The present form of mathematical logic originated in the twenties and early thirties from the partial merging of two different traditions, the algebra of logic and the logicist tradition (see [27], [41]). This resulted in a new form of logic in which several features of the two earlier traditions coexist. Clearly neither the algebra of logic nor the logicist’s logic is identical to the present ...

In judicial decision making, the doctrine of chances takes explicitly into account the odds. There is more to forensic statistics, as well as various probabilistic approaches which taken together form the object of an enduring controversy in the scholarship of legal evidence. In this paper, we reconsider the circumstances of the Jama murder and inquiry (dealt with in Part I of this paper: \The ...

The Goursat partial differential equation arises in linear and non linear partial differential equations with mixed derivatives. This equation is a second order hyperbolic partial differential equation which occurs in various fields of study such as in engineering, physics, and applied mathematics. There are many approaches that have been suggested to approximate the solution of the Goursat par...

The monument to the work initiated by Boole, the algebraization of logic, is the three volumes Algebra der Logik by Schröder (1841–1902), which appeared in the years 1890–1910, filling over 2,000 pages. Although the spirit of the subject came from the work of Boole and De Morgan, Schröder's volumes are really a tribute to the work of C.S. Peirce, along with Schröder's contributions. In addition...

– Bell’s inequalities are a variant of Boole’s legendary consistency “conditions of possible experience.” Although they do not specifically refer to spatially separated subsystems, they apply to spatially separated particles as well. Such an interpretation appears to be immune to arguments involving time dependencies put forward recently by Hess and Philipp [1]. In the middle of the 19th centur...

In this paper we develop a measure for calculating the association coe±cient between Atanassov's intuitionistic fuzzy sets (A-IFSs), and show its desirable axiomatic properties. Then we present an algorithm for clustering A-IFSs. The algorithm ̄rst utilizes the association coe±cient of A-IFSs to construct an association matrix, and then calculates the -cutting matrix of the association matrix no...

In this paper we describe a system, BOOLE, that generates the boundary representations (B-reps) of solids given as a CSG expression in the form of trimmed B ezier patches. The systemmakes use of techniques from computational geometry, numerical linear algebra and symbolic computation to generate the B-reps. Given two solids, the system rst computes the intersection curve between the two solids ...

The Berger-Felzenbaum-Fraenkel approach to Covering Systems is exposited. In particular their gorgeous proof of the famous an = an−1 theorem for exact covering systems (found independently by Jamie Simpson), is reviewed, and the analogy of their approach to Boolean tautologies in Disjunctive Normal Form is pointed out.