scholarly journals A Practical Approach to Forgetting in Description Logics with Nominals

2020 ◽  
Vol 34 (03) ◽  
pp. 3073-3079
Author(s):  
Yizheng Zhao ◽  
Renate Schmidt ◽  
Yuejie Wang ◽  
Xuanming Zhang ◽  
Hao Feng

This paper investigates the problem of forgetting in description logics with nominals. In particular, we develop a practical method for forgetting concept and role names from ontologies specified in the description logic ALCO, extending the basic ALC with nominals. The method always terminates, and is sound in the sense that the forgetting solution computed by the method has the same logical consequences with the original ontology. The method is so far the only approach to deductive forgetting in description logics with nominals. An evaluation of a prototype implementation shows that the method achieves a significant speed-up and notably better success rates than the Lethe tool which performs deductive forgetting for ALC-ontologies. Compared to Fame, a semantic forgetting tool for ALCOIH-ontologies, better success rates are attained. From the perspective of ontology engineering this is very useful, as it provides ontology curators with a powerful tool to produce views of ontologies.

Author(s):  
Yizheng Zhao ◽  
Renate A. Schmidt

Forgetting refers to a non-standard reasoning problem concerned with eliminating concept and role symbols from description logic-based ontologies while preserving all logical consequences up to the remaining symbols. Whereas previous research has primarily focused on forgetting concept symbols, in this paper, we turn our attention to role symbol forgetting. In particular, we present a practical method for semantic role forgetting for ontologies expressible in the description logic ALCOQH(universal role), i.e., the basic description logic ALC extended with nominals, qualified number restrictions, role inclusions and the universal role. Being based on an Ackermann approach, the method is the only approach so far for forgetting role symbols in description logics with qualified number restrictions. The method is goal-oriented and incremental. It always terminates and is sound in the sense that the forgetting solution is equivalent to the original ontology up to the forgotten symbols possibly with new concept definer symbols. Despite our method not being complete, performance results of an evaluation with a prototypical implementation have shown very good success rates on real-world ontologies.


Author(s):  
Yizheng Zhao ◽  
Renate Schmidt

This paper presents a practical method for computing solutions of concept forgetting in the description logic ALCOQ(neg,and,or), basic ALC extended with nominals, qualified number restrictions, role negation, role conjunction and role disjunction. The method is based on a non-trivial generalisation of Ackermann's Lemma, and attempts to compute either semantic solutions of concept forgetting or uniform interpolants in ALCOQ(neg,and,or). It is so far the only approach to concept forgetting in description logics with number restrictions plus nominals, as well as in description logics with ABoxes. Results of an evaluation with a prototypical implementation have shown that the method was successful in more than 90% of the test cases from a large corpus of biomedical ontologies. In only 13.2% of these cases the solutions were semantic solutions.


Author(s):  
Md Kamruzzaman Sarker ◽  
Pascal Hitzler

Concept Induction refers to the problem of creating complex Description Logic class descriptions (i.e., TBox axioms) from instance examples (i.e., ABox data). In this paper we look particularly at the case where both a set of positive and a set of negative instances are given, and complex class expressions are sought under which the positive but not the negative examples fall. Concept induction has found applications in ontology engineering, but existing algorithms have fundamental performance issues in some scenarios, mainly because a high number of invokations of an external Description Logic reasoner is usually required. In this paper we present a new algorithm for this problem which drastically reduces the number of reasoner invokations needed. While this comes at the expense of a more limited traversal of the search space, we show that our approach improves execution times by up to several orders of magnitude, while output correctness, measured in the amount of correct coverage of the input instances, remains reasonably high in many cases. Our approach thus should provide a strong alternative to existing systems, in particular in settings where other systems are prohibitively slow.


2020 ◽  
Vol 176 (3-4) ◽  
pp. 349-384
Author(s):  
Domenico Cantone ◽  
Marianna Nicolosi-Asmundo ◽  
Daniele Francesco Santamaria

In this paper we consider the most common TBox and ABox reasoning services for the description logic 𝒟ℒ〈4LQSR,x〉(D) ( 𝒟 ℒ D 4,× , for short) and prove their decidability via a reduction to the satisfiability problem for the set-theoretic fragment 4LQSR. 𝒟 ℒ D 4,× is a very expressive description logic. It combines the high scalability and efficiency of rule languages such as the SemanticWeb Rule Language (SWRL) with the expressivity of description logics. In fact, among other features, it supports Boolean operations on concepts and roles, role constructs such as the product of concepts and role chains on the left-hand side of inclusion axioms, role properties such as transitivity, symmetry, reflexivity, and irreflexivity, and data types. We further provide a KE-tableau-based procedure that allows one to reason on the main TBox and ABox reasoning tasks for the description logic 𝒟 ℒ D 4,× . Our algorithm is based on a variant of the KE-tableau system for sets of universally quantified clauses, where the KE-elimination rule is generalized in such a way as to incorporate the γ-rule. The novel system, called KEγ-tableau, turns out to be an improvement of the system introduced in [1] and of standard first-order KE-tableaux [2]. Suitable benchmark test sets executed on C++ implementations of the three mentioned systems show that in several cases the performances of the KEγ-tableau-based reasoner are up to about 400% better than the ones of the other two systems.


