A logic-algebraic tool for reasoning with Knowledge-Based Systems

A detailed exposition of foundations of a logic-algebraic model for reasoning with knowledge bases speci ed by propositional (Boolean) logic is presented. The model is conceived from the logical translation of usual derivatives on polynomials (on residue rings) which is used to design a new inference rule of algebro-geometric inspiration. Soundness and (refutational) completeness of the rule are proved. Some applications of the tools introduced in the paper are shown.Ministerio de Economía y Competitividad TIN2013-41086-

An Algebraic Approach to DC Railway Electrification Verification

Gröbner bases have been applied to a number of problems related to the verification of Knowledge-Based Systems (KBS) and other problems within graph theory. In particular, the authors have developed in previous papers algebraic approaches to decide whether a situation in a railway interlocking system is safe or not. These algebraic approaches stand out because of the briefness of the code (as they use implementations of well-known algorithms for solving linear or algebraic systems provided by computer algebra systems). The authors have also developed a matrix-based computer tool that helps an expert to check whether a proposed railway electrification scenario (given through the topology of the railway station and the position of the isolation devices and the position and state of the “electrical bypasses” and feeders) fulfills the mandatory requirements of the Spanish railway infrastructure administrator (ADIF) for 3000 V railway electrifications or not. The second author works in the field of railway electrifications and he compares the present-day methods for verification of railway electrifications with the way KBS were verified in the past (manually by experts). In this article we approach this latter problem using algebraic techniques. The new computer tool is based on an algebraic translation of the problem (instead of based on the use of matrices) and is really simple and fast. Determining which electrification sections are under electric tension is computed solving linear systems (because in this case the graph is undirected and no polynomials of degree >1 arise in the algebraic translation, so it is not necessary to use Gröbner bases, unlike in the two problems mentioned in the beginning of the Abstract). Therefore far bigger railway facilities can be addressed than if non-linear systems were involved

Diagnosis in Tennis Serving Technique

Tennis is a sport with a very complex technique. Amateur tennis players have trainers and/or coaches, but are not usually accompanied by them to championships. Curiously, in this sport, the result of many matches can be changed by a small hint like ‘hit the ball a little higher when serving’. However, the biomechanical of a tennis stroke is only clear to an expert. We, therefore, developed a prototype of a rule-based expert system (RBES) aimed at an amateur competition player that is not accompanied by his/her coach to a championship and is not serving as usual (the RBES is so far restricted to serving). The player has to answer a set of questions about how he/she is serving that day and his/her usual serving technique and the RBES obtains a diagnosis using logic inference about the possible reasons (according of the logic rules that have been previously given to the RBES). A certain knowledge of the tennis terminology and technique is required from the player, but that is something known at this level. The underlying logic is Boolean and the inference engine is algebraic (it uses Groebner bases)