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171
Spider diagrams
"... The use of diagrams in mathematics has traditionally been restricted to guiding intuition and communication. With rare exceptions such as Peirce’s α and β systems, purely diagrammatic formal reasoning has not been in the mathematicians or logicians toolkit. This paper develops a purely diagrammatic ..."
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Cited by 79 (32 self)
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The use of diagrams in mathematics has traditionally been restricted to guiding intuition and communication. With rare exceptions such as Peirce’s α and β systems, purely diagrammatic formal reasoning has not been in the mathematicians or logicians toolkit. This paper develops a purely diagrammatic reasoning system of ‘spider diagrams ’ that builds on Euler, Venn and Peirce diagrams. The system is known to be expressively equivalent to first order monadic logic with equality. We develop two levels of diagrammatic syntax: an ‘abstract ’ syntax that captures the structure of diagrams and a ‘concrete’ syntax that captures topological properties of drawn diagrams. A number of simple diagrammatic transformation rules are given and the resulting reasoning system is shown to be sound and complete. 1
Generating euler diagrams
 In Proceedings of Diagrams 2002
, 2002
"... Abstract. This article describes an algorithm for the automated generation of any Euler diagram starting with an abstract description of the diagram. An automated generation mechanism for Euler diagrams forms the foundations of a generation algorithm for notations such as Harel’s higraphs, constrain ..."
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Cited by 58 (22 self)
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Abstract. This article describes an algorithm for the automated generation of any Euler diagram starting with an abstract description of the diagram. An automated generation mechanism for Euler diagrams forms the foundations of a generation algorithm for notations such as Harel’s higraphs, constraint diagrams and some of the UML notation. An algorithm to generate diagrams is an essential component of a diagram tool for users to generate, edit and reason with diagrams. The work makes use of properties of the dual graph of an abstract diagram to identify which abstract diagrams are “drawable ” within given wellformedness rules on concrete diagrams. A Java program has been written to implement the algorithm and sample output is included. 1 Introduction and
Termination analysis for functional programs using term orderings
 IN PROCEEDINGS OF THE SECOND INTERNATIONAL STATIC ANALYSIS SYMPOSIUM, LNCS 983
, 1995
"... To prove the termination of a functional program there has to be a wellfounded ordering such that the arguments in each recursive call are smaller than the corresponding inputs. In this paper we present a procedure for automated termination proofs of functional programs. In contrast to previously p ..."
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Cited by 31 (12 self)
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To prove the termination of a functional program there has to be a wellfounded ordering such that the arguments in each recursive call are smaller than the corresponding inputs. In this paper we present a procedure for automated termination proofs of functional programs. In contrast to previously presented methods a suited wellfounded ordering does not have to be fixed in advance by the user, but can be synthesized automatically. For that purpose we use approaches developed in the area of term rewriting systems for the automated generation of suited wellfounded term orderings. But unfortunately term orderings cannot be directly used for termination proofs of functional programs which call other algorithms in the arguments of their recursive calls. The reason is that while for the termination of term rewriting systems orderings between terms are needed, for functional programs we need orderings between objects of algebraic data types. Our method solves this problem and enables term orderings to be used for termination proofs of functional programs.
A constraint diagram reasoning system
 Proc. Distributed Multimedia Systems, International Conference on Visual Languages and Computing (VLC '03
, 2003
"... Abstract — The Unified Modeling Language (UML) is a collection of notations which are mainly diagrammatic. These notations are used by software engineers in the process of object oriented modelling. The only textual notation in the UML is the Object Constraint Language (OCL). The OCL is used to expr ..."
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Cited by 30 (20 self)
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Abstract — The Unified Modeling Language (UML) is a collection of notations which are mainly diagrammatic. These notations are used by software engineers in the process of object oriented modelling. The only textual notation in the UML is the Object Constraint Language (OCL). The OCL is used to express logical constraints such as system invariants. Constraint diagrams are designed to provide a diagrammatic alternative to the OCL. Since constraint diagrams are visual they complement existing notations in the UML. Spider diagrams form the basis of constraint diagrams and sound and complete reasoning systems have been developed. Spider diagrams allow subset relations between sets and cardinality constraints on sets to be expressed. In addition to this, constraint diagrams allow universal quantification and relational navigation and hence are vastly more expressive. In this paper we present the first constraint diagram reasoning system. We give syntax and semantics for constraint diagrams we call CD1 diagrams. We identify syntactic criteria that allow us to determine whether a CD1 diagram is satisfiable. We give descriptions of a set of sound and complete reasoning rules for CD1 diagrams. I.
Conceptual Knowledge Discovery and Data Analysis
, 2000
"... . In this paper, we discuss Conceptual Knowledge Discovery in Databases (CKDD) in its connection with Data Analysis. Our approach is based on Formal Concept Analysis, a mathematical theory which has been developed and proven useful during the last 20 years. Formal Concept Analysis has led to a t ..."
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Cited by 26 (11 self)
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. In this paper, we discuss Conceptual Knowledge Discovery in Databases (CKDD) in its connection with Data Analysis. Our approach is based on Formal Concept Analysis, a mathematical theory which has been developed and proven useful during the last 20 years. Formal Concept Analysis has led to a theory of conceptual information systems which has been applied by using the management system TOSCANA in a wide range of domains. In this paper, we use such an application in database marketing to demonstrate how methods and procedures of CKDD can be applied in Data Analysis. In particular, we show the interplay and integration of data mining and data analysis techniques based on Formal Concept Analysis. The main concern of this paper is to explain how the transition from data to knowledge can be supported by a TOSCANA system. To clarify the transition steps we discuss their correspondence to the five levels of knowledge representation established by R. Brachman and to the steps of...
