the review covers picture description languages, grammars and tools such as generic editors and visual programming environments. The main problem of notation is found to be a lack of any coherent, rigorous description methods. The current approaches to this problem are analysed as lacking in consensus on syntax specification and also lacking a clear focus on a defined concept of notated expression. To address these deficiencies, the thesis embarks upon an exploration of serniotic, linguistic and logical theory; this culminates in a proposed formalization of serniosis in notations, using categorial model theory as a mathematical foundation. An argument about the structure of sign systems leads to an analysis of notation into a layered system of tractable theories, spanning the gap between expressive pictorial medium and subject domain. This notion of 'tectonic' theory aims to treat both diagrams and formulae together. The research gives details of how syntactic structure can be sketched in a mathematical sense, with examples applying to software development diagrams, offering a new solution to the problem of notation specification. Based on these methods, the thesis discusses directions for resolving the harder problems of supporting notation design, processing and computer-aided generic editing. A number of future research areas are thereby opened up. For practical trial of the ideas, the work proceeds to the development and partial implementation of a system to aid the design of notations and editors. Finally the thesis is evaluated as a contribution to theory in an area which has not attracted a standard approach

The Structure of Analog Representation

This paper develops a theory of analog representation. We first argue that the mark of the analog is to be found in the nature of a representational system’s interpretation function, rather than in its vehicles or contents alone. We then develop the rulebound structure theory of analog representation, according to which analog systems are those that use interpretive rules to map syntactic structural features onto semantic structural features. The theory involves three degree-theoretic measures that capture three independent ways in which a system can be more or less analog. We explain how our theory improves upon prior accounts of analog representation, provides plausible diagnoses for novel challenge cases, extends to hybrid systems that are partially analog and partially symbolic, and accounts for some of the advantages and disadvantages of representing analogically versus symbolically