scholarly journals Computing Optimal Repairs of Quantified ABoxes w.r.t. Static $$\mathcal {EL}$$ TBoxes

2021 ◽  
pp. 309-326
Author(s):  
Franz Baader ◽  
Patrick Koopmann ◽  
Francesco Kriegel ◽  
Adrian Nuradiansyah
Keyword(s):  
Automated Reasoning ◽  
Description Logic ◽  
Repair Process ◽  
Experimental Results ◽  
Worst Case

AbstractThe application of automated reasoning approaches to Description Logic (DL) ontologies may produce certain consequences that either are deemed to be wrong or should be hidden for privacy reasons. The question is then how to repair the ontology such that the unwanted consequences can no longer be deduced. An optimal repair is one where the least amount of other consequences is removed. Most of the previous approaches to ontology repair are of a syntactic nature in that they remove or weaken the axioms explicitly present in the ontology, and thus cannot achieve semantic optimality. In previous work, we have addressed the problem of computing optimal repairs of (quantified) ABoxes, where the unwanted consequences are described by concept assertions of the lightweight DL $$\mathcal {EL}$$ EL . In the present paper, we improve on the results achieved so far in two ways. First, we allow for the presence of terminological knowledge in the form of an $$\mathcal {EL}$$ EL TBox. This TBox is assumed to be static in the sense that it cannot be changed in the repair process. Second, the construction of optimal repairs described in our previous work is best case exponential. We introduce an optimized construction that is exponential only in the worst case. First experimental results indicate that this reduces the size of the computed optimal repairs considerably.

scholarly journals Automated Reasoning in Modal and Description Logics via SAT Encoding: the Case Study of K(m)/ALC-Satisfiability

2009 ◽  
Vol 35 ◽  
pp. 343-389 ◽  
Author(s):  
R. Sebastiani ◽  
M. Vescovi
Keyword(s):  
Automated Reasoning ◽  
Description Logic ◽  
State Of The Art ◽  
Description Logics ◽  
Worst Case ◽  
Current State ◽  
Database Theory ◽  
Sat Encoding ◽  
Better Than

In the last two decades, modal and description logics have been applied to numerous areas of computer science, including knowledge representation, formal verification, database theory, distributed computing and, more recently, semantic web and ontologies. For this reason, the problem of automated reasoning in modal and description logics has been thoroughly investigated. In particular, many approaches have been proposed for efficiently handling the satisfiability of the core normal modal logic K(m), and of its notational variant, the description logic ALC. Although simple in structure, K(m)/ALC is computationally very hard to reason on, its satisfiability being PSPACE-complete. In this paper we start exploring the idea of performing automated reasoning tasks in modal and description logics by encoding them into SAT, so that to be handled by state-of-the-art SAT tools; as with most previous approaches, we begin our investigation from the satisfiability in K(m). We propose an efficient encoding, and we test it on an extensive set of benchmarks, comparing the approach with the main state-of-the-art tools available. Although the encoding is necessarily worst-case exponential, from our experiments we notice that, in practice, this approach can handle most or all the problems which are at the reach of the other approaches, with performances which are comparable with, or even better than, those of the current state-of-the-art tools.

scholarly journals Betweenness centrality profiles in trees

2017 ◽  
Vol 5 (5) ◽  
pp. 776-794
Author(s):  
Benjamin Fish ◽  
Rahul Kushwaha ◽  
György Turán
Keyword(s):  
Betweenness Centrality ◽  
Shortest Paths ◽  
Random Trees ◽  
Experimental Results ◽  
Basic Notion ◽  
Worst Case ◽  
Scale Free ◽  
Order Of Magnitude

