On the KLM properties of a fuzzy DL with Typicality
This work addresses theoretical properties of a fuzzy logic framework for AI, but it is incremental as it builds on prior extensions without introducing new paradigms or broad applications.
The paper investigates the properties of a fuzzy logic extended with a typicality operator, originally proposed for interpreting multilayer perceptrons as conditional knowledge bases, by studying a monotonic extension called ALC^FT and its reformulation of KLM properties, finding that most properties hold depending on specific conditions.
The paper investigates the properties of a fuzzy logic of typicality. The extension of fuzzy logic with a typicality operator was proposed in recent work to define a fuzzy multipreference semantics for Multilayer Perceptrons, by regarding the deep neural network as a conditional knowledge base. In this paper, we study its properties. First, a monotonic extension of a fuzzy ALC with typicality is considered (called ALC^FT) and a reformulation the KLM properties of a preferential consequence relation for this logic is devised. Most of the properties are satisfied, depending on the reformulation and on the fuzzy combination functions considered. We then strengthen ALC^FT with a closure construction by introducing a notion of faithful model of a weighted knowledge base, which generalizes the notion of coherent model of a conditional knowledge base previously introduced, and we study its properties.