Extending Prolog with Incomplete Fuzzy Information

TL;DR

This paper extends Fuzzy Prolog to handle incomplete information using default reasoning, enabling the combination of crisp and fuzzy knowledge representations in logic programming, with a complete semantics and practical implementation.

Contribution

It introduces a new version of Fuzzy Prolog that incorporates default reasoning to manage incomplete information and combines fuzzy and crisp logic, with a complete semantics and implementation.

Findings

Enhanced Fuzzy Prolog handles incomplete information effectively.

The new framework combines fuzzy and crisp logic in Prolog.

Implementation is available in the Ciao system.

Abstract

Incomplete information is a problem in many aspects of actual environments. Furthermore, in many sceneries the knowledge is not represented in a crisp way. It is common to find fuzzy concepts or problems with some level of uncertainty. There are not many practical systems which handle fuzziness and uncertainty and the few examples that we can find are used by a minority. To extend a popular system (which many programmers are using) with the ability of combining crisp and fuzzy knowledge representations seems to be an interesting issue. Our first work (Fuzzy Prolog) was a language that models $\mathcal{B}([0,1])$-valued Fuzzy Logic. In the Borel algebra, $\mathcal{B}([0,1])$, truth value is represented using unions of intervals of real numbers. This work was more general in truth value representation and propagation than previous works. An interpreter for this language using Constraint Logic Programming over Real numbers (CLP(${\cal R}$)) was implemented and is available in the Ciao system. Now, we enhance our former approach by using default knowledge to represent incomplete information in Logic Programming. We also provide the implementation of this new framework. This new release of Fuzzy Prolog handles incomplete information, it has a complete semantics (the previous one was incomplete as Prolog) and moreover it is able to combine crisp and fuzzy logic in Prolog programs. Therefore, new Fuzzy Prolog is more expressive to represent real world. Fuzzy Prolog inherited from Prolog its incompleteness. The incorporation of default reasoning to Fuzzy Prolog removes this problem and requires a richer semantics which we discuss.