Reasoning about Typicality and Probabilities in Preferential Description Logics

A Description Logic Framework for Commonsense Conceptual Combination Integrating Typicality, Probabilities and Cognitive Heuristics

We propose a nonmonotonic Description Logic of typicality able to account for the phenomenon of concept combination of prototypical concepts. The proposed logic relies on the logic of typicality ALC TR, whose semantics is based on the notion of rational closure, as well as on the distributed semantics of probabilistic Description Logics, and is equipped with a cognitive heuristic used by humans for concept composition. We first extend the logic of typicality ALC TR by typicality inclusions whose intuitive meaning is that "there is probability p about the fact that typical Cs are Ds". As in the…

条件逻辑中多层感知机的典型性优先解释

A preferential interpretation of MultiLayer Perceptrons in a conditional logic with typicality

本文研究知识表示中可废止推理的多优先语义与多层神经网络的关系，利用带典型性的加权知识库为多层感知机提供优先解释，并通过模型检测和蕴含方法验证其条件性质。

Complexity and scalability of defeasible reasoning in many-valued weighted knowledge bases with typicality

Weighted knowledge bases for description logics with typicality under a "concept-wise" multi-preferential semantics provide a logical interpretation of MultiLayer Perceptrons. In this context, Answer Set Programming (ASP) has been shown to be suitable for addressing defeasible reasoning in the finitely many-valued case, providing a $Π^p_2$ upper bound on the complexity of the problem, nonetheless leaving unknown the exact complexity and only providing a proof-of-concept implementation. This paper fulfils the lack by providing a $P^{NP[log]}$-completeness result and new ASP encodings that deal …

An ASP approach for reasoning in a concept-aware multipreferential lightweight DL

In this paper we develop a concept aware multi-preferential semantics for dealing with typicality in description logics, where preferences are associated with concepts, starting from a collection of ranked TBoxes containing defeasible concept inclusions. Preferences are combined to define a preferential interpretation in which defeasible inclusions can be evaluated. The construction of the concept-aware multipreference semantics is related to Brewka's framework for qualitative preferences. We exploit Answer Set Programming (in particular, asprin) to achieve defeasible reasoning under the multi…

A framework for a modular multi-concept lexicographic closure semantics

We define a modular multi-concept extension of the lexicographic closure semantics for defeasible description logics with typicality. The idea is that of distributing the defeasible properties of concepts into different modules, according to their subject, and of defining a notion of preference for each module based on the lexicographic closure semantics. The preferential semantics of the knowledge base can then be defined as a combination of the preferences of the single modules. The range of possibilities, from fine grained to coarse grained modules, provides a spectrum of alternative semant…

面向答案集编程的条件推理框架

A framework for Conditional Reasoning in Answer Set Programming

本文提出了一种基于条件逻辑的ASP框架，用于实现条件推理，并给出了复杂度上界。