José A. Alonso

Universidad de Sevilla | US · Computer Science and Artificial Intelligence

A detailed exposition of foundations of a logic-algebraic model for reasoning with knowledge bases specified 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. Soundnes...

We have recently developed a package in Maple that allows to perform logical computations in any existing or proposed many-valued logic (that can be defined using truth tables). It has applications in logic engineering (e.g. when creating a new logic adapted to some requirements), in theoretical logic (e.g. checking if two axiomatizations of a logi...

Railway interlocking systems are apparatuses that prevent conflicting movements of trains through an arrangement of tracks. A railway interlocking system takes into consideration the position of the switches (of the turnouts) and only allows trains to be given clear signals if the routes to be used by the trains are disjoint. There are many differe...

Description Logics are a family of logics used to represent and reason about conceptual and terminological knowledge. One of the most basic description logics is ${\mathcal{ALC}}$ , used as a basis from which to obtain others. Description logics are particularly important to provide a logical basis for the web ontology languages (such as OWL) use...

Higman's lemma is an important result in infinitary combinatorics, which has been formalized in several theorem provers. In this paper we present a formalization and proof of Higman's Lemma in the ACL2 theorem prover. Our formalization is based on a proof by Murthy and Russell, where the key termination argument is justified by the multiset relatio...

The big computer algebra systems like Maple are no longer restricted to symbolic computations, but are becoming general purpose tools for engineers, mathematicians, and scientists instead. We have worked for a long time with many-valued logics and we believe that a flexible and comfortable tool that allowed to perform logical computations (for inst...

Railway interlocking systems are apparatuses that prevent conflicting movements of trains through an arrangement of tracks. A railway interlocking system takes into consideration the position of the switches (of the turnouts) and does not allow trains to be given clear signals unless the routes to be used by the trains do not intersect. A new model...

5. Máquina abstracta de cálculo aritmético 6. Declaraciones de clases y de instancias 2 / 47 IM Tema 9: Declaraciones de tipos y clases

The relationships between the logical and representational features on ontologies are analysed. Through several questions, this chapter restates the use of Computational logic in Ontology Engineering.

Description Logics are a family of logics used to represent and reason about conceptual and terminological knowledge. Recently, its importance has been increased since they are used as a basis for the Ontology Web Language (OWL) used for the Semantic Web. In previous work, we have developed in PVS a generic framework for reasoning in the ALCALC des...

Knowledge Representation & Reasoning (KR&R) is a fundamental topic in Artificial Intelligence. A basic KR language is First–Order Logic (FOL), the most representative logic–based representation language, which is part of almost any introductory AI course. In this work we present KRRT (Knowledge Representation & Reasoning Tutor). KRRT is a Web–based...

The Ontology Web Language (OWL) is a language used for the Semantic Web. OWL is based on Description Logics (DLs), a family of logical formalisms for representing and reasoning about conceptual and terminological knowledge. Among these, the logic ALC is a ground DL used in many practical cases. Moreover, the Semantic Web appears as a new field for...

Abstract In the Semantic Web, knowledge is usually structured in the form of ontologies, using the Web Ontology Language (OWL), which is based in part on the Description Logics (DLs). DLs are a family of logical formalisms,for representing and reasoning about conceptual and terminological knowledge. Among these, the logic ALC is a ground,DL used in...

Nowadays, Web-based data management needs tools to ensure secure, trustworthy performance. The Utopian future shows a semantic Web providing dependable framework that can solve many of today's data problems. However, the realistic immediate future raises several challenges, including foundational semantic Web issues, the abstract definition of data...

We present a case study using ACL2 to verify a nontrivial algorithm that uses efficient data structures. The algorithm receives as input two first-order terms, and it returns a most general unifier of these terms if they are unifiable, failure otherwise. The verified implementation stores terms as directed acyclic graphs by means of a pointer struc...

Nowadays, data management on the World Wide Web needs to consider very large knowledge databases (KDB). The larger is a KDB, the smaller the possibility of being consistent. Consistency in checking algorithms and systems fails to analyse very large KDBs, and so many have to work every day with inconsistent information.

In this paper we present a formalization and proof of Higman’s Lemma in ACL2. We formalize the constructive proof described in [10] where the result is proved using a termination argument justified by the multiset extension of a well-founded relation. To our knowledge, this is the first mechanization of this proof.

This article is a first approach to the use of Rete algorithm to design a team of robotic soccer playing agents for Robocup Soccer Server. Rete algorithm is widely used to design rule-based expert systems. Robocup Soccer Server is a system that simulates 2D robotic soccer matches. The paper presents an architecture based on CM United team architect...

