Catálogo de publicaciones - libros

In her book “The Iconic Logic of Peirce’s Graphs”, S. J. Shin elaborates the diagrammatic logic of Peirce’s Existential Graphs. Particularly, she provides translations from Existential Graphs to first order logic. Unfortunately, her translation is not in all cases correct. In this paper, the translation is fixed by means of so-called single object ligatures .

In a study of crew interaction with the automatic flight control system of the Boeing 757/767 aircraft, we observed 60 flights and recorded every change in the aircraft control modes, as well as every observable change in the operational environment. To quantify the relationships between the state of the operating environment and pilots’ actions and responses, we used canonical correlation because of its unique suitability for finding multiple patterns in large datasets. Traditionally, the results of canonical correlation analysis are presented by means of numerical tables, which are not conducive to recognizing multidimensional patterns in the data. We created a sun-ray-like diagram (which we call a heliograph) to present the multiple patterns that exist in the data by employing Alexander’s theory of centers.  The theory describes 15 heuristic properties that help create wholeness in a design, and can be extended to the problem of information abstraction and integration as well as packing of large amounts of data for visualization.

Propositional Statecharts, described in [3], are a variation of David Harel’s Statechart formalism [6] intended to enable both diagrammatic description of an agent interaction protocol, and interpretation as a theory in a dynamic logic. Here we provide an informal description of a diagrammatic extension to enable modular representation.

There is undoubtedly something like a ‘grammar of graphics’. Various syntactic principles can be identified in graphics of different types, and the nature of visual representation allows for visual nesting and recursion. We propose a limited set of possible ‘building blocks’ for constructing graphic spaces , and a limited set of possible syntactic functions of graphic objects . Based on these ingredients, and the rules for their combination, the syntactic structure of any visual representation can be drawn as a hierarchically nested tree . We claim that the presented visual syntax applies to all types of visual representations.

Many diagrammatic languages are based on closed curves, and various wellformedness conditions are often enforced (such as the curves are simple ). We use the term Euler diagram in a very general sense, to mean any .nite collection of closed curves which express information about intersection, containment or disjointness. Euler diagrams have many applications, including the visualization of statistical data [1], displaying the results of database queries [6] and logical reasoning [2, 4, 5]. Three important questions are: for any given piece of information can we draw a diagram representing that information, can we reliably interpret the diagrams and can we reason diagrammatically about that information? The desirable answer to all three questions is yes, but these desires can be con.icting. In this article we investigate the e.ects of enforcing the simplicity condition (as in [1, 2, 6]) or not enforcing it (as in [4, 5]).

Illustrating a dynamic process with an arrow-containing diagram is a widespread convention in people’s daily communications. In order to build a basis for capturing the structure and semantics of such diagrams, this paper formalizes the topological relations between two arrow symbols and discusses the influence of these topological relations on the diagram’s semantics. Topological relations of arrow symbols are established by two types of links, intersections and common references , which are further categorized into nine types based on the combination of the linked parts. The topological relations are captured by the existence/non-existence of these nine types of intersections and common references. Then, this paper demonstrates that arrow symbols with different types of intersections typically illustrate two actions with different interrelations, whereas the arrow symbols with common references illustrate a pair of semantics that may be mutually exclusive or synchronized.

This extended abstract describes a forthcoming book which should be of interest to those attending the Diagrams 2006 conference and to others generally interested in diagrammatic reasoning in the context of Euclidean Geometry. The book, Euclid and His Twentieth Century Rivals: Diagrams in the Logic of Euclidean Geometry , is still in preparation, but will be published by CSLI press once it is completed.

Drawings of water are the earliest, least abstract forms of flow diagram. Representations of ideal or generalised sequences for manufacturing or actual paths for materials between machines came next. Subsequently documentation of production and information flow become subjects for graphical representation. A similar level of abstraction was necessary for representations of invisible flows such as electricity. After initial use to define control, flow diagrams became a general purpose tool for planning automated computation at all levels of composition. Proliferation of syntax variants and the need for a common language for documentation were the motivations behind standardisation efforts. Public communication of metalevel systems information superseded private comprehension of detailed algorithmic processes as a primary function. Changes to programming language structures and their associated processes caused the initial demise of flow diagrams in software engineering.

In this paper we present a way of reasoning by interval-values over [0,1]. Logical inference is visualized by interval-values. Boolean operators are extended to these values in a natural way. Some other useful operators are also defined. The way of reasoning by Euler/Venn diagrams works by interval-values as well. Moreover based on the length of the intervals probabilistic and fuzzy reasoning is possible.

Recent times have seen various formal diagrammatic logics and reasoning systems emerging [1, 4, 5, 7]. Many of these logics are based on the popular and intuitive Euler diagrams; see [6] for an overview. The diagrams in figure 1 are all based on Euler diagrams and are examples of unitary diagrams. Compound diagrams are formed by joining unitary diagrams using connectives such as ‘or’. We generalize the syntax of spider diagrams (of which d _3 in figure 1 is an example), increasing the expressiveness of the unitary system. These generalizations give rise to a more natural way of expressing some statements because there is an explicit mapping from the statement to a generalized diagram. Our theoretical motivation is to provide the necessary underpinning required to develop efficient automated theorem proving techniques: developing such techniques for compound systems is challenging and enhancing the expressiveness of unitary diagrams will enable more theorems to be proved efficiently.