Weighted defeasible knowledge bases and a multipreference semantics for a deep neural network model

From Weighted Conditionals of Multilayer Perceptrons to Gradual Argumentation and Back

A fuzzy multipreference semantics has been recently proposed for weighted conditional knowledge bases, and used to develop a logical semantics for Multilayer Perceptrons, by regarding a deep neural network (after training) as a weighted conditional knowledge base. This semantics, in its different variants, suggests some gradual argumentation semantics, which are related to the family of the gradual semantics studied by Amgoud and Doder. The relationships between weighted conditional knowledge bases and MLPs extend to the proposed gradual semantics to capture the stationary states of MPs, in ag…

A conditional, a fuzzy and a probabilistic interpretation of self-organising maps

In this paper we establish a link between fuzzy and preferential semantics for description logics and Self-Organising Maps, which have been proposed as possible candidates to explain the psychological mechanisms underlying category generalisation. In particular, we show that the input/output behavior of a Self-Organising Map after training can be described by a fuzzy description logic interpretation as well as by a preferential interpretation, based on a concept-wise multipreference semantics, which takes into account preferences with respect to different concepts and has been recently propose…

From Common Sense Reasoning to Neural Network Models through Multiple Preferences: an overview

In this paper we discuss the relationships between conditional and preferential logics and neural network models, based on a multi-preferential semantics. We propose a concept-wise multipreference semantics, recently introduced for defeasible description logics to take into account preferences with respect to different concepts, as a tool for providing a semantic interpretation to neural network models. This approach has been explored both for unsupervised neural network models (Self-Organising Maps) and for supervised ones (Multilayer Perceptrons), and we expect that the same approach might b…

一阶c-表示与基于代价的语义之间的语义桥梁：初步视角

Semantic Bridges Between First Order c-Representations and Cost-Based Semantics: An Initial Perspective

该研究在语义层面比较了加权知识库的基于代价语义与c-表示非单调推理方法，证明特定条件下二者语义结构在相对代价下等价、部分蕴涵概念可等价表达，为两类研究的后续工作提供助力。

多值论证、条件句与渐进论证的概率语义

Many-valued Argumentation, Conditionals and a Probabilistic Semantics for Gradual Argumentation

本文提出渐进论证语义的多值偏好解释框架，支持条件推理与布尔组合，并以 ASP 实现有限值加权论证图推理，进而构建概率语义。

Reasoning on Multi-Relational Contextual Hierarchies via Answer Set Programming with Algebraic Measures

Dealing with context dependent knowledge has led to different formalizations of the notion of context. Among them is the Contextualized Knowledge Repository (CKR) framework, which is rooted in description logics but links on the reasoning side strongly to logic programs and Answer Set Programming (ASP) in particular. The CKR framework caters for reasoning with defeasible axioms and exceptions in contexts, which was extended to knowledge inheritance across contexts in a coverage (specificity) hierarchy. However, the approach supports only this single type of contextual relation and the reasonin…

On the KLM properties of a fuzzy DL with Typicality

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 …