Weak SLD Resolution

We present experimental results that indicate that SLD-resolution could be considered as a unifying framework for the studying of query rewriting algorithms. Indeed, adding constraints to the control of SLD-resolution makes it simulate some of the classical query rewriting algorithms used in mediation systems. We propose 4 such constraints and link SLD-resolution to 3 classical algorithms: the bucket, the inverse-rules and the MINICON algorithms.

We discuss the problem of specializing a definite program with respect to sets of positive and negative examples, following Bostrom and Idestam-Almquist. This problem is very relevant in the field of inductive learning. First we show that there exist sets of examples that have no correct program, i.e., no program which implies all positive and no negative examples. Hence it only makes sense to talk about specialization problems for which a solution (a correct program) exists. To solve such problems, we first introduce UD1-specialization, based upon the transformation rule unfolding. We show UD1-specialization is incomplete - some solvable specialization problems do not have a UD1-specialization as solution - and generalize it to the stronger UD2-specialization. UD2 also turns out to be incomplete. An analysis of program specialization, using the subsumption theorem for SLD-resolution, shows the reason for this incompleteness. Based on that analysis, we then define UDS-specialization...

In (Gerla and Sessa, Fuzzy Logic and Soft Computing, Kluwer, Norwell, 1999, pp. 19-31) a methodology that allows to manage uncertain and imprecise information in the frame of the declarative paradigm of Logic Programming has been proposed. With this aim, a Similarity relation R between function and predicate symbols in the language of a logic program is considered. Approximate inferences are then possible since similarity relation allows us to manage alternative instances of entities that can be considered "equal" with a given degree. The declarative semantics of the proposed transformation technique of logic programs is analyzed. The notion of fuzzy least Herbrand model is also introduced. In this paper the corresponding operational semantics is provided by introducing a modiÿed version of SLD resolution. This top-down refutation procedure overcomes failure situations in the uniÿcation process by using the similarity relation. A generalized notion of most general uniÿer provides a numeric value which gives a measure of the exploited approximation. In this way, the SLD resolution is enhanced since it is possible both to handle uncertain or imprecise information, and to compute approximate answer substitutions, with an associated approximation-degree, when failures of the exact inference process occur. It can lead to the implementation of a more general PROLOG interpreter, without detracting from the elegance of the language.

In this paper we present the main features an implementation details of a programming language that we call Bousi∼Prolog. It can be seen as an extension of Prolog able to deal with similarity-based fuzzy unification ("Bousi" is the Spanish acronym for "fuzzy unification by similarity"). The main goal is the implementation of a declarative programming language well suited for flexible query answering. The operational semantics of Bousi∼Prolog is an adaptation of the SLD resolution principle where classical unification has been replaced by an algorithm based on similarity relations defined on a syntactic domain. A similarity relation is an extension of the crisp notion of equivalence relation and it can be useful in any context where the concept of equality must be weakened. Hence, the syntax of Bousi∼Prolog is an extension of the Prolog's language: in general, a Bousi∼Prolog program is a set of Prolog clauses plus a set of similarity equations.

FASILL (acronym of "Fuzzy Aggregators and Similarity Into a Logic Language") is a fuzzy logic programming language with implicit/explicit truth degree annotations, a great variety of connectives and unification by similarity. FASILL integrates and extends features coming from MALP (Multi-Adjoint Logic Programming, a fuzzy logic language with explicitly annotated rules) and Bousi~Prolog (which uses a weak unification algorithm and is well suited for flexible query answering). Hence, it properly manages similarity and truth degrees in a single framework combining the expressive benefits of both languages. This paper presents the main features and implementations details of FASILL. Along the paper we describe its syntax and operational semantics and we give clues of the implementation of the lattice module and the similarity module, two of the main building blocks of the new programming environment which enriches the FLOPER system developed in our research group.

We present a new fuzzy logic programming Language, called LIKELOG, to be used for approximated reat;oning and for fuzzy deductive database applications. The core component of the system is the algori thm of unification, which expands the Martelli-Montanari unification algorithm introducing two similarity relations. The resolution mechanism is a straightforward application of this kind of expanded unification. Given such a fuzzy resolution ruLe we present a fuzzy logic programming system where computed answert; are suppLied wit.h a degree of derivation. The LIKELOG system is more flexible respect to the traditional information systerru;. LIKELOG retrieves answers that are "similar" to the user query. In LIKELOG the user can not only insert queries, hut can also introduce his/ her own relation of similarity, in order to obtain answers that, although approximate, meet hi::i/ her own particular preferenc!:'.:;.

