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

Defeasible Reasoning in SROEL: from Rational Entailment to Rational Closure

In this work we study a rational extension $SROEL^R T$ of the low complexity description logic SROEL, which underlies the OWL EL ontology language. The extension involves a typicality operator T, whose semantics is based on Lehmann and Magidor's ranked models and allows for the definition of defeasible inclusions. We consider both rational entailment and minimal entailment. We show that deciding instance checking under minimal entailment is in general $Π^P_2$-hard, while, under rational entailment, instance checking can be computed in polynomial time. We develop a Datalog calculus for instance…

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…

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。

Approximating Defeasible Logics to Improve Scalability

Defeasible rules are used in providing computable representations of legal documents and, more recently, have been suggested as a basis for explainable AI. Such applications draw attention to the scalability of implementations. The defeasible logic $DL(\partial_{||})$ was introduced as a more scalable alternative to $DL(\partial)$, which is better known. In this paper we consider the use of (implementations of) $DL(\partial_{||})$ as a computational aid to computing conclusions in $DL(\partial)$ and other defeasible logics, rather than as an alternative to $DL(\partial)$. We identify condition…

时态多值条件逻辑：初步报告

Temporal Many-valued Conditional Logics: a Preliminary Report

该研究提出多值时态条件逻辑，将含典型性的多值逻辑与LTL时态算子结合以刻画系统动态性，并探索了其在渐进式论证中的实例化应用。