Abstract Betweenness centrality of a vertex in a graph measures the fraction of shortest paths going through the vertex. This is a basic notion for determining the importance of a vertex in a network. The $k$-betweenness centrality of a vertex is defined similarly, but only considers shortest paths of length at most $k$. The sequence of $k$-betweenness centralities for all possible values of $k$ forms the betweenness centrality profile of a vertex. We study properties of betweenness centrality profiles in trees. We show that for scale-free random trees, for fixed $k$, the expectation of $k$-betweenness centrality strictly decreases as the index of the vertex increases. We also analyse worst-case properties of profiles in terms of the distance of profiles from being monotone, and the number of times pairs of profiles can cross. This is related to whether $k$-betweenness centrality, for small values of $k$, may be used instead of having to consider all shortest paths. Bounds are given that are optimal in order of magnitude. We also present some experimental results for scale-free random trees.

Conceptual Design Knowledge Management and the Semantic Web

2005 ◽  
Author(s):  
Joseph B. Kopena ◽  
Christopher D. Cera ◽  
William C. Regli
Keyword(s):  
Semantic Web ◽  
Conceptual Design ◽  
Automated Reasoning ◽  
Description Logic ◽  
Design Knowledge ◽  
Semantic Web Technology ◽  
Design Engineers ◽  
Conceptual Design Phase ◽  
Mechanical Devices ◽  
New Applications

The early stages of engineering design are critical, as the decisions made at this point have the most impact on the final product. However, little software is available to support engineers during the initial, conceptual design phase. In addition, at this and all other stages of design, engineers are increasingly tasked with utilizing unwieldy collections of data such as databases of legacy designs and catalogs. This work addresses both of these issues. A conceptual design interface with several advancements crucial to industrial deployment is developed and used to aid design. Among these are provisions for real-time collaboration and security. A representation of mechanical devices based on intended function is developed and used by the conceptual design interface to capture design semantics. This representation is defined using a description logic, enabling automated reasoning. The descriptions created using the conceptual design interface can thus be employed to annotate designs, create search queries, and to organize collections of designs. Further, this work incorporates Semantic Web technology, enabling conceptual design knowledge to be published and accessed effectively on the World Wide Web. New applications of design repositories are made possible by this but new issues must be investigated and addressed, as discussed here.

scholarly journals Representing and classifying arguments on the Semantic Web

2011 ◽  
Vol 26 (4) ◽  
pp. 487-511 ◽  
Author(s):  
Iyad Rahwan ◽  
Bita Banihashemi ◽  
Chris Reed ◽  
Douglas Walton ◽  
Sherief Abdallah
Keyword(s):  
Automated Reasoning ◽  
Description Logic ◽  
Research Community ◽  
Argumentation Schemes ◽  
Web Based ◽  
Argument Analysis ◽  
Ontology Language ◽  
Support Tools ◽  
Interchange Format ◽  
Web Based System

AbstractUntil recently, little work has been dedicated to the representation and interchange of informal, semi-structured arguments of the type found in natural language prose and dialogue. To redress this, the research community recently initiated work towards an Argument Interchange Format (AIF). The AIF aims to facilitate the exchange of semi-structured arguments among different argument analysis and argumentation-support tools. In this paper, we present a Description Logic ontology for annotating arguments, based on a new reification of the AIF and founded in Walton's theory of argumentation schemes. We demonstrate how this ontology enables a new kind of automated reasoning over argument structures, which complements classical reasoning about argument acceptability. In particular, Web Ontology Language reasoning enables significantly enhanced querying of arguments through automatic scheme classifications, instance classification, inference of indirect support in chained argument structures, and inference of critical questions. We present the implementation of a pilot Web-based system for authoring and querying argument structures using the proposed ontology.

scholarly journals Finding Small Proofs for Description Logic Entailments: Theory and Practice

10.29007/nhpp ◽  
2020 ◽  
Author(s):  
Christian Alrabbaa ◽  
Franz Baader ◽  
Stefan Borgwardt ◽  
Patrick Koopmann ◽  
Alisa Kovtunova
Keyword(s):  
Description Logic ◽  
Theory And Practice ◽  
Proof Complexity ◽  
Reasoning Task ◽  
Worst Case ◽  
Derivation Step ◽  
Worst Case Complexity ◽  
Directed Hypergraphs ◽  
The Individual ◽  
Theoretical Side

