Luis M. Laita

A polynomial model for multi-valued logics with a touch of algebraic geometry and computer algebra

In this paper, a polynomial model (residue class ring) for a given p-valued propositional Logic (p prime), is constructed. This will allow the study of logical deductions using Computer Algebra techniques (Grobner Bases). Also, an interesting interpretation of ⊨ and Kleenes style → and their relation from the point of view of Algebraic Geometry (in terms of algebraic varieties) will be given. Only modest requirements about the good behaviour of the Logic will be assumed. This approach makes it possible to move a step forward and treat Knowledge Based Systems (KBSs) based on multi-valued Logics.

A computer algebra approach to verification and deduction in many-valued knowledge systems

Abstract A theoretical result [10] that relates tautological consequence in many-valued logics to the ideal membership problem in algebra is revisited. The intended use of the approach in this article and its implementation is the verification of consistency and the automated extraction of knowledge in rule-based knowledge systems. Programs are written in the CoCoA language. Four RBS are studied to illustrate the implementation.

Railway interlocking systems and Gröbner bases

Railway interlocking systems are designed to prevent conflicting actions (related to the position of switches and signals) during everyday railway exploitation. A decision model (independent from the topology of the station) based on the use of polynomial ideals and Grobner bases is presented. This decision model can also be used to check whether a given section is accessible by a train located in another section or not. The fact that trains could occupy more than one section does not affect the model.

A logic and computer algebra-based expert system for diagnosis of anorexia

Anorexia is a serious condition which more and more men and women, especially young women, are contracting. In this article, we propose an expert system for the diagnosis of anorexia. The ‘knowledge base’ of the expert system is a set of bivalued logic production rules. The inference engine uses Grobner bases and normal forms to draw consequences from the information contained in the knowledge base. A user interface is also provided.

An Expert System for Managing Medical Appropriateness Criteria Based on Computer Algebra Techniques

Abstract This article presents the development of an expert system for managing medical appropriateness criteria together with an outline of its theoretical foundations. Techniques borrowed from computer algebra (Grobner bases) are applied to this field of medicine. The steps of the expert system construction process are as follows. First, the knowledge provided in table format by experts in coronary diseases is translated into a set of production rules of a rule-based expert system (RBES). Kleenes three-valued logic augmented with modal operators is chosen in order to manage uncertainty.

An applicable topology-independent model for railway interlocking systems

In this article, two decision models for railway interlocking systems are presented. The first – for the case that the turnouts have spring switches- and the second – for the case that the turnouts should not be trailed through a switch set against-. In both cases, the algorithm is independent of the topology of the station and is based on the calculation of accessibility in an oriented graph.

Knowledge representation for diagnosis of care problems through an expert system: Model of the auto-care deficit situations

The caregiver role strain is today an increasing problem because of the population aging; moreover, its diagnosis is highly difficult. In this article, we summarize the design of an Expert System for the diagnosis of this health problem. The Expert System Knowledge Base is composed by a set of production rules written in classic bi-valued logic and by a set of potential facts. In order to build this Knowledge Base it has been necessary to design previously a Model of the problem treatment. The Expert System Inference Engine uses Grobner Bases and Normal Form to obtain the diagnosis from the information stored in the Knowledge Base. Furthermore, a Graphic Users Interface has been implemented to make easier the access to the System by all kinds of users.

A computational system for diagnosis of depressive situations

Abstract The purpose of this article is to describe a computational system for automated diagnosis of depression. It has a user interface, which allows non-specialists in mathematics and computer science to obtain automatically a fast diagnosis of the illness by simply pointing at keys in the computer screens. It can be used by family doctors to obtain a tentative diagnosis before sending the patient to a specialist. It can also be useful to specialists who want to compare their own diagnoses with those given by the computer.

The geometry of algebraic systems and their exact solving using Grobner bases

Although exact methods for solving general polynomial systems are incorporated into well-known computer algebra systems such as Derive, Maple, Mathematica, MuPad, and Reduce, only a small portion of the scientific community knows about them. This article introduces one such method - Grobner bases - for non-mathematicians in an intuitive way. Specifically, we show the analogies and differences between linear and algebraic system solving, with an emphasis on the underlying geometric aspects.

Validation and verification of knowledge-based systems: report on EUROVAV99

Knowledge-Based (KB) technology is being applied to complex problem solving and safety and business critical tasks in many application domains. Concerns have naturally arisen as to the dependability of Knowledge-Based Systems (KBS). As with any software, attention to quality and safety must be paid throughout development of a KBS, and rigorous Verification and Validation (V&V) techniques must be employed. Research in V&V of KBSs has emerged as a distinct field only in the last decade, and is intended to address issues associated with quality and safety aspects of KBSs, and to provide such applications with the same degree of dependability as conventional applications. In recent years, V&V of KBSs has been the topic of annual workshops associated with the main AI conferences, such as AAAI, IJCAI and ECAI.