Spider Diagrams of Order
نویسندگان
چکیده
Spider diagrams are a visual logic capable of makeing statements about relationships between sets and their cardinalities. Various meta-level results for spider diagrams have been established, including their soundness, completeness and expressiveness. Recent work has established various relationships between spider diagrams and regular languages, which highlighted various classes of languages that spider diagrams could not define. In particular, this work illustrated the inability of spider diagrams to place an order on certain letters in words. To overcome this limitation, in this paper we introduce spider diagrams of order, incorporating an order relation and present a formalisation of the syntax and semantics. Subsequently, we define the language of such a diagram and establish that the class of such languages includes that of the piecewise testable languages.
منابع مشابه
Defining star-free regular languages using diagrammatic logic
Spider diagrams are a recently developed visual logic that make statements about relationships between sets, their members and their cardinalities. By contrast, the study of regular languages is one of the oldest active branches of computer science research. The work in this thesis examines the previously unstudied relationship between spider diagrams and regular languages. In this thesis, the ...
متن کاملOn the Relative Expressiveness of Second-Order Spider Diagrams and Regular Expressions
This paper is about spider diagrams, an extension of Euler diagrams that includes syntax to make assertions about set cardinalities. Like many diagrammatic logics, spider diagrams are a monadic and first-order, so they are inexpressive. The limitation to first-order precludes the formalisation of many fundamental concepts such as the cardinality of a set being even. To this end, second-order sp...
متن کاملSpider Diagrams of Order and a Hierarchy of Star-Free Regular Languages
The spider diagram logic forms a fragment of constraint diagram logic and is designed to be primarily used as a diagrammatic software specification tool. Our interest is in using the logical basis of spider diagrams and the existing known equivalences between certain logics, formal language theory classes and some automata to inform the development of diagrammatic logic. Such developments could...
متن کاملReasoning with Spider Diagrams
Spider diagrams combine and extend Venn diagrams and Euler circles to express constraints on sets and their relationships with other sets. These diagrams can usefully be used in conjunction with object-oriented modelling notations such as the Unified Modelling Language. This paper summarises the main syntax and semantics of spider diagrams and introduces four inference rules for reasoning with ...
متن کاملEnhancing the Expressiveness of Spider Diagram Systems
Many visual languages based on Euler diagrams have emerged for expressing relationships between sets. The expressive power of these languages varies, but the majority are monadic and some include equality. Spider diagrams are one such language, being equivalent in expressive power to monadic first order logic with equality. Spiders are used to represent the existence of elements or specific ind...
متن کامل