Defeasible RDFS via rational closure
Casini G., Straccia U.
In the field of non-monotonic logics, the notion of Rational Closure (RC) is acknowledged as a prominent approach. In recent years, RC has gained even more popularity in the context of Description Logics (DLs), the logic underpinning the semantic web standard ontology language OWL 2, whose main ingredients are classes and roles. In this work, we show how to integrate RC within the triple language RDFS, which together with OWL2 are the two major standard semantic web ontology languages. To do so, we start from ?df, which is the logic behind RDFS, and then extend it to ?df?, allowing to state that two entities are incompatible. Eventually, we propose defeasible ?df? via a typical RC construction. The main features of our approach are: (i) unlike most other approaches that add an extra non-monotone rule layer on top of monotone RDFS, defeasible ?df? remains syntactically a triple language and is a simple extension of ?df? by introducing some new predicate symbols with specific semantics. In particular, any RDFS reasoner/store may handle them as ordinary terms if it does not want to take account for the extra semantics of the new predicate symbols; (ii) the defeasible ?df? entailment decision procedure is build on top of the ?df? entailment decision procedure, which in turn is an extension of the one for ?df via some additional inference rules favouring an potential implementation; and (iii) defeasible ?df? entailment can be decided in polynomial time.Source: ISTI Technical Reports 008/2020, 2020, 2020
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BKLM - An expressive logic for defeasible reasoning
Paterson-jones G., Casini G., Meyer T.
Propositional KLM-style defeasible reasoning involves a core propositional logic capable of expressing defeasible (or conditional) implications. The semantics for this logic is based on Kripke-like structures known as ranked interpretations. KLM-style defeasible entailment is referred to as rational whenever the defeasible entailment relation under consideration generates a set of defeasible implications all satisfying a set of rationality postulates known as the KLM postulates. In a recent paper Booth et al. proposed PTL, a logic that is more expressive than the core KLM logic. They proved an impossibility result, showing that defeasible entailment for PTL fails to satisfy a set of rationality postulates similar in spirit to the KLM postulates. Their interpretation of the impossibility result is that defeasible entailment for PTL need not be unique. In this paper we continue the line of research in which the expressivity of the core KLM logic is extended. We present the logic Boolean KLM (BKLM) in which we allow for disjunctions, conjunctions, and negations, but not nesting, of defeasible implications. Our contribution is twofold. Firstly, we show (perhaps surprisingly) that BKLM is more expressive than PTL. Our proof is based on the fact that BKLM can characterise all single ranked interpretations, whereas PTL cannot. Secondly, given that the PTL impossibility result also applies to BKLM, we adapt the different forms of PTL entailment proposed by Booth et al. to apply to BKLM.Source: 18th INTERNATIONAL WORKSHOP ON NON-MONOTONIC REASONING (NMR 2020), pp. 170–178, online conference, due to COVID-19 pandemic, 12-14/09/2020
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Rational Defeasible Belief Change
Casini G., Meyer T., Varzinczak I.
We present a formal framework for modelling belief change within a nonmonotonic reasoning system. Belief change and non-monotonic reasoning are two areas that are formally closely related, with recent attention being paid towards the analysis of belief change within a non-monotonic environment. In this paper we consider the classical AGM belief change operators, contraction and revision, applied to a defeasible setting in the style of Kraus, Lehmann, and Magidor. The investigation leads us to the consideration of the problem of iterated change, generalising the classical work of Darwiche and Pearl. We characterise a family of operators for iterated revision, followed by an analogous characterisation of operators for iterated contraction. We start considering belief change operators aimed at preserving logical consistency, and then characterise analogous operators aimed at the preservation of coherence--an important notion within the field of logic-based ontologies.Source: 17th International Conference on Principles of Knowledge Representation and Reasoning (KR2020), pp. 213–222, Online conference, due to the Covid-19 pandemic, 12-18/09/2020
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Principles of KLM-style Defeasible Description Logics
Britz K., Casini G., Meyer T., Moodley K., Sattler U., Varzinczak I.
The past 25 years have seen many attempts to introduce defeasible-reasoning capabilities into a description logic setting. Many, if not most, of these attempts are based on preferential extensions of description logics, with a significant number of these, in turn, following the so-called KLM approach to defeasible reasoning initially advocated for propositional logic by Kraus, Lehmann, and Magidor. Each of these attempts has its own aim of investigating particular constructions and variants of the (KLM-style) preferential approach. Here our aim is to provide a comprehensive study of the formal foundations of preferential defeasible reasoning for description logics in the KLM tradition.
We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus, Lehmann, and Magidor in the propositional case. In particular, we consider a natural and intuitive semantics for defeasible subsumption, and we investigate KLM-style syntactic properties for both preferential and rational subsumption. Our contribution includes two representation results linking our semantic constructions to the set of preferential and rational properties considered. Besides showing that our semantics is appropriate, these results pave the way for more effective decision procedures for defeasible reasoning in description logics. Indeed, we also analyse the problem of non-monotonic reasoning in description logics at the level of entailment and present an algorithm for the computation of rational closure of a defeasible knowledge base. Importantly, our algorithm relies completely on classical entailment and shows that the computational complexity of reasoning over defeasible knowledge bases is no worse than that of reasoning in the underlying classical DL ALC.Source: ACM transactions on computational logic 22 (2020): 1–46. doi:10.1145/3420258
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