scholarly journals Hybrid Unification in the Description Logic EL

10.29007/h59c ◽  
2018 ◽  
Author(s):  
Franz Baader ◽  
Oliver Fernandez Gil ◽  
Barbara Morawska
Keyword(s):  
Description Logic ◽  
Description Logics ◽  
General Concept ◽  
Biomedical Ontologies ◽  
Declarative Semantics ◽  
Np Complete ◽  
Unification Algorithms

Unification in Description Logics (DLs) has been proposed as an inferenceservice that can, for example, be used to detect redundancies in ontologies.For the DL EL, which is used to define several largebiomedical ontologies, unification is NP-complete. However, the unification algorithms for EL developeduntil recently could not deal with ontologies containing general concept inclusions (GCIs).In a series of recent papers we have made some progress towards addressing this problem, but the ontologies thedeveloped unification algorithms can deal with need to satisfy a certain cycle restriction.In the present paper, we follow a different approach. Instead of restricting the input ontologies,we generalize the notion of unifiers to so-called hybrid unifiers. Whereas classical unifiers can be viewed as acyclic TBoxes,hybrid unifiers are cyclic TBoxes, which are interpreted together with the ontology of the input using a hybrid semantics thatcombines fixpoint and declarative semantics. We show that hybrid unification in EL is NP-complete

scholarly journals On Concept Forgetting in Description Logics with Qualified Number Restrictions

2018 ◽  
Author(s):  
Yizheng Zhao ◽  
Renate Schmidt
Keyword(s):  
Description Logic ◽  
Description Logics ◽  
Practical Method ◽  
Test Cases ◽  
Biomedical Ontologies ◽  
Large Corpus

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.

scholarly journals A Temporal Description Logic for Reasoning about Actions and Plans

1998 ◽  
Vol 9 ◽  
pp. 463-506 ◽  
Author(s):  
A. Artale ◽  
E. Franconi
Keyword(s):  
Temporal Logic ◽  
Description Logic ◽  
Description Logics ◽  
Temporal Networks ◽  
Reasoning About Actions ◽  
Basic Language ◽  
The Family ◽  
Temporal Side ◽  
Np Complete ◽  
Computational Properties

A class of interval-based temporal languages for uniformly representing and reasoning about actions and plans is presented. Actions are represented by describing what is true while the action itself is occurring, and plans are constructed by temporally relating actions and world states. The temporal languages are members of the family of Description Logics, which are characterized by high expressivity combined with good computational properties. The subsumption problem for a class of temporal Description Logics is investigated and sound and complete decision procedures are given. The basic language TL-F is considered first: it is the composition of a temporal logic TL -- able to express interval temporal networks -- together with the non-temporal logic F -- a Feature Description Logic. It is proven that subsumption in this language is an NP-complete problem. Then it is shown how to reason with the more expressive languages TLU-FU and TL-ALCF. The former adds disjunction both at the temporal and non-temporal sides of the language, the latter extends the non-temporal side with set-valued features (i.e., roles) and a propositionally complete language.

scholarly journals Recent Advances in Unification for the EL Family

10.29007/q5px ◽  
2018 ◽  
Author(s):  
Franz Baader ◽  
Stefan Borgwardt ◽  
Barbara Morawska
Keyword(s):  
Description Logics ◽  
General Concept ◽  
Snomed Ct ◽  
Recent Advances ◽  
Unification Algorithms ◽  
New Algorithms

Unification in description logics (DLs) has been proposed as a means to detect redundancies in ontologies. The DL EL, even though quite inexpressive, can be used to formulate large medical ontologies like SNOMED CT. Previously, several unification algorithms for EL were developed that can only deal with acyclic terminologies. In this paper, we give an overview over our recent efforts to generalize these algorithms to allow for general concept inclusions, transitive roles, and role hierarchies. For our new algorithms to be complete, the ontology needs to satisfy a certain cycle restriction.

scholarly journals Matching in the Description Logic FL0 with respect to General TBoxes

