A Normal Form for Euler Diagrams with Shading

@incollection{fish:anffedws, abstract = {In logic, there are various normal forms for formulae; for example, disjunctive and conjunctive normal form for formulae of propositional logic or prenex normal form for formulae of predicate logic. There are algorithms for 'reducing' a given formula to a semantically equivalent formula in normal form. Normal forms are used in a variety of contexts including proofs of completeness, automated theorem proving, logic programming etc. In this paper, we develop a normal form for unitary Euler diagrams with shading. We give an algorithm for reducing a given Euler diagram to a semantically equivalent diagram in normal form and hence a decision procedure for determining whether two Euler diagrams are semantically equivalent. Potential applications of the normal form include clutter reduction and automated theorem proving in systems based on Euler diagrams.}, author = {Fish, Andrew and John, Chris and Taylor, John}, citeulike-article-id = {3322352}, doi = {10.1007/978-3-540-87730-1_20}, journal = {Diagrammatic Representation and Inference}, keywords = {diagrams, euler-diagrams}, pages = {206--221}, posted-at = {2008-09-23 16:34:19}, priority = {3}, title = {A Normal Form for Euler Diagrams with Shading}, url = {http://dx.doi.org/10.1007/978-3-540-87730-1_20}, year = {2008} }

TY - CHAP ID - fish:anffedws L3 - citeulike-article-id:3322352 N2 - In logic, there are various normal forms for formulae; for example, disjunctive and conjunctive normal form for formulae of propositional logic or prenex normal form for formulae of predicate logic. There are algorithms for ‘reducing’ a given formula to a semantically equivalent formula in normal form. Normal forms are used in a variety of contexts including proofs of completeness, automated theorem proving, logic programming etc. In this paper, we develop a normal form for unitary Euler diagrams with shading. We give an algorithm for reducing a given Euler diagram to a semantically equivalent diagram in normal form and hence a decision procedure for determining whether two Euler diagrams are semantically equivalent. Potential applications of the normal form include clutter reduction and automated theorem proving in systems based on Euler diagrams. JF - Diagrammatic Representation and Inference EP - 221 TI - A Normal Form for Euler Diagrams with Shading SP - 206 KW - diagrams KW - euler-diagrams AU - Fish, Andrew AU - John, Chris AU - Taylor, John PY - 2008/// UR - http://dx.doi.org/10.1007/978-3-540-87730-1_20 ER -