A New Language for the Visualization of Logic and reasoning

Many visual languages based on Euler diagrams have emerged for expressing relationships between sets. The expressive power of these languages varies, but the majority can only express statements involving unary relations and, sometimes, equality. We present a new visual language called Visual First Order Logic (VFOL) that was developed from work on constraint diagrams which are designed for software specification. VFOL is likely to be useful for software specification, because it is similar to constraint diagrams, and may also fit into a Z-like framework. We show that for every First Order Predicate Logic (FOPL) formula there exists a semantically equivalent VFOL diagram. The translation we give from FOPL to VFOL is natural and, as such, VFOL could also be used to teach FOPL, for example

Euler diagram-based notations

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 set-theoretic 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

Reasoning with Diagrams: Observation, Inference and Overspecificity

The ability of diagrams to convey information effectivelycomes, in part, from their ability to make facts explicit that would otherwise need to be inferred. This type of advantagehas often been referred to as a free ride and was deemed to occur only when a diagram was obtained by translating asymbolic representation of information. Recent work generalised free rides, introducing the idea of an observational advantage, where the existence of such a translation is not required. In this paper, I will provide an overview of the theory of observation. It has been shown that Euler diagrams without existential import have significant observational advantages over set theory: they are observationallycomplete. I will then explore to what extent Euler diagrams with existential import are observationally complete with respect to set-theoretic sentences. In particular, has been shown that existential import significantly limits the cases when observational completeness arises, due to the potentialfor overspecificity. These two results formally support Larkin and Simon's claim that "a diagram is (sometimes)worth ten thousand words". The work in this invited paperis derived from previously published results as cited in the text