Non-expansive Fuzzy ALC

TL;DR

This paper introduces non-expansive fuzzy ALC, a logic that balances expressiveness and computational complexity by combining Zadeh and Lukasiewicz connectives with constant shift operators, enabling efficient reasoning.

Contribution

It proposes a novel fuzzy description logic that extends Zadeh with Lukasiewicz connectives restricted by rational constants, and provides a tableau reasoning method with EXPTIME complexity.

Findings

The logic supports modeling dampened inheritance of properties.

A tableau method for reasoning over TBoxes is developed.

Reasoning complexity remains in EXPTIME, comparable to classical ALC.

Abstract

Fuzzy description logics serve the representation of vague knowledge, typically letting concepts take truth degrees in the unit interval. Expressiveness, logical properties, and complexity vary strongly with the choice of propositional base. The Lukasiewicz propositional base is generally perceived to have preferable logical properties but often entails high complexity or even undecidability. Contrastingly, the less expressive Zadeh propositional base comes with low complexity but entails essentially no change in logical behaviour compared to the classical case. To strike a balance between these poles, we propose non-expansive fuzzy ALC, in which the Zadeh base is extended with Lukasiewicz connectives where one side is restricted to be a rational constant, that is, with constant shift operators. This allows, for instance, modelling dampened inheritance of properties along roles. We present an unlabelled tableau method for non-expansive fuzzy ALC, which allows reasoning over general TBoxes in EXPTIME like in two-valued ALC.