We present a continuation to our previous work, in which we developed the MR-CKR framework to reason with knowledge overriding across contexts organized in multi-relational hierarchies. Reasoning is realized via ASP with algebraic measures, allowing for flexible definitions of preferences. In this paper, we show how to apply our theoretical work to real autonomous-vehicle scene data. Goal of this work is to apply MR-CKR to the problem of generating challenging scenes for autonomous vehicle learning. In practice, most of the scene data for AV learning models common situations, thus it might be difficult to capture cases where a particular situation occurs (e.g. partial occlusions of a crossing pedestrian). The MR-CKR model allows for data organization exploiting the multi-dimensionality of such data (e.g., temporal and spatial). Reasoning over multiple contexts enables the verification and configuration of scenes, using the combination of different scene ontologies. We describe a framework for semantically guided data generation, based on a combination of MR-CKR and Algebraic Measures. The framework is implemented in a proof-of-concept prototype exemplifying some cases of scene generation.

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 reasoning procedures work only for restricted hierarchies, due to non-trivial issues with model preference under exceptions. In this paper, we overcome these limitations and present a generalization of CKR hierarchies to multiple contextual relations, along with their interpretation of defeasible axioms and preference. To support reasoning, we use ASP with algebraic measures, which is a recent extension of ASP with weighted formulas over semirings that allows one to associate quantities with interpretations depending on the truth values of propositional atoms. Notably, we show that for a relevant fragment of CKR hierarchies with multiple contextual relations, query answering can be realized with the popular asprin framework. The algebraic measures approach is more powerful and enables e.g.

Reasoning on defeasible knowledge is a topic of interest in the area of description logics, as it is related to the need of representing exceptional instances in knowledge bases. In this direction, in our previous works we presented a framework for representing (contextualized) OWL RL knowledge bases with a notion of justified exceptions on defeasible axioms: reasoning in such framework is realized by a translation into ASP programs. The resulting reasoning process for OWL RL, however, introduces a complex encoding in order to capture reasoning on the negative information needed for reasoning on exceptions. In this paper, we apply the justified exception approach to knowledge bases in $\textit{DL-Lite}_{\cal R}$, i.e., the language underlying OWL QL. We provide a definition for $\textit{DL-Lite}_{\cal R}$ knowledge bases with defeasible axioms and study their semantic and computational properties. In particular, we study the effects of exceptions over unnamed individuals. The limited form of $\textit{DL-Lite}_{\cal R}$ axioms allows us to formulate a simpler ASP encoding, where reasoning on negative information is managed by direct rules. The resulting materialization method gives rise to a complete reasoning procedure for instance checking in $\textit{DL-Lite}_{\cal R}$ with defeasible axioms. Under consideration in Theory and Practice of Logic Programming (TPLP).

Representation of defeasible information is of interest in description logics, as it is related to the need of accommodating exceptional instances in knowledge bases. In this direction, in our previous works we presented a datalog translation for reasoning on (contextualized) OWL RL knowledge bases with a notion of justified exceptions on defeasible axioms. While it covers a relevant fragment of OWL, the resulting reasoning process needs a complex encoding in order to capture reasoning on negative information. In this paper, we consider the case of knowledge bases in $\textit{DL-Lite}_{\cal R}$, i.e. the language underlying OWL QL. We provide a definition for $\textit{DL-Lite}_{\cal R}$ knowledge bases with defeasible axioms and study their properties. The limited form of $\textit{DL-Lite}_{\cal R}$ axioms allows us to formulate a simpler encoding into datalog (under answer set semantics) with direct rules for reasoning on negative information. The resulting materialization method gives rise to a complete reasoning procedure for instance checking in $\textit{DL-Lite}_{\cal R}$ with defeasible axioms.

This paper is an appendix to the paper "Reasoning with Justifiable Exceptions in Contextual Hierarchies" by Bozzato, Serafini and Eiter, 2018 [2]. It provides further details on the language, the complexity results and the datalog translation introduced in the main paper.