In this paper, we present the formal verification of a Common Lisp implementation of Buchberger’s algorithm for computing Gröbner bases of polynomial ideals. This work is carried out in the Acl2 system and shows how verified Computer Algebra can be achieved in an executable logic.

We present in this paper an application of the ACL2 system to generate and reason about propositional satisabilit y provers. For that purpose, we develop a framework where we dene a generic SAT-prover based on transformation rules, and we formalize this generic framework in the ACL2 logic, carrying out a formal proof of its termination, soundness a...

This paper is concerned with a formal verification of the Formal Concept Analysis framework. We use the PVS system to represent and formally verify some algorithms of this theory. We also develop a method to transform specifications of algorithms based on finite sets into other executable ones, preserving its correctness. We illustrate this method...

In this paper we present a class of operators for Machine Learning based on Logic Programming which represents a characterization of the subsumption relation in the following sense: The clause C 1 subsumes the clause C 2 iff C 1 can be reached from C 2 by applying these operators. We give a formalization of the closeness among clauses based on thes...

In this paper, we present the formal verification of a Common Lisp implementation of Buchberger’s algorithm for computing Gröbner bases of polynomial ideals. This work is carried out in the ACL2 system and shows how verified Computer Algebra can be achieved in an executable logic.

A mereotopological semantics to manage ontologies is presented. The aim is to provide a formal basis for ontology cleaning. It allows us to arrange, in a consistent manner, the concepts in early steps of the building of an ontology as well as to repair anomalies. The semantics supports cleaning cycle that combines several AI techniques as closed wo...

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Dickson's Lemma is the main result needed to prove the ter- mination of Buchberger's algorithm for computing Grobner basis of poly- nomial ideals. In this case study, we present a formal proof of Dickson's Lemma using the ACL2 system. Due to the limited expressiveness of the ACL2 logic, the classical non-constructive proof of this result cannot be...

We describe in this paper the formal verification, using the ACL2 system, of a syntactic unification algorithm where terms are represented as directed acyclic graphs (dags) and these graphs are stored in a single-threaded object (stobj). The use of stobjs allows destructive operations on data (thus improving the performance of the algorithm), while...

We present in this paper an application of the ACL2 system to reason about propositional satisfiability provers. For that purpose, we present a framework where we define a generic transformation based SAT-prover, and we show how this generic framework can be formalized in the ACL2 logic, making a formal proof of its termination, soundness and compl...

Classical database management can be flawed if the Know- ledge database is built within a complex Knowledge Domain. We must th en deal withinconsistencies and, in general, withanomalies of several types. In this paper we study computational and cognitive problems in dealing qualitative spatial databases.

Theorem proving is a classical AI problem with a broad range of applications. Since its complexity is exponential in the size of the problem, many methods to parallelize the process has been proposed. One of these approaches is based on the massive parallelism of molecular reactions. ACL2 is an automated theorem prover especially adequate for algor...

We present a case study of the use of the ACL2 system, describing an ACL2 formalization of multiset relations, and showing how multisets can be used to prove non-trivial termination properties. Every relation on a set A induces a relation on finite multisets over A; it can be shown that the multiset relation induced by a well-founded relation is al...

In environments with complex cognitive structure (such as semantic web or sophisticated spatial databases for geographical information systems), classical methods for detecting anomalies can be inadequate. In this paper the use of an automated theorem prover to detect anomalies in knowledge bases within a complex ontology is proposed. The authors a...

The subsumption relation is crucial in the Machine Learning systems based on a clausal representation. In this paper we present a class of operators for Machine Learning based on clauses which is a characterization of the subsumption relation in the following sense: The clause C 1 subsumes the clause C 2 iff C 1 can be reached from C 2 by applying...

We present an application of the ACL2 theorem prover to reason about rewrite systems theory. We describe the formalization and representation aspects of our work using the first-order, quantifier-free logic of ACL2 and we sketch some of the main points of the proof effort. First, we present a formalization of abstract reduction systems and then we...

Resumen En este trabajo, presentamos una formalización en PVS del Análisis Formal de Conceptos. Inicialmente, formalizamos la noción de concepto y establecemos que el conjunto de conceptos de un contexto formal tiene estructura de retículo completo. A continuación, realiza-mos una especificación en PVS de un algoritmo para obtener todos los concept...

We describe the development in ACL2 of a library of results about first-order terms. In particular, we present the formalization of some of the main properties of the complete lattice of first-order terms with respect to the subsumption relation. As a byproduct, verified executable implementations are obtained for some basic operations on firstorde...

