Monotone Logic Programming

We propose a notion of an abstract logic. Based on this notion, we define abstract logic programs to be sets of sentences of an abstract logic. When these abstract logics possess certain logical properties (some properties considered are compactness, finitariness, and monotone consequence relations) we show how to develop a fixed-point, model-state-theoretic and proof theoretic semantics for such programs. The work of Melvin Fitting on developing a generalized semantics for multivalued logic programming is extended here to arbitrary abstract logics. We present examples to show how our semantics is robust enough to be applicable to various non-classical logics like temporal logic and multivalued logics, as well as to extensions of classical logic programming such as disjunctive logic programming. We also show how some aspects of the declarative semantics of distributed logic programming, particularly work of Ramanujam, can be incorporated into our framework

Programming in three-valued logic

AbstractThe aim of this paper is to propose a logical and algebraic theory which seems well-suited to logic programs with negation and deductive databases. This theory has similar properties to those of Prolog theory limited to programs with Horn clauses and thus can be considered as an extension of the usual theory. This parallel with logic programming without negation lies in the introduction of a third truth value (Indefinite) and of a new non-monotonic implication connective. Our proposition is different from the other ways of introducing a third truth value already used in Logic Programming and databases but it is somehow related to some of them, especially to Fitting's theory. We introduce a “consequence” operator associated with a logic program with negation which extends the operator of Apt and Van Emden. In the case of a consistent program, the post-fixpoints of this operator are the models of the program as they are usually. This operator is related to Fitting's one, the relation being obtained by completing the program. We finally give an operational semantics for a program with negation by the obtention of a three-valued interpreter from a bivalued one

Fixpoint semantics for logic programming a survey

AbstractThe variety of semantical approaches that have been invented for logic programs is quite broad, drawing on classical and many-valued logic, lattice theory, game theory, and topology. One source of this richness is the inherent non-monotonicity of its negation, something that does not have close parallels with the machinery of other programming paradigms. Nonetheless, much of the work on logic programming semantics seems to exist side by side with similar work done for imperative and functional programming, with relatively minimal contact between communities. In this paper we summarize one variety of approaches to the semantics of logic programs: that based on fixpoint theory. We do not attempt to cover much beyond this single area, which is already remarkably fruitful. We hope readers will see parallels with, and the divergences from the better known fixpoint treatments developed for other programming methodologies

A Unified Framework For Three-Valued Semantical Treatments of Logic Programming

Based on Fiting\u27s Φ operator a unified framework for three-valued semantics of logic programming is presented. The truth space used in the framework is the class of partial interpretations. Underlying the truth space is two partial orderings, knowledge ordering and truth ordering. It turns out that the truth space with the truth ordering is a complete lattice and the truth space with knowledge ordering is a semi-complete lattice. Φ is proved to be continuous over the complete lattice and monotonic over the semi-complete lattice. With the use of Φ operator two well-known three-valued semantics for logic programming, Fitting\u27s three-valued semantics and well-founded semantics, are characterized within the framework in a simple and elegant way. We show that Fitting\u27s semantics is the least stable three-valued model with respect to the knowledge ordering and well-founded semantics is the least stable three-valued model with respect to the truth ordering

Reducciones totales y parciales para el análisis de validez y construcción de modelos en M3

Esta tesis estudia la demostración automática de teoremas en lógicas trivaluadas. Concretamente se presenta un demostrador denominado tas-m3 para la lógica trivaluada completa m3. Esta tesis cuenta con una orientación a las aplicaciones y es de gran importancia la forma en la que se genera el modelo para la negación de la formula de entrada. Es un método que no está basado en resolución y por tanto no adolece de las deficiencias de este método(poca interacción con el ser humano, dificultad de obtener formas normales en lógicas no clásicas, etc.). Además de la demostración de corrección y completitud del método se demuestran otros teoremas relacionados con los procesos. El trabajo se complementa con un estudio comparativo con los métodos actualmente más utilizados. También se añaden capítulos en los que se introducen los conceptos que se utilizan a lo largo del trabajo así como un capítulo dedicado a las lógicas multivaluadas. Se añade un apéndice en el que se resume el demostrador para la lógica clásica TAS-D al que se le incorporan las mejoras que el estudio del caso multivaluado ha motivado. En la exposición y defensa se utiliza una implementación del método para entornos gráficos realizada en C++

Una lógica trivalorada para funciones recursivas parciales

Tesis de la Universidad Complutense de Madrid.Facultad de Ciencias Matemáticas, Departamento de Informática y Automática, leída en Madrid el 3 de febrero de 1990; Dirigida por Mario Rodríguez Artalejo.Sección Deptal. de Sistemas Informáticos y ComputaciónFac. de Ciencias MatemáticasTRUEProQuestpu