A Query Tool for $\mathcal{EL}$ with Non-monotonic Rules

Ivanov, Vadim; Knorr, Matthias; Leite, João

doi:10.1007/978-3-642-41335-3_14

Cited by 13 publications

(4 citation statements)

References 19 publications

(66 reference statements)

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“…Redl recently presented a generalization of this rewriting approach to external atoms in general HEX-programs (Redl 2017), still its applicability for reasoning with DL ontologies was demonstrated only using the lightweight logic DL-Lite. An implementation of reasoning in hybrid MKNF KBs (with lightweight ontologies) under the Well-Founded Semantics is also available (Alferes, Knorr, and Swift 2013;Ivanov, Knorr, and Leite 2013). The work in (Swift 2004) shows how reasoning about DL concepts, but not general TBoxes, can be implemented in ASP.…”

Section: Discussionmentioning

confidence: 99%

Combining Rules and Ontologies into Clopen Knowledge Bases

Bajraktari

Ortiz

Šimkus

2018

AAAI

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We propose Clopen Knowledge Bases (CKBs) as a new formalism combining Answer Set Programming (ASP) with ontology languages based on first-order logic. CKBs generalize the prominent r-hybrid and DL+LOG languages of Rosati, and are more flexible for specification of problems that combine open-world and closed-world reasoning. We argue that the guarded negation fragment of first-order logic(GNFO)—a very expressive fragment that subsumes many prominent ontology languages like Description Logics (DLs) and the guarded fragment—is an ontology language that can be used in CKBs while enjoying decidability for basic reasoning problems. We further show how CKBs can be used with expressive DLs of the ALC family, and obtain worst-case optimal complexity results in this setting. For DL-based CKBs, we define a fragment called separable CKBs (which still strictly subsumes r-hybrid and DL+LOG knowledge bases), and show that they can be rather efficiently translated into standard ASP programs. This approach allows us to perform basic inference from separable CKBs by reusing existing efficient ASP solvers. We have implemented the approach for separable CKBs containing ontologies in the DL ALCH, and present in this paper some promising empirical results for real-life data. They show that our approach provides a dramatic improvement over a naive implementation based on a translation of such CKBs into dl-programs.

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Section: Discussionmentioning

confidence: 99%

Combining Rules and Ontologies into Clopen Knowledge Bases

Bajraktari

Ortiz

Šimkus

2018

AAAI

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“…[8,27], in order to avoid an unnecessary replication, for a general in-depth discussion on non-monotone DLs and their characteristics. Also, but somewhat less related, are approaches based on some form of integration of non-monotone logic programs with DLs, as [20,33,34,36,42,43,44,47], although we will not address them here, except for those cases involving tractable computational complexity.…”

Section: Related Workmentioning

confidence: 99%

“…those that in some way combine non-monotone logic programs with (low-complexity) DLs, there are some results that still preserve tractability (but only w.r.t. data complexity), such as [20,33,34,36,42,43,44]. Very roughly, in these works data complexity tractability is preserved for some form of hybrid normal logic programs under some well-founded semantics, provided that the underlying DL has a tractable instance checking procedure.…”

Section: Related Workmentioning

confidence: 99%

A polynomial Time Subsumption Algorithm for Nominal SafeELO⊥under Rational Closure