In some cases, when we develop a formal theory in ACL2, it would be desirable that the definitions and theorems of the theory be as independent of a concrete implementation as possible. This is particularly interesting when we design theories about basic data types, making those developments more general, reusable and extensible. At the same time,...

In this paper we present an ACL2 formalization of a molecular computing model: Adle- man's restricted model (2). This is a årst step to formalize unconventional models of compu- tation in ACL2. As an application of this model, an implementation of Lipton's experiment solving SAT (7) is described, based on the formalization given in (6). We use ACL2...

In this paper we present the formalization of a decision procedure for Propositional Logic based on polynomial normalization. This formalization is suitable for its automatic verification in an applicative logic like Acl2. This application of polynomials has been developed by reusing a previous work on polynomial rings [19], showing that a proper f...

We present in this paper a formalization of multiset relations in the ACL2 theorem prover [6], and we show how multisets can be used to mechanically prove non-trivial termination properties. Every relation on a set A induces a relation on finite multisets over A ;i t can be shown that the multiset relation induced by a well-founded relation is also...

We present in this paper a formalization of multiset relations in ACL2, and we show how multisets can be used to prove non-trivial termination properties in ACL2. Intuitively, multisets are sets that admit multiple occurrences of elements.

reductions and Newman's lemma: An abstract reduction [1] is simply a binary relation, and equational reductions are a particular case of abstract reductions. As part of our project to formalize properties of equational reasoning, we developed books proving results about abstract reduction relations. Concepts like Church-Rosser property, local conue...

We present an application of the ACL2 theorem prover to formalize and reason about rewrite systems theory. This can be seen as a first approach to apply formal methods, using ACL2, to the design of symbolic computation systems, since the notion of rewriting or simplification is ubiquitous in such systems. We concentrate here in formalization and re...

. In this paper, General Topology and ILP are brought together.The closeness between clauses is formalized using a non-metrictopology which can be seen as the topological translation of the subsumptionorder: the Alexandrov topology. The denitions of the upwardrenement operators in ILP are formalized as mappings " : C R =! C =where C = and C R = are...

 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...

In the case of classical logic, the Stone isomorphism between Boolean Algebras and Boolean Rings is at the basis of the methods which reduce a logical problem to an algebraic one about polynomials. In this paper, we generalize this kind of reduction to the case of any multi-valued logic. Our main result is the Theorem 4.4 which transforms a deducti...

The Ontology Web Language (OWL) is a language used for the Semantic Web. OWL is based on Description Logics (DLs), a family of logical formalisms for representing and reasoning about conceptual and terminological knowledge. Among these, the logic ALC\mathcal{ALC\,} is a ground DL used in many practical cases. Moreover, the Semantic Web appears as...

We explore in this paper the use of ecient data structures to implement oper- ations on first-order terms, that can be formally verified. Specifically, we present the status of our work on defining and verifying a unification algorithm acting on terms represented as directed acyclic graphs (dags). This implementation is done using single threaded o...

Resumen En este trabajo presentamos un caso de estudio consistente en la aplicacion del sistema ACL2 a la definicion y verificacion formal de un algoritmo de unificacion de terminos de primer orden, usando es- tructuras de datos eficientes: los terminos se representan mediante grafos ac´iclicos dirigidos y estos grafos se almacenan en un objeto de...

The decidability method, given in (6), for modal system S5 uses the reduced modal normal form. In this paper we present a recursive algorithm for computing the reduced modal normal form and use this algorithm as a subroutine for an algorithm deciding validity of formulas of system S5.

A.1.1. Definición del tipo abstracto de datos de conceptos,de ALC . . . . . . . . .,29 A.1.2. Definiciones sobre la sintaxis de ALC . . . . . . . . . . . . . . . . . . . . . .,29 A.1.3. Conocimiento,terminológico y asertivo,. . . . . . . . . . . . . . . . . . . . .,31 A.2. Semántica de ALC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

Palabras clave: Lógica Computacional, métodos formales, razonamiento automático, len-guaje de programación aplicativo, programación genérica, algoritmos genéricos, ACL2 Resumen En este artículo se estudia un caso de formalización y demostración automática en ACL2 relacionado con la programación genérica. Tras una definición axiomática del concepto...

We present a case study of using ACL2 to verify an non-trivial algorithm that uses efficient data structures. The algorithm receives as input two first-order terms and it returns a most general unifier of these terms if they are unifiable, failure otherwise. The verified implementation stores terms as directed acyclic graphs in a stobj by means of...