Euler diagrams as an introduction to set-theoretical models
نویسنده
چکیده
Understanding the notion of a model is not always easy in logic courses. Hence, tools such as Euler diagrams are frequently applied as informal illustrations of set-theoretical models. We formally investigate Euler diagrams as an introduction to set-theoretical models. We show that the model-theoretic notions of validity and invalidity are characterized by Euler diagrams, and, in particular, that model construction can be described as a manipulation of Euler diagrams. 1998 ACM Subject Classification I.2.0 Philosophical foundations
منابع مشابه
Counter-Example Construction with Euler Diagrams
One of the traditional applications of Euler diagrams is as a representation or counterpart of the usual set-theoretical models of given sentences. However, Euler diagrams have recently been investigated as the counterparts of logical formulas, which constitute formal proofs. Euler diagrams are rigorously defined as syntactic objects, and their inference systems, which are equivalent to some sy...
متن کاملEuler Diagram Encodings
Euler Diagrams are a well-known visualisation of set-based relationships, used in many application areas and at the basis of more complex notations. We propose a static code for concrete Euler Diagrams, which enables efficient storage (vs. storage of concrete diagrams), and transformations preserving concrete-level structure, hence the viewer’s mental map. We provide the theoretical underpinnin...
متن کاملPositive Semantics of Projections in Venn-Euler Diagrams
Venn diagrams and Euler circles have long been used as a means of expressing relationships among sets using visual metaphors such as “disjointness” and “containment” of topological contours. Although the notation is effective in delivering a clear visual modeling of set theoretical relationships, it does not scale well. The topology of Venn diagrams of four or more contours is so cluttered that...
متن کاملTheoretical Formulations for Finite Element Models of Functionally Graded Beams with Piezoelectric Layers
In this paper an overview of functionally graded materials and constitutive relations of electro elasticity for three-dimensional deformable solids is presented, and governing equations of the Bernoulli–Euler and Timoshenko beam theories which account for through-thickness power-law variation of a two-constituent material and piezoelectric layers are developed using the principle of virtua...
متن کاملThe Online Abstraction Problem for Euler Diagrams
A Euler diagrams are an accessible and effective visualisation of data involving simple set-theoretic relationships. Efficient algorithms to quickly compute the abstract regions of an Euler diagram upon curve addition and removal have been developed, but a strict set of drawing conventions (called wellformedness conditions) were enforced, meaning that some abstract diagrams are not representabl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1507.03684 شماره
صفحات -
تاریخ انتشار 2015