scholarly journals The Logical Difference for the Lightweight Description Logic EL

2012 ◽  
Vol 44 ◽  
pp. 633-708 ◽  
Author(s):  
B. Konev ◽  
M. Ludwig ◽  
D. Walther ◽  
F. Wolter
Keyword(s):  
Polynomial Time ◽  
Description Logic ◽  
Snomed Ct ◽  
Conjunctive Queries ◽  
Polynomial Time Algorithms ◽  
The Difference

We study a logic-based approach to versioning of ontologies. Under this view, ontologies provide answers to queries about some vocabulary of interest. The difference between two versions of an ontology is given by the set of queries that receive different answers. We investigate this approach for terminologies given in the description logic EL extended with role inclusions and domain and range restrictions for three distinct types of queries: subsumption, instance, and conjunctive queries. In all three cases, we present polynomial-time algorithms that decide whether two terminologies give the same answers to queries over a given vocabulary and compute a succinct representation of the difference if it is non- empty. We present an implementation, CEX2, of the developed algorithms for subsumption and instance queries and apply it to distinct versions of Snomed CT and the NCI ontology.

scholarly journals Actively Learning Concepts and Conjunctive Queries under ELr-Ontologies

2021 ◽  
Author(s):  
Maurice Funk ◽  
Jean Christoph Jung ◽  
Carsten Lutz
Keyword(s):  
Active Learning ◽  
Polynomial Time ◽  
Description Logic ◽  
Learning Algorithm ◽  
Domain Expert ◽  
Conjunctive Queries ◽  
Membership Queries ◽  
Equivalence Queries

We consider the problem to learn a concept or a query in the presence of an ontology formulated in the description logic ELr, in Angluin's framework of active learning that allows the learning algorithm to interactively query an oracle (such as a domain expert). We show that the following can be learned in polynomial time: (1) EL-concepts, (2) symmetry-free ELI-concepts, and (3) conjunctive queries (CQs) that are chordal, symmetry-free, and of bounded arity. In all cases, the learner can pose to the oracle membership queries based on ABoxes and equivalence queries that ask whether a given concept/query from the considered class is equivalent to the target. The restriction to bounded arity in (3) can be removed when we admit unrestricted CQs in equivalence queries. We also show that EL-concepts are not polynomial query learnable in the presence of ELI-ontologies.

scholarly journals Closed-World Semantics for Conjunctive Queries with Negation over ELH-bottom Ontologies

2019 ◽  
Author(s):  
Stefan Borgwardt ◽  
Walter Forkel
Keyword(s):  
Polynomial Time ◽  
Description Logic ◽  
Background Knowledge ◽  
Query Answering ◽  
Canonical Model ◽  
Closed Domain ◽  
Data Complexity ◽  
Conjunctive Queries ◽  
Closed World Assumption ◽  
Closed World

Ontology-mediated query answering is a popular paradigm for enriching answers to user queries with background knowledge.  For querying the absence of information, however, there exist only few ontology-based approaches.  Moreover, these proposals conflate the closed-domain and closed-world assumption, and therefore are not suited to deal with the anonymous objects that are common in ontological reasoning. We propose a new closed-world semantics for answering conjunctive queries with negation over ontologies formulated in the description logic ELH-bottom, based on the minimal canonical model.  We propose a rewriting strategy for dealing with negated query atoms, which shows that query answering is possible in polynomial time in data complexity.

scholarly journals An Overview of Algorithms for Network Survivability

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
F. A. Kuipers
Keyword(s):  
Polynomial Time ◽  
Network Connectivity ◽  
Network Survivability ◽  
Disjoint Paths ◽  
Polynomial Time Algorithms ◽  
Concise Overview ◽  
Main Components

Network survivability—the ability to maintain operation when one or a few network components fail—is indispensable for present-day networks. In this paper, we characterize three main components in establishing network survivability for an existing network, namely, (1) determining network connectivity, (2) augmenting the network, and (3) finding disjoint paths. We present a concise overview of network survivability algorithms, where we focus on presenting a few polynomial-time algorithms that could be implemented by practitioners and give references to more involved algorithms.

scholarly journals Reconstruction of score sets

2014 ◽  
Vol 6 (2) ◽  
pp. 210-229
Author(s):  
Antal Iványi
Keyword(s):  
Polynomial Time ◽  
Constructive Proof ◽  
Construction Algorithm ◽  
Polynomial Time Algorithms ◽  
General Polynomial ◽  
Degree Set ◽  
New Algorithms

Abstract The score set of a tournament is defined as the set of its different outdegrees. In 1978 Reid [15] published the conjecture that for any set of nonnegative integers D there exists a tournament T whose degree set is D. Reid proved the conjecture for tournaments containing n = 1, 2, and 3 vertices. In 1986 Hager [4] published a constructive proof of the conjecture for n = 4 and 5 vertices. In 1989 Yao [18] presented an arithmetical proof of the conjecture, but general polynomial construction algorithm is not known. In [6] we described polynomial time algorithms which reconstruct the score sets containing only elements less than 7. In [5] we improved this bound to 9. In this paper we present and analyze new algorithms Hole-Map, Hole-Pairs, Hole-Max, Hole-Shift, Fill-All, Prefix-Deletion, and using them improve the above bound to 12, giving a constructive partial proof of Reid’s conjecture.

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