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Unification in a Description Logic with Transitive Closure of Roles [chapter]

Franz Baader, Ralf Küsters
2001 Lecture Notes in Computer Science  
The present paper shows that the complexity does not increase if one additionally allows for composition, union, and transitive closure of roles.  ...  Uni cation of concept descriptions was introduced by Baader and Narendran as a tool for detecting redundancies in knowledge bases.  ...  In the present paper, we study uni cation in FL reg , the DL that extends FL 0 by the role constructors identity role ("), empty role (;), union (R S), composition (R S), and re exive-transitive closure  ... 
doi:10.1007/3-540-45653-8_15 fatcat:bqbsl3wu5nfibfiwgbkxnf47su

Unification in modal and description logics

F. Baader, S. Ghilardi
2010 Logic Journal of the IGPL  
In this article, we give a survey of the results on unification obtained in two closely related, yet different, application areas of unification: description logics and modal logics.  ...  Unification was originally introduced in automated deduction and term rewriting, but has recently also found applications in other fields.  ...  In most cases, unification problems in modal logics and in description logics Equational unification also plays a rôle in the context of modal logics in a quite different setting.  ... 
doi:10.1093/jigpal/jzq008 fatcat:hrew2tewyrfopf2a5egnmhm23q

A Decomposition Rule for Decision Procedures by Resolution-Based Calculi [chapter]

Ullrich Hustadt, Boris Motik, Ulrike Sattler
2005 Lecture Notes in Computer Science  
In this paper, we present a new decomposition inference rule, which can be combined with any resolution-based calculus compatible with the standard notion of redundancy.  ...  We combine decomposition with basic superposition to obtain three new decision procedures: (i) for the description logic SHIQ, (ii) for the description logic ALCHIQb, and (iii) for answering conjunctive  ...  Answering conjunctive queries over the related description logic SHf was considered in [19] . In this approach, transitive roles can be used in the queries, but SHf does not provide inverse roles.  ... 
doi:10.1007/978-3-540-32275-7_2 fatcat:vm25lzogenbudij2knpbvhkf7u

Undecidability of the unification and admissibility problems for modal and description logics

Frank Wolter, Michael Zakharyaschev
2008 ACM Transactions on Computational Logic  
The undecidability proof for K with the universal modality can be used to show that the unification problem relative to role boxes is undecidable for Boolean description logics with transitive roles, inverse  ...  We show that the unification problem 'is there a substitution instance of a given formula that is provable in a given logic?'  ...  Moreover, if a Boolean description logic has transitive roles, inverse roles and role hierarchies, then a role box can be used to define a universal role.  ... 
doi:10.1145/1380572.1380574 fatcat:ts3c3wnptnboravpvrl3nzspli

Undecidability of the unification and admissibility problems for modal and description logics [article]

Frank Wolter, Michael Zakharyaschev
2006 arXiv   pre-print
We show that the unification problem 'is there a substitution instance of a given formula that is provable in a given logic?'  ...  The undecidability proof for K with the universal modality can be used to show that the unification problem relative to role boxes is undecidable for Boolean description logic with transitive roles, inverse  ...  Moreover, if a Boolean description logic has transitive roles, inverse roles and role hierarchies, then a role box can be used to define a universal role.  ... 
arXiv:cs/0609052v1 fatcat:6jwhm2e5mvgnbmgbxtak2m3tq4

Page 6297 of Mathematical Reviews Vol. , Issue 2003h [page]

2003 Mathematical Reviews  
{For the entire collection see MR 2003c:68003. } 2003h:68133 68T30 68Q25 68Q45 Baader, Franz (D-AACH; Aachen); Kiisters, Ralf (D-KIEL; Kiel) Unification in a description logic with transitive closure of  ...  Summary: “Unification of concept descriptions was introduced by Baader and Narendran as a tool for detecting redundancies in knowledge bases.  ... 

Representation and reasoning with attributive descriptions [chapter]

Bernhard Nebel, Gert Smolka
1990 Lecture Notes in Computer Science  
This paper surveys terminological representation languages and feature-based unification grammars pointing out the similarities and differences between these two families of attributive description formalisms  ...  Emphasis is given to the logical foundations of these formalisms. * Funded by the EUREKA Project Protos (EU 56).  ...  We use → * C to denote the reflexive and transitive closure of → C on the set of all variables.  ... 
doi:10.1007/3-540-52337-6_21 fatcat:b6yn2rbr2jafph76bvo3bteg4u

A Fuzzy Logic Programming Environment for Managing Similarity and Truth Degrees

Pascual Julián-Iranzo, Ginés Moreno, Jaime Penabad, Carlos Vázquez
2015 Electronic Proceedings in Theoretical Computer Science  
FASILL (acronym of "Fuzzy Aggregators and Similarity Into a Logic Language") is a fuzzy logic programming language with implicit/explicit truth degree annotations, a great variety of connectives and unification  ...  FASILL integrates and extends features coming from MALP (Multi-Adjoint Logic Programming, a fuzzy logic language with explicitly annotated rules) and Bousi~Prolog (which uses a weak unification algorithm  ...  We center our attention on the description of the similarity module, providing insights of the internal representation of a similarity relation and its automatic construction, via built-in closure algorithms  ... 
doi:10.4204/eptcs.173.6 fatcat:b6zucsg3sbctrbhouvku2p4bri