An observational study of how objects support engineering design thinking and communication: implications for the design of tangible media
 In Proceedings of CHI 2000
, 2000
"... There has been an increasing interest in objects within the HCI field particularly with a view to designing tangible interfaces. However, little is known about how people make sense of objects and how objects support thinking. This paper presents a study of groups of engineers using physical objects ..."
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Cited by 24 (0 self)
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There has been an increasing interest in objects within the HCI field particularly with a view to designing tangible interfaces. However, little is known about how people make sense of objects and how objects support thinking. This paper presents a study of groups of engineers using physical objects to prototype designs, and articulates the roles that physical objects play in supporting their design thinking and communications. The study finds that design thinking is heavily dependent upon physical objects, that designers are active and opportunistic in seeking out physical props and that the interpretation and use of an object depends heavily on the activity. The paper discusses the tradeoffs that designers make between speed and accuracy of models, and specificity and generality in choice of representations. Implications for design of tangible interfaces are discussed.
Bayesian generic priors for causal learning
 Psychological Review
, 2008
"... The article presents a Bayesian model of causal learning that incorporates generic priors—systematic assumptions about abstract properties of a system of cause–effect relations. The proposed generic priors for causal learning favor sparse and strong (SS) causes—causes that are few in number and high ..."
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Cited by 21 (0 self)
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The article presents a Bayesian model of causal learning that incorporates generic priors—systematic assumptions about abstract properties of a system of cause–effect relations. The proposed generic priors for causal learning favor sparse and strong (SS) causes—causes that are few in number and high in their individual powers to produce or prevent effects. The SS power model couples these generic priors with a causal generating function based on the assumption that unobservable causal influences on an effect operate independently (P. W. Cheng, 1997). The authors tested this and other Bayesian models, as well as leading nonnormative models, by fitting multiple data sets in which several parameters were varied parametrically across multiple types of judgments. The SS power model accounted for data concerning judgments of both causal strength and causal structure (whether a causal link exists). The model explains why human judgments of causal structure (relative to a Bayesian model lacking these generic priors) are influenced more by causal power and the base rate of the effect and less by sample size. Broader implications of the Bayesian framework for human learning are discussed.
Parts of recognition
 Cognition
, 1984
"... We propose that, for the task of object recognition, the visual system decomposes shapes into parts, that it does so using a rule defining part boundaries rather than part shapes, that the rule exploits a uniformity of naturetransversal@, and that parts with their descriptions and spatial relatio ..."
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Cited by 18 (0 self)
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We propose that, for the task of object recognition, the visual system decomposes shapes into parts, that it does so using a rule defining part boundaries rather than part shapes, that the rule exploits a uniformity of naturetransversal@, and that parts with their descriptions and spatial relations provide a first index into a memory of shapes. This rule allows an explanation of several visual illusions. We stress the role inductive inference in our theory and conclude with a p&is of unsolved problems. 1.
On the Completeness and Expressiveness of Spider Diagram Systems
 PROC. DIAGRAMS 2000, EDINBURGH, SEPT 2000. LNAI 1889
, 2000
"... Spider diagram systems provide a visual language that extends the popular and intuitive Venn diagrams and Euler circles. Designed to complement objectoriented modelling notations in the specification of large software systems they can be used to reason diagrammatically about sets, their cardinalit ..."
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Cited by 17 (7 self)
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Spider diagram systems provide a visual language that extends the popular and intuitive Venn diagrams and Euler circles. Designed to complement objectoriented modelling notations in the specification of large software systems they can be used to reason diagrammatically about sets, their cardinalities and their relationships with other sets. A set of reasoning rules for a spider diagram system is shown to be sound and complete. We discuss the extension of this result to diagrammatically richer notations and also consider their expressiveness. Finally, we show that for a rich enough system we can diagrammatically express the negation of any diagram.
Characteristica Universalis
 Language, Truth and Ontology
, 1990
"... iments made upon diagrams. The latter are 'questions put to the [48] Nature of the relations concerned'  precisely in virtue of the fact that we are here experimenting with diagrams which are to enjoy the property that the forms of relations exemplified in reality will be the very same as ..."
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Cited by 16 (10 self)
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iments made upon diagrams. The latter are 'questions put to the [48] Nature of the relations concerned'  precisely in virtue of the fact that we are here experimenting with diagrams which are to enjoy the property that the forms of relations exemplified in reality will be the very same as the forms of relations in the diagrams themselves. A similar idea is of course present also in Wittgenstein. As the Tractatus has it: 'What constitutes a picture is that its elements are related to one another in a determinate way.' (2.41 ) Indeed:' There must be something identical in a picture and what it depicts, to enable the one to be a picture of the other at all.' (2.16) Wittgenstein's 'pictorial form', then, is Peirce's 'form of a relation', and our task here will be one of taking further the idea of a universal characteristic which both philosophers shared. 2. From Leibniz to Frege The project of such a characteristic had of course been envisaged by Leibniz, and the idea is present already