Abstract
AbstractDealing 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 nontrivial 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, for example, reasoning with epistemic queries over CKRs, which opens interesting perspectives for the use of quantitative ASP extensions in other applications.
Highlights
Representing and reasoning with context dependent knowledge is a fundamental theme in AI, with proposals dating back to the works of McCarthy (1993) and Giunchiglia and Serafini (1994)
Reasoning from Contextualized Knowledge Repositories (CKR) strongly links to logic programming, as the knowledge bases (KBs) are over a Horn-description logic and the working of defeasible axioms was inspired by conflict handling in inheritance logic programs (Buccafurri et al . 1999)
We show that in case of a multirelational hierarchy, the answer sets of P K(K) ∪ Ppref found optimal by the asprin preference GlobPref coincide with the sets I(I(χ)) where χ is the clashing assumption of a named preferred CAS model (i.e. CKR model) of K
Summary
Representing and reasoning with context dependent knowledge is a fundamental theme in AI, with proposals dating back to the works of McCarthy (1993) and Giunchiglia and Serafini (1994). 2018b) to cater for defeasible axioms in local contexts and knowledge inheritance across hierarchies, based on a coverage contextual relation (Serafini and Homola 2012). This approach, is limited to reason only on hierarchies based on this single type of contextual relation. Reasoning on Multirelational Contextual Hierarchies via ASP with Algebraic Measures 595 connectedness condition, multirelational CKRs can be expressed in asprin. This enables us to use the asprin solver to evaluate preferences for CKRs, which is showcased in a prototype implementation. ASP extended with preferences or algebraic computations is a valuable tool to express CKR extensions and reasoning on them, with a promising perspective for further research
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