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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 18 (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.
A Survey of Reasoning Systems Based on Euler Diagrams
 EULER DIAGRAMS 2004 PRELIMINARY VERSION
, 2004
"... Euler diagrams have been used for centuries as a means for conveying ideas in an intuitive, informal way. Recently much research has been conducted to develop formal, diagrammatic reasoning systems based on Euler diagrams. Most of these systems extend Euler diagrams by adding further syntax to incre ..."
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Cited by 15 (2 self)
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Euler diagrams have been used for centuries as a means for conveying ideas in an intuitive, informal way. Recently much research has been conducted to develop formal, diagrammatic reasoning systems based on Euler diagrams. Most of these systems extend Euler diagrams by adding further syntax to increase expressiveness. In this paper we survey such systems and draw comparisons between them. Key words: Visual Logic, Diagrammatic Reasoning.
Reasoning with Constraint Diagrams
 School of Computing, Mathematical and Information Sciences
, 2004
"... Constraint diagrams are designed for the formal specification of software systems. However, their applications are broader than this since constraint diagrams are a logic that can be used in any formal setting. This document summarizes the main results presented in my PhD thesis, the focus of which ..."
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Cited by 14 (3 self)
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Constraint diagrams are designed for the formal specification of software systems. However, their applications are broader than this since constraint diagrams are a logic that can be used in any formal setting. This document summarizes the main results presented in my PhD thesis, the focus of which is on a fragment of the constraint diagram language, called spider diagrams, and constraint diagrams themselves. In the thesis, sound and complete systems of spider diagrams and constraint diagrams are presented and the expressiveness of the spider diagram language is established. 1
Visualising and specifying ontologies using diagrammatic logics
 In 5th Australasian Ontologies Workshop
, 2009
"... This paper proposes a diagrammatic logic that is suitable for specifying ontologies. We take a case study style approach to presenting the diagrammatic logic, and draw contrast with RDF graphs and description logics. We provide specifications of two ontologies and show how to depict instances. Diagr ..."
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Cited by 10 (9 self)
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This paper proposes a diagrammatic logic that is suitable for specifying ontologies. We take a case study style approach to presenting the diagrammatic logic, and draw contrast with RDF graphs and description logics. We provide specifications of two ontologies and show how to depict instances. Diagrammatic reasoning is used to show that an instance conforms to a specification. We also include examples to show how diagrammatic rules can be used to (a) constrain ontology specifications and (b) define mappings between ontologies. The framework also allows the specification of queries. The positive features of the diagrammatic logic are discussed, supporting a claim that the new logic is intuitive and appropriate for ontology specification. Finally, we discuss the possibilities for developing tools to support the use of the diagrammatic logic, including automated diagram drawing and reasoning procedures. 1
Heterogeneous proofs: Spider diagrams meet higherorder provers
 In ITP, volume 6898 of LNCS
, 2011
"... Abstract. We present an interactive heterogeneous theorem proving framework, which performs formal reasoning by arbitrarily mixing diagrammatic and sentential proof steps. We use Isabelle to enable formal reasoning with either traditional sentences or spider diagrams. We provide a mechanisation of t ..."
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Abstract. We present an interactive heterogeneous theorem proving framework, which performs formal reasoning by arbitrarily mixing diagrammatic and sentential proof steps. We use Isabelle to enable formal reasoning with either traditional sentences or spider diagrams. We provide a mechanisation of the theory of abstract spider diagrams and establish a formal link between diagrammatic concepts and the existing theories in Isabelle/HOL. 1
The expressiveness and completeness of spider diagrams augmented with constants. Submitted to Formal Aspects of Computing
, 2004
"... Abstract Diagrammatic reasoning can be described formally by a number of diagrammatic logics; spider diagrams are one of these, and are used for expressing logical statements about set membership and containment. Here, existing work on spider diagrams is extended to include constant spiders that r ..."
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Abstract Diagrammatic reasoning can be described formally by a number of diagrammatic logics; spider diagrams are one of these, and are used for expressing logical statements about set membership and containment. Here, existing work on spider diagrams is extended to include constant spiders that represent specific individuals. We give a formal syntax and semantics for the extended diagram language before introducing a collection of reasoning rules encapsulating logical equivalence and logical consequence. We prove that the resulting logic is sound, complete and decidable.
Euler Diagrambased Notations
"... Abstract. Euler diagrams have been used for centuries as a means for conveying logical statements in a simple, intuitive way. They form the basis of many diagrammatic notations used to represent settheoretic relationships in a wide range of contexts including software modelling, logical reasoning s ..."
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Abstract. Euler diagrams have been used for centuries as a means for conveying logical statements in a simple, intuitive way. They form the basis of many diagrammatic notations used to represent settheoretic relationships in a wide range of contexts including software modelling, logical reasoning systems, statistical data representation, database search queries and file system management. In this paper we survey notations based on Euler diagrams with particular emphasis on formalization and the development of software tool support.
Diagrammatic Logics: Past, Present and Future
"... Diagrams have many practical applications and are used in numerous settings. Indeed, it is widely recognized that diagrams are a valuable aid to intuition and help to convey ideas and information in a clear way. Traditionally, however, logicians have viewed diagrams as informal tools and, thus, coul ..."
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Diagrams have many practical applications and are used in numerous settings. Indeed, it is widely recognized that diagrams are a valuable aid to intuition and help to convey ideas and information in a clear way. Traditionally, however, logicians have viewed diagrams as informal tools and, thus, could not be a part of any formal argument; only symbolic logics were seen to fulfil this role. Recently, this perception was overturned in seminal work by Shin. This paper explores the evolution of diagrammatic logics, focusing mainly on those based on the popular and intuitive Euler diagrams. Also discussed are some challenges faced in the area, some of which are specifically related to diagrams. 1.
Journal of Visual Languages Journal of Visual Languages and Comp The expressiveness of spider diagr
"... ogica been soun syntactic elements analogous to constants in first order predicate logic. We extend the spider diagram language to include importance of diagrams in computing systems and statements about certain relationships between sets. Her work is widely regarded as seminal, overturning ..."
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ogica been soun syntactic elements analogous to constants in first order predicate logic. We extend the spider diagram language to include importance of diagrams in computing systems and statements about certain relationships between sets. Her work is widely regarded as seminal, overturning