A Normal Form for Spider Diagrams of Order
نویسندگان
چکیده
We develop a reasoning system for an Euler diagram based visual logic, called spider diagrams of order. We define a normal form for spider diagrams of order and provide an algorithm, based on the reasoning system, for producing diagrams in our normal form. Normal forms for visual logics have been shown to assist in proving completeness of associated reasoning systems. We wish to use the reasoning system to allow future direct comparison of spider diagrams of order and linear temporal logic.
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 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 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 کاملOn the expressiveness of spider diagrams and commutative star-free regular languages
Spider diagrams provide a visual logic to express relations between sets and their elements, extending the expressiveness of Venn diagrams. Sound and complete inference systems for spider diagrams have been developed and it is known that they are equivalent in expressive power to monadic first-order logic with equality, MFOL[1⁄4]. languages that are finite unions of languages of the form K G , ...
متن کاملThe Mathematics of Diagrammatic Logical Systems
The focus of my PhD was on spider diagrams and constraint diagrams. Constraint diagrams are a visual language for expressing logical statements. The spider diagram language forms a fragment of the constraint diagram language. I developed two diagrammatic reasoning systems. The first of these, based on spider diagrams, directly extends previous work. The second system is based on the more expres...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Vis. Lang. Comput.
دوره 25 شماره
صفحات -
تاریخ انتشار 2014