On the KLM Properties of a Fuzzy DL with Typicality

Weighted Conditional EL^bot Knowledge Bases with Integer Weights: an ASP Approach

“…Undecidability results for fuzzy description logics with general inclusion axioms [12,4] motivate the investigation of multi-valued approximations of fuzzy multipreference entailment. This is a first step towards the definition of proof methods for multi-valued extensions of our concept-wise preferential semantics based on a notion of faithful interpretations [15]. Other possible extensions concern the definition of multiple typicality operators, based on the combination of selected concepts, and a temporal extension to capture the transient behavior of Multilayer Perceptrons.…”

An ASP approach for reasoning on neural networks under a finitely many-valued semantics for weighted conditional knowledge bases

“…of some typicality inclusion T(C i ) ⊑ D. The definition of a weighted Ł n ALCT knowledge base is defined similarly. Let us consider the following example adapted from [19].…”

“…The weaker notion of faithfulness allows to define a larger class of fuzzy multipreference models of a weighted knowledge base, compared to the class of coherent models. This allows a larger class of monotone non-decreasing activation functions in neural network models to be captured, whose activation function is monotonically non-decreasing (we refer to [25], extended version, and [19].…”

“…The properties of faithful entailment have been studied in [19]. Faithful entailment is well-behaved: it deals with specificity and irrelevance; it is not subject to inheritance blocking; it satisfies many KLM properties of a preferential consequence relation [32,34], depending on their fuzzy reformulation and on the chosen combination functions.…”

“…Undecidability results for fuzzy DLs with general inclusion axioms [13,6] motivate the investigation of multi-valued approximations of fuzzy multipreference entailment. In this paper, we restrict to the case of finitely many-valued Description Logics [17,4,3,7], and reconsider the fuzzy multipreference semantics based on the notions of coherent [25], faithful [19] and ϕ-coherent [18] model of a defeasible KB. The last notion is suitable to characterize the stationary states of MLPs and is related to the previously introduced notion of coherent multipreference interpretation.…”