2015 ◽  
Vol 24 ◽  
pp. 42-48 ◽  
Author(s):  
Mauro Fois ◽  
Giuseppe Fenu ◽  
Alba Cuena Lombraña ◽  
Donatella Cogoni ◽  
Gianluigi Bacchetta

2008 ◽  
Vol 40 (2) ◽  
pp. 117-122 ◽  
Author(s):  
K. Maca ◽  
V. Pouchly ◽  
A.R. Boccaccini

This article summarizes the usage of high-temperature dilatometry in ceramic processing and powder technology with special attention on the description of the sintering process. A practical method for transformation of dilatometric shrinkage data into densification curves (the dependence of the sample density on sintering temperature or time) is described in detail. A new automatic procedure to recalculate sintering shrinkage data allowing the plot of the densification curve has been developed, which is presented here.


2010 ◽  
Vol 42 (1) ◽  
pp. 25-32 ◽  
Author(s):  
V. Pouchly ◽  
K. Maca

The concept of a Master Sintering Curve (MSC) is a strong tool for optimizing the sintering process. However, constructing the MSC from sintering data involves complicated and time-consuming calculations. A practical method for the construction of a MSC is presented in the paper. With the help of a few dilatometric sintering experiments the newly developed software calculates the MSC and finds the optimal activation energy of a given material. The software, which also enables sintering prediction, was verified by sintering tetragonal and cubic zirconia, and alumina of two different particle sizes.


2016 ◽  
Vol 13 (1) ◽  
pp. 287-308 ◽  
Author(s):  
Zhang Tingting ◽  
Liu Xiaoming ◽  
Wang Zhixue ◽  
Dong Qingchao

A number of problems may arise from architectural requirements modeling, including alignment of it with business strategy, model integration and handling the uncertain and vague information. The paper introduces a method for modeling architectural requirements in a way of ontology-based and capability-oriented requirements elicitation. The requirements can be modeled within a three-layer framework. The Capability Meta-concept Framework is provided at the top level. The domain experts can capture the domain knowledge within the framework, forming the domain ontology at the second level. The domain concepts can be used for extending the UML to produce a domain-specific modeling language. A fuzzy UML is introduced to model the vague and uncertain features of the capability requirements. An algorithm is provided to transform the fuzzy UML models into the fuzzy Description Logics ontology for model verification. A case study is given to demonstrate the applicability of the method.


1999 ◽  
Vol 11 ◽  
pp. 199-240 ◽  
Author(s):  
D. Calvanese ◽  
M. Lenzerini ◽  
D. Nardi

The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues underlying such representation formalisms and single out both their common characteristics and their distinguishing features. Such investigation leads us to propose a unifying framework in which we are able to capture the fundamental aspects of several representation languages used in different contexts. The proposed formalism is expressed in the style of description logics, which have been introduced in knowledge representation as a means to provide a semantically well-founded basis for the structural aspects of knowledge representation systems. The description logic considered in this paper is a subset of first order logic with nice computational characteristics. It is quite expressive and features a novel combination of constructs that has not been studied before. The distinguishing constructs are number restrictions, which generalize existence and functional dependencies, inverse roles, which allow one to refer to the inverse of a relationship, and possibly cyclic assertions, which are necessary for capturing real world domains. We are able to show that it is precisely such combination of constructs that makes our logic powerful enough to model the essential set of features for defining class structures that are common to frame systems, object-oriented database languages, and semantic data models. As a consequence of the established correspondences, several significant extensions of each of the above formalisms become available. The high expressiveness of the logic we propose and the need for capturing the reasoning in different contexts forces us to distinguish between unrestricted and finite model reasoning. A notable feature of our proposal is that reasoning in both cases is decidable. We argue that, by virtue of the high expressive power and of the associated reasoning capabilities on both unrestricted and finite models, our logic provides a common core for class-based representation formalisms.


2011 ◽  
pp. 24-43
Author(s):  
J. Bruijn

This chapter introduces a number of formal logical languages which form the backbone of the Semantic Web. They are used for the representation of both ontologies and rules. The basis for all languages presented in this chapter is the classical first-order logic. Description logics is a family of languages which represent subsets of first-order logic. Expressive description logic languages form the basis for popular ontology languages on the Semantic Web. Logic programming is based on a subset of first-order logic, namely Horn logic, but uses a slightly different semantics and can be extended with non-monotonic negation. Many Semantic Web reasoners are based on logic programming principles and rule languages for the Semantic Web based on logic programming are an ongoing discussion. Frame Logic allows object-oriented style (frame-based) modeling in a logical language. RuleML is an XML-based syntax consisting of different sublanguages for the exchange of specifications in different logical languages over the Web.


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