This paper provides equational semantics for Dung’s argumentation networks. The network nodes get numerical values in [0,1], and are supposed to satisfy certain equations. The solutions to these equations correspond to the “extensions” of the network. This approach is very general and includes the Caminada labelling as a special case, as well as many other so-called network extensions, support ...

– The theorem of Bell is a variant of Boole’s legendary consistency “conditions of possible experience.” Such an interpretation appears to be immune to arguments involving time dependencies put forward recently by Hess and Philipp [Europhysics Letters 57(6), 775-781, 2002], although experiments need not be. Boole’s “conditions of possible experience” and Pitowsky correlation polytopes. – In the...

We present a system to compute Boolean combinations of sculptured solids The surface of each solid is represented as a collection of trimmed and untrimmed spline surfaces and a connectivity graph Based on algorithms for trapezoidation of polygons partitioning of polygons using polygonal chains surface intersection of high degree spline surfaces and ray shooting we compute the boundaries of the ...

In discussions of mathematical practice the role axiomatics has often been confined to providing the starting points for formal proofs, with little or no effect on the discovery or creation of new mathematics. For example, quite recently Patras wrote that the axiomatic method “never allows for authentic creation” (Patras 2001, 159), and similar views have been popular with philosophers of scien...

‎from hilbert's theorem of zeroes‎, ‎and from noether's ideal theory‎, ‎birkhoff derived certain algebraic concepts (as explained by tholen) that have a dual significance in general toposes‎, ‎similar to their role in the original examples of algebraic geometry‎. ‎i will describe a simple example that illustrates some of the aspects of this relationship‎. the dualization from algebra ...