Luis de Ledesma

A Methodology for Constructing Expert Systems for Medical Diagnosis

We propose a methodology, based on Computer Algebra and implemented in CoCoA language, for constructing rule based expert systems, that can be applied to the diagnosis of some illnesses. For the sake of clarity, our proposal uses a simplified description of depression, assuming that our aim is the proposal of a general methodology rather than the study of this particular illness.

An Interpretation of the Propositional Boolean Algebra as k-algebra. Effective Calculus

We construct in the first part of the paper a Boolean algebra, isomorphic to a propositional Boolean algebra (C, ∀, λ, ¬, →), that is also a k-algebra, and such that the ideals of the Boolean algebra correspond exactly to the ideals of the k-algebra.

A computational approach to George Boole's discovery of mathematical logic

Abstract This paper reports a computational model of Booles discovery of Logic as a part of Mathematics. George Boole (1815–1864) found that the symbols of Logic behaved as algebraic symbols, and he then rebuilt the whole contemporary theory of Logic by the use of methods such as the solution of algebraic equations. Study of the different historical factors that influenced this achievement has served as background for our two main contributions: a computational representation of Booles Logic before it was mathematized; and a production system, BOOLE2, that rediscovers Logic as a science that behaves exactly as a branch of Mathematics, and that thus validates to some extent the historical explanation. The systems discovery methods are found to be general enough to handle three other cases: two versions of a Geometry due to a contemporary of Boole, and a small subset of the Differential Calculus.

Computer Algebra Based Verification and Knowledge Extraction in RBS - Application to Medical Fitness Criteria

This article deals with the application to automated extraction of knowledge and verification of consistency in Rule-Based Knowledge Systems (to be denoted as RBS), of a theoretical result that relates tautological consequence in many-valued logics to the ideal membership problem in Algebra. An implementation in a Computer Algebra System is described.

Showing the non-existence of solutions in systems of linear Diophantine equations

The present paper is concerned with expounding an altogether new method specifically designed to provide a straightforward proof that there is no possible solution for some family of systems of Diophantine linear equations which share the same dependent terms while differing in its independent terms. On the basis of this novel approach, a definition of testers is given and consequently used to shape this particular method, as illustrated with some suitable examples.

A Symbolic Computation-Based Expert System for Alzheimer's Disease Diagnosis

In this paper we summarize a method of construction of a rule-based expert system (denoted RBES) for Alzheimers disease diagnosis. Once the RBES is constructed, Symbolic Computation techniques are applied to automatically both verify (that is, check for consistency) and extract new knowledge to produce a diagnosis.

A system simulating representation change phenomena while problem solving

This paper deals with a computer programme offering a valid simulation of cognitive human processes related to representation changes while problem solving. An introductory and brief recollection of preceding contributions by psychologists, cognitive scientists and AI researchers provides the necessary background and motivation for our work. A relevant trend of the present research concerns the formal mathematical study of representation phenomena, including precisions about isomorphic and homomorphic representation changes. In order to simplify problem resolution processes, the implemented system performs certain representation changes, by making use of specific procedures which assign and modify a certain relevance value to every attribute involved in the problem representation, on behalf of their respective importance so as to actually solve the problem. The paper includes a full account of mathematical definitions and propositions involved in this system.

A formal model for knowledge‐based systems verification

A logico‐algebraic model for verification of Knowledge Based Systems, based on Abraham Robinsons meta‐algebra, is presented in this article. the set of rules of Knowledge Based System is considered to be the set of axioms of a theory “T”. the model consists of: (i) the collection “P” of all well formed formulas of the language of T, (ii) a subset P0 of P that has as its elements the axioms of a given logic (bivalued, intuitionistic, or other), plus all the theorems that can be deduced from this logic inside the language of T, (iii) some distinguished subsets of P, to be called m‐ideals and m‐filters, that depend on T and P0. Important concepts that are involved in the verification of Knowledge Based Systems are considered, such as forward and backward reasoning consistencies. Appropriate characterizations are obtained by using properties of m‐ideals and m‐filters.

A technique for dynamically measuring and modifying relevance while problem solving

Although there is general agreement that efficiency of problem resolution is strongly related to the problem representation adopted, computer problem solvers have been traditionally designed to keep the same representation throughout the whole of the problem solving process. A system able to change representation whilst the actual problem solving process occurs has advantages over traditional ones, not only because a representation change can improve the efficiency of problem resolution (as already proven through much research), but also because the choice of the most suitable representation may be decisively enhanced after learning about the problem during its resolution process. A natural and interesting way of performing representation changes is related to detecting irrelevant elements which can be removed out of the problem representation. In this paper, we deal formally with a new technique for assigning and changing the relevance of the elements involved in the representation during the problem resolution, on behalf of their respective importance so as to actually solve the problem.ResumenAunque existe un consenso general sobre la fuerte dependencia entre la eficiencia en la resolución de problemas y la representación de los mismos que se adopta, los programas resolvedores de problemas tradicionalmente se han diseñado teniendo en cuenta únicamente una sola representación a lo largo de todo el proceso de resolución. Un sistema capaz de cambiar la representación mientras el mismo proceso de resolución tiene lugar ofrece ventajas respecto de los tradicionales, no sólo porque ciertos cambios de representación pueden mejorar la eficiencia del proceso de resolución (como muchas investigaciones han demostrado), sino también debido a que la tarea de seleccionar la representación más adecuada para un problema puede facilitarse decisivamente mediante el conocimiento adquirido durante el proceso de su resolución. Una manera interesante y natural de ejecutar cambios de representación se apoya en detectar la información irrelevante que puede eliminarse de la representación del problema. En el presente trabajo, presentamos formalmente una nueva técnica para asignar y modificar valores de relevancia a los elementos que integran la representación de los problemas durante el mismo proceso de resolución, de acuerdo con la importancia que tienen para resolverlos.

A Rule-Based Knowledge System for Diagnosis of Mental Retardation

We present in this paper a Rule-Based Knowledge System that both verifies the consistency of the knowledge explicitly provided by experts in mental retardation, and automatically extracts consequences (in this case: diagnoses) from that knowledge.