Bousi∼Prolog is an extension of the standard Prolog language. Its operational semantics is an adaptation of the SLD resolution principle where classical unification has been replaced by a fuzzy unification algorithm based on fuzzy relations defined on a syntactic domain. In this paper we describe how Bousi∼Prolog may contribute to resolve several problems extracted from different application areas, where it is mandatory to deal with vagueness and uncertain knowledge, such as: flexible deductive databases, fuzzy control, fuzzy experts systems, data retrieval or approximate reasoning. Hence, through several (small but meaningful) examples we show the great potential of this programming language.

Bousi∼Prolog is a fuzzy logic programming language whose main objective is to make flexible the query answering process. Its operational mechanism is a extension of the SLD-resolution (called weak resolution) where the classical syntactic unification algorithm has been replaced by a fuzzy one. This paper presents a generic method for the unification of linguistic terms (i.e. fuzzy sets) which is also applicable to other programming languages with an operational semantics based on some kind of weak resolution mechanism. The basic idea is to compile the information provided by fuzzy sets, generating a binary fuzzy relation on the set of their associated linguistic labels. Subsequently, this fuzzy relation can be used in a standard, completely integrated way inside the unification mechanism of the Bousi∼Prolog system, what allows us to handle linguistic labels on an equal basis with regard other syntactic symbols occurring in the source program. This is a novel approach because it is the first time that fuzzy sets are introduced into the core of a Prolog system by means of compilation techniques and combining fuzzy relations with weak unification. An important feature of this approach is its simplicity, since the inclusion is carried out in a very natural way without affecting the operational semantics of the Bousi∼Prolog language and with very few syntactical modifications. All these reasons convert our approach in a good alternative to the techniques used by other fuzzy Prolog systems.

This paper was motivated by a need to consider the time efficiency of Prolog programs. In the context of logic programming, we consider the minimal lengths of refutations of a goal with respect to a program. We present proofs of a number of results of this type. We are especially interested in the special case of testing for membership in a given set of terms. Concomitantly, we are led to classify sets of terms in a way appropriate for these considerations. Since our results for logic programming provide lower bounds, they will immediately imply corresponding lower bounds for pure Prolog.

The simplicity and elegance of definite clauses makes this formalism attractive from a theoretical point of view. The objects in this formalism are the uninterpreted terms over the Herbrand universe. Programming however is not done exclusively in the Herbrand universe, but uses higher level concepts such as arithmetic. In that sense we can view definite clauses as the Turing machines of Logic Programming. This gap between theory and programming practice can be reduced by introducing user-oriented domains into the formalism.

Page 1. THE DENOTATIONAL SEMANTICS OF HORN CLAUSES AS A PRODUCTION SYSTEM JL. Lassez and M. Maher Dept. of Computer Science University of Melbourne Parkville, Victoria, 3052 Australia. ABSTRACT We show how one of Nilsson's tenets on rule-based production systems, when applied to Horn clause programs, leads to a denotational semantics. This formalism, in turn provides a striking illustration of a second Nilsson tenet.

Bousi~Prolog is an extension of the standard Prolog language. Its operational semantics is an adaptation of the SLD resolution principle where classical unification has been replaced by a fuzzy unification algorithm based on fuzzy relations defined on a syntactic domain. In this paper we describe how BousiProlog may contribute to resolve several problems extracted from different application areas, where it is mandatory to deal with vagueness and uncertain knowledge, such as: flexible deductive databases, fuzzy control, fuzzy experts systems, data retrieval or approximate reasoning. Hence, through several (small but meaningful) examples we show the great potential of this programming language.

The classic approach to text categorisation is based on a learning process that requires a large number of labelled training texts to achieve an accurate performance. The most notable problem is that labelled texts are difficult to generate because categorising shorts texts as snippets or messages must be done by human developers, although unlabelled short texts could be easily collected. In this paper, we present an approach to categorising unlabelled short texts which only require, as user input, the category names defined by means of an ontology of terms modelled by a set of proximity equations. The proposed classification process is based on the ability of a fuzzy extension of the standard Prolog language named Bousi∼Prolog for flexible matching and knowledge representation. This declarative approach provides a text classifier which is fast and easy to build, as well as a classification process that is easy for the user to understand. The results of the experiment showed that the proposed method achieved a reasonably good performance.

tVe use the notions of closures and fair chaotic iterations to give a semantics to logic programs. The relationships between the semantics c;f individual rules and the semantics of the whole program are established and an applicationjto parallel processing is mentioncti. A chaotic fixed point theorem is given. which carries the non-determinism inherent to resolution. Finally. \ve introduce a general definition of finite failure and the concept of fair SLD resolution, and show that this procedure is sound and strongly complete with respect to both success and finite failure. thus extending a result of Apt and Van Emden (1982).