Carlos Viegas Damásio

Monotonic and Residuated Logic Programs

In this paper we define the rather general framework of Monotonic Logic Programs, where the main results of (definite) logic programming are validly extrapolated. Whenever defining new logic programming extensions, we can thus turn our attention to the stipulation and study of its intuitive algebraic properties within the very general setting. Then, the existence of a minimum model and of a monotonic immediate consequences operator is guaranteed, and they are related as in classical logic programming. Afterwards we study the more restricted class of residuated logic programs which is able to capture several quite distinct logic programming semantics. Namely: Generalized Annotated Logic Programs, Fuzzy Logic Programming, Hybrid Probabilistic Logic Programs, and Possibilistic Logic Programming. We provide the embedding of possibilistic logic programming.

A survey of paraconsistent semantics for logic programs

Our contribution to this volume consists in giving a logic programmer’s view on handling program inconsistency. The semantics we cover will touch several aspects of implementing reasoning in the presence of contradiction. Logic programming has already shown a wide applicability for representings knowledge [Barai and Gel-fond, 1994]. Also, the most important non-monotonic formalisms, for instance Default Logic [Reiter, 1980] and Autoepistemic logics [Moore, 1984; Moore, 1985], have a counterpart semantics on the logic programming side.1 Moreover, logic programming has turned out to be vehicle for implementing and exploring other important aspects of Artificial Intelligence such as updates and belief revision. Therefore, it is not strange that a lot of work in the logic programming community has been carried out to understand the integration of paraconsistent reasoning with logic programming, in preparation for an applicational and implementational role of great potential, now emerging.

Antitonic Logic Programs

In a previous work we have defined Monotonic Logic Programs which extend definite logic programming to arbitrary complete lattices of truth-values with an appropriate notion of implication. We have shown elsewhere that this framework is general enough to capture Generalized Annotated Logic Programs, Probabilistic Deductive Databases, Possibilistic Logic Programming, Hybrid Probabilistic Logic Programs and Fuzzy Logic Programming [3,4]. However, none of these semantics define a form of non-monotonic negation, which is fundamental for several knowledge representation applications. In the spirit of our previous work, we generalise our framework of Monotonic Logic Programs to allow for rules with arbitrary antitonic bodies over general complete lattices, of which normal programs are a special case. We then show that all the standard logic programming theoretical results carry over to Antitonic Logic Programs, defining Stable Model and Well-founded Model alike semantics. We also apply and illustrate our theory to logic programs with costs, extending the original presentation of [17] with a class of negations.

Hybrid Probabilistic Logic Programs as Residuated Logic Programs

In this paper we show the embedding of Hybrid Probabilistic Logic Programs into the rather general framework of Residuated Logic Programs, where the main results of (definite) logic programming are validly extrapolated, namely the extension of the immediate consequences operator of van Emden and Kowalski. The importance of this result is that for the first time a framework encompassing several quite distinct logic programming semantics is described, namely Generalized Annotated Logic Programs, Fuzzy Logic Programming, Hybrid Probabilistic Logic Programs, and Possibilistic Logic Programming. Moreover, the embedding provides a more general semantical structure paving the way for defining paraconsistent probabilistic reasoning logic programming semantics.

REVISE: An Extended Logic Programming System for Revising Knowledge Bases

Abstract In this paper we describe REVISE, an extended logic programming system for revising knowledge bases. REVISE is based on logic programming with explicit negation, plus a two-valued assumption revision to face contradiction, encompasses the notion of preference levels. Its reliance on logic programming allows efficient computation and declarativity, whilst its use of explicit negation, revision and preference levels enables modeling of a variety of problems including default reasoning, belief revision and model-based reasoning. It has been implemented as a Prolog-meta interpreter and tested on a spate of examples, namely the representation of diagnosis strategies in modelbased reasoning systems.

MWeb: A principled framework for modular web rule bases and its semantics

We present a principled framework for modular Web rule bases, called MWeb. According to this framework, each predicate defined in a rule base is characterized by its defining reasoning mode, scope, and exporting rule base list. Each predicate used in a rule base is characterized by its requesting reasoning mode and importing rule base list. For legal MWeb modular rule bases S, the MWebAS and MWebWFS semantics of each rule base s ∈ S with respect to S are defined model-theoretically. These semantics extend the answer set semantics (AS) and the well-founded semantics with explicit negation (WFSX) on ELPs, respectively, keeping all of their semantical and computational characteristics. Our framework supports: (1) local semantics and different points of view, (2) local closed-world and open-world assumptions, (3) scoped negation-as-failure, (4) restricted propagation of local inconsistencies, and (5) monotonicity of reasoning, for fully shared predicates.

Extended RDF as a semantic foundation of rule markup languages

Ontologies and automated reasoning are the building blocks of the Semantic Web initiative. Derivation rules can be included in an ontology to define derived concepts, based on base concepts. For example, rules allow to define the extension of a class or property, based on a complex relation between the extensions of the same or other classes and properties. On the other hand, the inclusion of negative information both in the form of negation-as-failure and explicit negative information is also needed to enable various forms of reasoning. In this paper, we extend RDF graphs with weak and strong negation, as well as derivation rules. The ERDF stable model semantics of the extended framework (Extended RDF) is defined, extending RDF(S) semantics. A distinctive feature of our theory, which is based on Partial Logic, is that both truth and falsity extensions of properties and classes are considered, allowing for truth value gaps. Our framework supports both closed-world and open-world reasoning through the explicit representation of the particular closed-world assumptions and the ERDF ontological categories of total properties and total classes.

On Fixed-Points of Multivalued Functions on Complete Lattices and Their Application to Generalized Logic Programs

Unlike monotone single-valued functions, multivalued mappings may have zero, one, or (possibly infinitely) many minimal fixed-points. The contribution of this work is twofold. First, we overview and investigate the existence and computation of minimal fixed-points of multivalued mappings, whose domain is a complete lattice and whose range is its power set. Second, we show how these results are applied to a general form of logic programs, where the truth space is a complete lattice. We show that a multivalued operator can be defined whose fixed-points are in one-to-one correspondence with the models of the logic program.

Supporting open and closed world reasoning on the web

In this paper general mechanisms and syntactic restrictions are explored in order to specify and merge rule bases in the Semantic Web. Rule bases are expressed by extended logic programs having two forms of negation, namely strong (or explicit) and weak (also known as default negation or negation-as-failure). The proposed mechanisms are defined by very simple modular program transformations, and integrate both open and closed world reasoning. These program transformations are shown to be appropriate for the two major semantics for extended logic programs: answer set semantics and well-founded semantics with explicit negation. Moreover, the results obtained by both semantics are compared.

Debugging by Diagnosing Assumptions

We present a novel and uniform technique for normal logic program declarative error diagnosis. We lay down the foundations on a general approach to diagnosis using logic programming, and bring out the close relationship between debugging and fault-finding.