Casini

Straccia

Meyer

2019

Information Sciences

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Description Logics (DLs) under Rational Closure (RC) is a well-known framework for nonmonotonic reasoning in DLs. In this paper, we address the concept subsumption decision problem under RC for nominal safe E LO ⊥ , a notable and practically important DL representative of the OWL 2 profile OWL 2 EL.Our contribution here is to define a polynomial time subsumption procedure for nominal safe E LO ⊥ under RC that relies entirely on a series of classical, monotonic E L ⊥ subsumption tests. Therefore, any existing classical monotonic E L ⊥ reasoner can be used as a black box to implement our method. We then also adapt the method to one of the known extensions of RC for DLs, namely Defeasible Inheritance-based DLs without losing the computational tractability. * This is a preprint version of a paper accepted for publication in Information Sciences, DOI: https://doi.org/10.1016/j.ins.2018.09.037 1 https://www.w3.org/TR/owl2-overview/ 2.1 The DLs EL ⊥ , ELO ⊥ , and nominal safe ELO ⊥ EL ⊥ is the DL EL with the addition of the empty concept ⊥ [3]. It is a proper sublanguage of ALC. Note that considering EL alone would not make sense in our case as EL ontologies are always concept-satisfiable, while the notion of defeasible reasoning is built over a notion of conflict (see Example 1) which needs to be expressible in the language. ELO ⊥ is EL ⊥ extended with so-called nominal concepts (denoted with the letter O in the DL literature, while nominal safe ELO ⊥ is ELO ⊥ with some restrictions on the occurrence of nominals.Syntax. The vocabulary is given by a set of atomic concepts N C = {A 1 , . . . , A n }, a set of atomic roles N R = {r 1 , . . . , r m } and a set of individuals N O = {a, b, c, . . . }. All these sets are assumed to be finite. ELO ⊥ concept expressions C, D, . . . are built according to the following syntax:An ontology T (or TBox, or knowledge base) is a finite set of Generalised Concept Inclusion (GCI) axioms C ⊑ D (C is subsumed by D), meaning that all the objects in the concept C are also in the concept D. We use the expression C = D as shorthand for having both C ⊑ D and D ⊑ C.The DL EL ⊥ . A concept of the form {a} is called a nominal. EL ⊥ is ELO ⊥ without nominals.The DL nominal safe ELO ⊥ . Nominal safe ELO ⊥ is ELO ⊥ with some restrictions on the occurrence of nominals and is defined as follows [35]. An ELO ⊥ concept C is safe if C has only occurrences of nominals in subconcepts of the form ∃r.{a}; C is negatively safe (in short, n-safe) if C is either safe or a nominal. A GCI C ⊑ D is safe if C is n-safe and D is safe. An ELO ⊥ ontology is nominal safe if all its GCIs are safe. It is worth noting that nominal safeness is a quite commonly used pattern of nominals in OWL EL ontologies, as reported in [35].Semantics. An interpretation is a pair I = ∆ I , · I , where ∆ I is a non-empty set, called interpretation domain and · I is an interpretation function that 1. maps atomic concepts A into a set A I ⊆ ∆ I ; 2. maps ⊤ (resp. ⊥) into a set ⊤ I = ∆ I (resp. ⊥ I = ∅); 3. maps roles r into a set r I ⊆ ∆ I ×...

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“…Multi-Context Systems (MCSs) were introduced in [6], building on the work in [12,23], to address the need for a general framework that integrates knowledge bases expressed in heterogeneous KR formalisms. Intuitively, instead of designing a unifying language (see e.g., [13,22], and [19] with its reasoner NoHR [18]) to which other languages could be translated, in an MCS the different formalisms and knowledge bases are considered as modules, and means are provided to model the flow of information between them (cf. [1,17,20] and references therein for further motivation on hybrid languages and their connection to MCSs).…”

Section: Introductionmentioning

confidence: 99%

Minimal Change in Evolving Multi-Context Systems

Gonçalves

Knorr

Leite

2015

Progress in Artificial Intelligence

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Managed Multi-Context Systems (mMCSs) provide a general framework for integrating knowledge represented in heterogeneous KR formalisms. However, mMCSs are essentially static as they were not designed to run in a dynamic scenario. Some recent approaches, among them evolving Multi-Context Systems (eMCSs), extend mMCSs by allowing not only the ability to integrate knowledge represented in heterogeneous KR formalisms, but at the same time to both react to, and reason in the presence of commonly temporary dynamic observations, and evolve by incorporating new knowledge. The notion of minimal change is a central notion in dynamic scenarios, specially in those that admit several possible alternative evolutions. Since eMCSs combine heterogeneous KR formalisms, each of which may require different notions of minimal change, the study of minimal change in eMCSs is an interesting and highly nontrivial problem. In this paper, we study the notion of minimal change in eMCSs, and discuss some alternative minimal change criteria.

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A Query Tool for $\mathcal{EL}$ with Non-monotonic Rules

Cited by 13 publications

References 19 publications

Combining Rules and Ontologies into Clopen Knowledge Bases

Combining Rules and Ontologies into Clopen Knowledge Bases

A polynomial Time Subsumption Algorithm for Nominal SafeELO⊥under Rational Closure

Minimal Change in Evolving Multi-Context Systems

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