Deciding Unifiability and Computing Local Unifiers in the Description Logic $\mathcal{E\!L}$ without Top Constructor

Franz Baader, Nguyen Thanh Binh, Stefan Borgwardt, Barbara Morawska
2016 Notre Dame Journal of Formal Logic  
Unification in Description Logics has been proposed as a novel inference service that can, for example, be used to detect redundancies in ontologies.  ...  On the other hand, unification in EL has been shown to be NP-complete, and thus of considerably lower complexity than unification in other description logics of similarly restricted expressive power.  ...  There is also a strong connection between description logics and modal logics, and therefore between unification in these formalisms.  ... 
doi:10.1215/00294527-3555507 fatcat:furoxuvajnhbtdgqhqbeakoo24

UEL: Unification Solver for the Description Logic $\mathcal{EL}$ – System Description [chapter]

Franz Baader, Julian Mendez, Barbara Morawska
2012 Lecture Notes in Computer Science  
UEL is a system that computes unifiers for unification problems formulated in the description logic EL.  ...  EL is a description logic with restricted expressivity, but which is still expressive enough for the formal representation of biomedical ontologies, such as the large medical ontology SNOMED CT.  ...  Such an assignment induces the following relation > S on N v : > S is the transitive closure of {(X, Y ) ∈ N v ×N v | Y occurs in an element of S X }.  ... 
doi:10.1007/978-3-642-31365-3_6 fatcat:v574y6sbmve6pml6gh4witnjdq

Unification in the Description Logic EL

Franz Baader, Barbara Morawska, Ralf Treinen
2010 Logical Methods in Computer Science  
Unification in Description Logics has been proposed as a novel inference service that can, for example, be used to detect redundancies in ontologies.  ...  We also show that, w.r.t. the unification type, EL is less well-behaved: it is of type zero, which in particular implies that there are unification problems that have no finite complete set of unifiers  ...  In Section 4, we show the main result of the paper: unification in EL is NP-complete. More information about Description Logics can be found in [3] , and about unification theory in [10] .  ... 
doi:10.2168/lmcs-6(3:17)2010 fatcat:vc433m2sc5cm7mueyclecbkyf4

A Syntactic Approach to Unification in Transitive Reflexive Modal Logics

Rosalie Iemhoff
2016 Notre Dame Journal of Formal Logic  
This paper contains a proof-theoretic account of unification in transitive reflexive modal logics, which means that the reasoning is syntactic and uses as little semantics as possible.  ...  In particular, a syntactic proof of Ghilardi's result that S4 has finitary unification is provided.  ...  proof-theoretic analysis of unification in transitive modal logics.  ... 
doi:10.1215/00294527-345997 fatcat:lfk7c62aebd3lef6a4gb6v7ybu

Attributive description formalisms ... and the rest of the world [chapter]

Bernhard Nebel, Gert Smolka
1991 Lecture Notes in Computer Science  
Recently, a number of formal results in the area of attributive description formalisms have been obtained by exploiting other research fields, such as formal language theory, automata theory, and modal  ...  In this paper, we will show how attributive description formalisms relate to "the rest of the world."  ...  Attributive Description Formalisms . . . and the Rest of the World  ... 
doi:10.1007/3-540-54594-8_74 fatcat:btaxsc3ftva5bbkah4ip34ba2i

Page 2861 of Mathematical Reviews Vol. , Issue 2003d [page]

2003 Mathematical Reviews  
Fermiiller, Herbrand’s theorem for prenex Gédel logic and its consequences for theorem proving (201-216); Franz Baader and Ralf Kiisters, Unification in a description logic with transitive closure of roles  ...  (249-265); Carsten Schiirmann, A type-theoretic approach to induction with higher-order encodings (266-281); Jan-Georg Smaus, Analysis of polymorphically typed logic programs using ACI-unification (282  ... 

Query Answering for OWL-DL with Rules [chapter]

Boris Motik, Ulrike Sattler, Rudi Studer
2004 Lecture Notes in Computer Science  
We discuss the expressive power of such a combination and present an algorithm for query answering in the related logic SHIQ extended with DL-safe rules, based on a reduction to disjunctive programs.  ...  Both OWL-DL and function-free Horn rules are decidable fragments of first-order logic with interesting, yet orthogonal expressive power.  ...  A comprehensive study of the effects of combining datalog rules with description logics is presented in [22] .  ... 
doi:10.1007/978-3-540-30475-3_38 fatcat:46r3wvfzsrdv7i6gkjvkuj75yy
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