Logic-based approaches to AI have the advantage that their behaviour can in principle be explained by providing their users with proofs for the derived consequences. However, if such proofs get very large, then it may be hard to understand a consequence even if the individual derivation steps are easy to comprehend. This motivates our interest in finding small proofs for Description Logic (DL) entailments. Instead of concentrating on a specific DL and proof calculus for this DL, we introduce a general framework in which proofs are represented as labeled, directed hypergraphs, where each hyperedge corresponds to a single sound derivation step. On the theoretical side, we investigate the complexity of deciding whether a certain consequence has a proof of size at most n along the following orthogonal dimensions: (i) the underlying proof system is polynomial or exponential; (ii) proofs may or may not reuse already derived consequences; and (iii) the number n is represented in unary or binary. We have determined the exact worst-case complexity of this decision problem for all but one of the possible combinations of these options. On the practical side, we have developed and implemented an approach for generating proofs for expressive DLs based on a non-standard reasoning task called forgetting. We have evaluated this approach on a set of realistic ontologies and compared the obtained proofs with proofs generated by the DL reasoner ELK, finding that forgetting-based proofs are often better w.r.t. different measures of proof complexity.

scholarly journals Provable Guarantees on the Robustness of Decision Rules to Causal Interventions

2021 ◽  
Author(s):  
Benjie Wang ◽  
Clare Lyle ◽  
Marta Kwiatkowska
Keyword(s):  
Decision Making ◽  
Bayesian Networks ◽  
Lower Bounds ◽  
Decision Rules ◽  
Experimental Results ◽  
Upper And Lower Bounds ◽  
Worst Case ◽  
Data Generating Process ◽  
Causal Bayesian Networks ◽  
Novel Model

Robustness of decision rules to shifts in the data-generating process is crucial to the successful deployment of decision-making systems. Such shifts can be viewed as interventions on a causal graph, which capture (possibly hypothetical) changes in the data-generating process, whether due to natural reasons or by the action of an adversary. We consider causal Bayesian networks and formally define the interventional robustness problem, a novel model-based notion of robustness for decision functions that measures worst-case performance with respect to a set of interventions that denote changes to parameters and/or causal influences. By relying on a tractable representation of Bayesian networks as arithmetic circuits, we provide efficient algorithms for computing guaranteed upper and lower bounds on the interventional robustness probabilities. Experimental results demonstrate that the methods yield useful and interpretable bounds for a range of practical networks, paving the way towards provably causally robust decision-making systems.

scholarly journals Lyndon Factorization Algorithms for Small Alphabets and Run-Length Encoded Strings

Algorithms ◽  
2019 ◽  
Vol 12 (6) ◽  
pp. 124
Author(s):  
Sukhpal Ghuman ◽  
Emanuele Giaquinta ◽  
Jorma Tarhio
Keyword(s):  
Time Complexity ◽  
Linear Time ◽  
Experimental Results ◽  
The Other ◽  
Worst Case ◽  
Run Length ◽  
Original Algorithm ◽  
Factorization Algorithms

We present two modifications of Duval’s algorithm for computing the Lyndon factorization of a string. One of the algorithms has been designed for strings containing runs of the smallest character. It works best for small alphabets and it is able to skip a significant number of characters of the string. Moreover, it can be engineered to have linear time complexity in the worst case. When there is a run-length encoded string R of length ρ , the other algorithm computes the Lyndon factorization of R in O ( ρ ) time and in constant space. It is shown by experimental results that the new variations are faster than Duval’s original algorithm in many scenarios.