10.29007/q74p ◽  
2018 ◽  
Author(s):  
Franz Baader ◽  
Oliver Fernandez Gil ◽  
Pavlos Marantidis
Keyword(s):  
Polynomial Time ◽  
Description Logic ◽  
Description Logics ◽  
General Concept ◽  
Finite Sets ◽  
Matching Algorithm ◽  
Restricted Form ◽  
Matching Concept ◽  
Inference Task

Matching concept descriptions against concept patterns was introduced as a new inference task in Description Logics two decades ago, motivated by applications in the Classic system. Shortly afterwards, a polynomial-time matching algorithm was developed for the DL FL0. However, this algorithm cannot deal with general TBoxes (i.e., finite sets of general concept inclusions). Here we show that matching in FL0 w.r.t. general TBoxes is in ExpTime, which is the best possible complexity for this problem since already subsumption w.r.t. general TBoxes is ExpTime-hard in FL0. We also show that, w.r.t. a restricted form of TBoxes, the complexity of matching in FL0 can be lowered to PSpace.

A Set-theoretic Approach to Reasoning Services for the Description Logic 𝒟 ℒ D 4,×

2020 ◽  
Vol 176 (3-4) ◽  
pp. 349-384
Author(s):  
Domenico Cantone ◽  
Marianna Nicolosi-Asmundo ◽  
Daniele Francesco Santamaria
Keyword(s):  
Description Logic ◽  
Description Logics ◽  
Theoretic Approach ◽  
The Novel ◽  
Data Types ◽  
Left Hand ◽  
Rule Languages ◽  
Tableau System ◽  
High Scalability ◽  
Better Than

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.

scholarly journals Capability-oriented architectural analysis method based on fuzzy description logic

2016 ◽  
Vol 13 (1) ◽  
pp. 287-308 ◽  
Author(s):  
Zhang Tingting ◽  
Liu Xiaoming ◽  
Wang Zhixue ◽  
Dong Qingchao
Keyword(s):  
Business Strategy ◽  
Domain Knowledge ◽  
Description Logic ◽  
Description Logics ◽  
Model Verification ◽  
Architectural Analysis ◽  
Requirements Modeling ◽  
Strategy Model ◽  
Domain Specific Modeling ◽  
Fuzzy Description

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.

scholarly journals Unifying Class-Based Representation Formalisms

1999 ◽  
Vol 11 ◽  
pp. 199-240 ◽  
Author(s):  
D. Calvanese ◽  
M. Lenzerini ◽  
D. Nardi
Keyword(s):  
Knowledge Representation ◽  
Description Logic ◽  
Description Logics ◽  
Expressive Power ◽  
Finite Model ◽  
Functional Dependencies ◽  
Semantic Data ◽  
Representation Systems ◽  
Frame Systems ◽  
Essential Set

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.

scholarly journals Role-Value Maps and General Concept Inclusions in the Minimal Description Logic with Value Restrictions or Revisiting Old Skeletons in the DL Cupboard

2020 ◽  
Vol 34 (3) ◽  
pp. 291-301
Author(s):  
Franz Baader ◽  
Clément Théron
Keyword(s):  
Description Logic ◽  
Direct Proof ◽  
General Concept ◽  
The Other ◽  
Other Hand ◽  
The One ◽  
Minimal Description ◽  
The Impact

Abstract We investigate the impact that general concept inclusions and role-value maps have on the complexity and decidability of reasoning in the description logic $$\mathcal{FL}_0$$ FL 0 . On the one hand, we give a more direct proof for ExpTime-hardness of subsumption w.r.t. general concept inclusions in $$\mathcal{FL}_0$$ FL 0 . On the other hand, we determine restrictions on role-value maps that ensure decidability of subsumption, but we also show undecidability for the cases where these restrictions are not satisfied.

Logics for the Semantic Web

2011 ◽  
pp. 24-43
Author(s):  
J. Bruijn
Keyword(s):  
Semantic Web ◽  
Logic Programming ◽  
Description Logic ◽  
Description Logics ◽  
Order Logic ◽  
First Order Logic ◽  
Horn Logic ◽  
First Order ◽  
Logical Language ◽  
Rule Languages

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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