Susana Munoz-Hernandez

RFuzzy: Syntax, semantics and implementation details of a simple and expressive fuzzy tool over Prolog

We present the RFuzzy framework, a Prolog-based tool for representing and reasoning with fuzzy information. The advantages of our framework in comparison to previous tools along this line of research are its easy, user-friendly syntax, and its expressivity through the availability of default values and types. In this approach we describe the formal syntax, the operational semantics and the declarative semantics of RFuzzy (based on a lattice). A least model semantics, a least fixpoint semantics and an operational semantics are introduced and their equivalence is proven. We provide a real implementation that is free and available. (It can be downloaded from http://babel.ls.fi.upm.es/software/rfuzzy/.) Besides implementation details, we also discuss some actual applications using RFuzzy.

How to Incorporate Negation in a Prolog Compiler

Knowledge representation based applications require a more complete set of capabilities than those offered by conventional Prolog compilers. Negation is, probably, the most important one. The inclusion of negation among the logical facilities of LP has been a very active area of research, and several techniques have been proposed. However, the negation capabilities accepted by current Prolog compilers are very limited. In this paper, we discuss the possibility to incorporate some of these techniques in a Prolog compiler in an efficient way. Our idea is to mix some of the existing proposals guided by the information provided by a global analysis of the source code.

Solving collaborative fuzzy agents problems with CLP( FD )

Truth values associated to fuzzy variables can be represented in an ordeal of different flavors, such as real numbers, percentiles, intervals, unions of intervals, and continuous or discrete functions on different domains. Many of the most interesting fuzzy problems deal with a discrete range of truth values. In this work we represent these ranges using Constraint Logic Programming over Finite Domains (CLP(

Efficient Negation Using Abstract Interpretation

\mathcal{FD}

Constructive Intensional Negation

)). This allows to produce finite enumerations of constructive answers instead of complicated, hardly self-explanatory, constraints expressions. Another advantage of representing fuzzy models through finite domains is that some of the existing techniques and algorithms of the field of distributed constraint programming can be borrowed. In this paper we exploit these considerations in order to create a new generation of collaborative fuzzy agents in a distributed environment.

RFuzzy: An Expressive Simple Fuzzy Compiler

While negation has been a very active area of research in logic programming, comparatively few papers have been devoted to implementation issues. Furthermore, the negation-related capabilities of current Prolog systems are limited. We recently presented a novel method for incorporating negation in a Prolog compiler which takes a number of existing methods (some modified and improved by us) and uses them in a combined fashion. The method makes use of information provided by a global analysis of the source code. Our previous work focused on the systematic description of the techniques and the reasoning about correctness and completeness of the method, but provided no experimental evidence to evaluate the proposal. In this paper, we provide experimental data which indicates that the method is not only feasible but also quite promising from the efficiency point of view. In addition, the tests have provided new insight as to how to improve the proposal further. Abstract interpretation techniques (in particular those included in the Ciao Prolog system preprocessor) are important for the strategy to success.

Fuzzy Cognitive Layer in RoboCupSoccer

Although negation is an active area of research in Logic Programming, sound and complete implementations are still absent from actual Prolog systems. One of the most promising techniques in the literature is Intensional Negation (IN), which follows a transformational approach: for each predicate p in a program its negative counterpart \({\mathit{intneg}}(p)\) is generated. However, implementations of IN have not been included in Prolog environments due, in part, to the lack of details and explicit techniques, such as the treatment of universally quantified goals. In this paper, we describe a variant of IN, which we have called Constructive Intensional Negation (CIN). Unlike earlier proposals, CIN does not resort to a special resolution strategy when dealing with universally quantified formulae, which has been instrumental in having an effective implementation. Among the contributions of this work we can mention a full implementation being tested for its integration in the Ciao Prolog system and some formal results with their associated proofs.

Implementation results in classical constructive negation

Fuzzy reasoning is a very productive research field that during the last years has provided a number of theoretical approaches and practical implementation prototypes. Nevertheless, the classical implementations, like Fril, are not adapted to the latest formal approaches, like multi-adjoint logic semantics. Some promising implementations, like Fuzzy Prolog, are so general that the regular user/programmer does not feel comfortable because either the representation of fuzzy concepts is complex or the results of the fuzzy queries are difficult to interpret. In this paper we present a modern framework, RFuzzy , that is modeling multi-adjoint logic in a practical way. It provides some extensions as default values (to represent missing information), partial default values (for a subset of data) and typed variables. RFuzzy represents the truth value of predicates using facts, rules and also can define fuzzy predicates as continuous functions. Queries are answered with direct results (instead of providing complex constraints), so it is easy to use for any person that wants to represent a problem using fuzzy reasoning in a simple way (just using the classical fuzzy representation with real numbers). The most promising characteristic of RFuzzy is that the user can obtain constructive answers to queries that restrict the truth value.

RFuzzy∔A framework for multi-adjoint Fuzzy Logic Programming

RoboCupSoccer domain has several leagues which varies in the rule of play such as specification of players, number of players, field size, and time length. Nevertheless, each RoboCup league is a variant of a soccer league and therefore they are based on some basic rules of soccer. A layered design of agents system presented in [1] shows a modular approach to build control for a team of robots participating in RoboCupSoccer E-League. Based on this design, we propose a generalized architecture offering flexibility to switch between leagues and programming language while maintaining Prolog as cognitive layer. Prolog is a perfect tool to design strategies for soccer players using simple rules close to human reasoning. Sometimes this reasoning needs to deal with uncertainty, fuzziness or incompleteness of the information. In these cases it is useful Fuzzy Prolog [11,8,10,9]. In this paper we propose to use a combination of Prolog (that is crisp) and Fuzzy Prolog to implement the cognitive layer in RoboCupSoccer, which has the advantage of incorporating as conventional logic as fuzzy logic in this layer. A prototype of a team based on this architecture has been build for RoboCup Soccer Simulator, and we show that this approach provides a convenient way of incorporating a team strategy in high level (human-like) manner, where technical details are encapsulated and fuzzy information is represented.

Computational thinking: Panorama of the Americas

Logic Programming has been advocated as a language for system specification, especially for those involving logical behaviours, rules and knowledge. However, modeling problems involving negation, which is quite natural in many cases, is somewhat limited if Prolog is used as the specification / implementation language. These restrictions are not related to theory viewpoint, where users can find many different models with their respective semantics; they concern practical implementation issues. The negation capabilities supported by current Prolog systems are rather constrained, and there is no a correct and complete implementation available. In this paper, we refine and propose some extensions to the classical method of constructive negation, providing the complete theoretical algorithm. Furthermore, we also discuss implementation issues providing a preliminary implementation and also an optimized one to negate predicates with a finite number of solutions.