Towards Practical ABox Abduction in Large Description Logic Ontologies

2012 ◽  
Vol 8 (2) ◽  
pp. 1-33 ◽  
Author(s):  
Jianfeng Du ◽  
Guilin Qi ◽  
Yi-Dong Shen ◽  
Jeff Z. Pan
Keyword(s):  
Finite Number ◽  
Finite Time ◽  
Description Logic ◽  
Description Logics ◽  
Experimental Results ◽  
New Method ◽  
Standard Language ◽  
Minimal Sets

ABox abduction is an important reasoning facility in Description Logics (DLs). It finds all minimal sets of ABox axioms, called abductive solutions, which should be added to a background ontology to enforce entailment of an observation which is a specified set of ABox axioms. However, ABox abduction is far from practical by now because there lack feasible methods working in finite time for expressive DLs. To pave a way to practical ABox abduction, this paper proposes a new problem for ABox abduction and a new method for computing abductive solutions accordingly. The proposed problem guarantees finite number of abductive solutions. The proposed method works in finite time for a very expressive DL, , which underpins the W3C standard language OWL 2, and guarantees soundness and conditional completeness of computed results. Experimental results on benchmark ontologies show that the method is feasible and can scale to large ABoxes.

Two-Phase Flow-Induced Forces on Bends in Small Scale Tubes

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
M. F. Cargnelutti ◽  
S. P. C. Belfroid ◽  
W. Schiferli
Keyword(s):  
Experimental Data ◽  
Structural Integrity ◽  
Two Phase Flow ◽  
Experimental Results ◽  
Small Scale ◽  
Phase Flow ◽  
Momentum Exchange ◽  
Two Phase ◽  
Worst Case ◽  
Good Agreement

Two-phase flow occurs in many situations in industry. Under certain circumstances, it can be a source of flow-induced vibrations. The forces generated can be sufficiently large to affect the performance or efficiency of an industrial device. In the worst-case scenario, the mechanical forces that arise may endanger structural integrity. Thus, it is important to take these forces into account in designing industrial machinery to avoid problems during operation. Although the occurrence of such forces is well known, not much is known about their magnitudes because, unfortunately, the amount of experimental data available in literature are rather limited. This paper describes the experiments performed to measure forces in 6 mm diameter tubing containing a bend. Experiments are performed on bends of different radii, with the bend positioned horizontally or vertically. The experimental results are analyzed based on flow regime and bend configuration. A comparison with available experimental results for bigger internal pipe diameter shows a general good agreement. To improve future predictions, a simple model based on momentum exchange is proposed to estimate the forces generated by multiphase flow. The proposed model shows a good agreement with the experimental data.

scholarly journals Translating OWL and semantic web rules into prolog: Moving toward description logic programs

2008 ◽  
Vol 8 (3) ◽  
pp. 301-322 ◽  
Author(s):  
KEN SAMUEL ◽  
LEO OBRST ◽  
SUZETTE STOUTENBERG ◽  
KAREN FOX ◽  
PAUL FRANKLIN ◽  
...  
Keyword(s):  
Semantic Web ◽  
Knowledge Base ◽  
Automated Reasoning ◽  
Description Logic ◽  
Logic Programs ◽  
Dynamic Changes ◽  
General Rules ◽  
Alternative Approaches ◽  
Run Time

AbstractWe are researching the interaction between the rule and the ontology layers of the Semantic Web, by comparing two options: 1) using OWL and its rule extension SWRL to develop an integrated ontology/rule language, and 2) layering rules on top of an ontology with RuleML and OWL. Toward this end, we are developing the SWORIER system, which enables efficient automated reasoning on ontologies and rules, by translating all of them into Prolog and adding a set of general rules that properly capture the semantics of OWL. We have also enabled the user to make dynamic changes on the fly, at run time. This work addresses several of the concerns expressed in previous work, such as negation, complementary classes, disjunctive heads, and cardinality, and it discusses alternative approaches for dealing with inconsistencies in the knowledge base. In addition, for efficiency, we implemented techniques called extensionalization, avoiding reanalysis, and code minimization.

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