scholarly journals Guarded hybrid knowledge bases

2008 ◽  
Vol 8 (3) ◽  
pp. 411-429 ◽  
Author(s):  
STIJN HEYMANS ◽  
JOS DE BRUIJN ◽  
LIVIA PREDOIU ◽  
CRISTINA FEIER ◽  
DAVY VAN NIEWENBORGH
Keyword(s):  
Description Logic ◽  
Description Logics ◽  
Logic Program ◽  
Knowledge Bases ◽  
The Body ◽  
Knowledge Representation And Reasoning ◽  
Advantages And Disadvantages ◽  
Hybrid Knowledge ◽  
Satisfiability Checking ◽  
Answer Set Semantics

AbstractRecently, there has been a lot of interest in the integration of Description Logics (DL) and rules on the Semantic Web. We defineguarded hybrid knowledge bases(org-hybrid knowledge bases) as knowledge bases that consist of a Description Logic knowledge base and aguardedlogic program, similar to the$\mathcal{DL}$+logknowledge bases from Rosati (In Proceedings of the 10th International Conference on Principles of Knowledge Representation and Reasoning, AAAI Press, Menlo Park, CA, 2006, pp. 68–78.). g-Hybrid knowledge bases enable an integration of Description Logics and Logic Programming where, unlike in other approaches, variables in the rules of a guarded program do not need to appear in positive non-DL atoms of the body, i.e., DL atoms can act asguardsas well. Decidability of satisfiability checking of g-hybrid knowledge bases is shown for the particular DL$\mathcal{DLRO}^{\-{le}}$, which is close to OWL DL, by a reduction to guarded programs under the open answer set semantics. Moreover, we show 2-Exptime-completeness for satisfiability checking of such g-hybrid knowledge bases. Finally, we discuss advantages and disadvantages of our approach compared with$\mathcal{DL}$+logknowledge bases.

scholarly journals Reasoning with Forest Logic Programs and f-hybrid knowledge bases

2011 ◽  
Vol 13 (3) ◽  
pp. 395-463
Author(s):  
CRISTINA FEIER ◽  
STIJN HEYMANS
Keyword(s):  
Answer Set Programming ◽  
Knowledge Bases ◽  
Logic Programs ◽  
Decidability Result ◽  
Tree Shape ◽  
Alternative Approach ◽  
Hybrid Framework ◽  
Hybrid Knowledge ◽  
Satisfiability Checking ◽  
Answer Set

AbstractOpen Answer Set Programming (OASP) is an undecidable framework for integrating ontologies and rules. Although several decidable fragments of OASP have been identified, few reasoning procedures exist. In this paper, we provide a sound, complete, and terminating algorithm for satisfiability checking w.r.t. Forest Logic Programs (FoLPs), a fragment of OASP where rules have a tree shape and allow for inequality atoms and constants. The algorithm establishes a decidability result for FoLPs. Although believed to be decidable, so far only the decidability for two small subsets of FoLPs, local FoLPs and acyclic FoLPs, has been shown. We further introduce f-hybrid knowledge bases, a hybrid framework where knowledge bases and FoLPs coexist, and we show that reasoning with such knowledge bases can be reduced to reasoning with FoLPs only. We note that f-hybrid knowledge bases do not require the usual (weakly) DL-safety of the rule component, thus providing a genuine alternative approach to current integration approaches of ontologies and rules.

scholarly journals Conjunctive Query Answering for the Description Logic SHIQ

2008 ◽  
Vol 31 ◽  
pp. 157-204 ◽  
Author(s):  
B. Glimm ◽  
C. Lutz ◽  
I. Horrocks ◽  
U. Sattler
Keyword(s):  
Description Logic ◽  
Query Language ◽  
Description Logics ◽  
Knowledge Bases ◽  
Deterministic Algorithm ◽  
Query Answering ◽  
Conjunctive Query ◽  
Conjunctive Queries ◽  
Complexity Bounds ◽  
Double Exponential

Conjunctive queries play an important role as an expressive query language for Description Logics (DLs). Although modern DLs usually provide for transitive roles, conjunctive query answering over DL knowledge bases is only poorly understood if transitive roles are admitted in the query. In this paper, we consider unions of conjunctive queries over knowledge bases formulated in the prominent DL SHIQ and allow transitive roles in both the query and the knowledge base. We show decidability of query answering in this setting and establish two tight complexity bounds: regarding combined complexity, we prove that there is a deterministic algorithm for query answering that needs time single exponential in the size of the KB and double exponential in the size of the query, which is optimal. Regarding data complexity, we prove containment in co-NP.

scholarly journals Formal Ontologies in Biomedical Knowledge Representation

2013 ◽  
Vol 22 (01) ◽  
pp. 132-146 ◽  
Author(s):  
L. Jansen ◽  
S. Schulz
Keyword(s):  
Decision Support ◽  
Knowledge Representation ◽  
Description Logics ◽  
Clinical Decision Support Systems ◽  
Knowledge Bases ◽  
Medical Decision ◽  
Knowledge Representation And Reasoning ◽  
Digital Information ◽  
Biomedical Knowledge ◽  
Formal Ontologies

Summary Objectives: Medical decision support and other intelligent applications in the life sciences depend on increasing amounts of digital information. Knowledge bases as well as formal ontologies are being used to organize biomedical knowledge and data. However, these two kinds of artefacts are not always clearly distinguished. Whereas the popular RDF(S) standard provides an intuitive triple-based representation, it is semantically weak. Description logics based ontology languages like OWL-DL carry a clear-cut semantics, but they are computationally expensive, and they are often misinterpreted to encode all kinds of statements, including those which are not ontological. Method: We distinguish four kinds of statements needed to comprehensively represent domain knowledge: universal statements, terminological statements, statements about particulars and contingent statements. We argue that the task of formal ontologies is solely to represent universal statements, while the non-ontological kinds of statements can nevertheless be connected with ontological representations. To illustrate these four types of representations, we use a running example from parasitology. Results: We finally formulate recommendations for semantically adequate ontologies that can efficiently be used as a stable framework for more context-dependent biomedical knowledge representation and reasoning applications like clinical decision support systems.

scholarly journals Tightly Coupled Fuzzy Description Logic Programs under the Answer Set Semantics for the Semantic Web

2010 ◽  
pp. 237-256 ◽  
Author(s):  
Thomas Lukasiewicz ◽  
Umberto Straccia
Keyword(s):  
Query Processing ◽  
Description Logic ◽  
Description Logics ◽  
Logic Programs ◽  
New Formalism ◽  
Disjunctive Logic Programs ◽  
Tightly Coupled ◽  
Answer Set Semantics ◽  
Fuzzy Description ◽  
Answer Set

This chapter presents a novel approach to fuzzy description logic programs (or simply fuzzy dl-programs) under the answer set semantics, which is a tight integration of fuzzy disjunctive logic programs under the answer set semantics with fuzzy description logics. From a different perspective, it is a generalization of tightly coupled disjunctive dl-programs by fuzzy vagueness in both the description logic and the logic program component. The authors show that the new formalism faithfully extends both fuzzy disjunctive logic programs and fuzzy description logics, and that under suitable assumptions, reasoning in the new formalism is decidable. The authors present a polynomial reduction of certain fuzzy dl-programs to tightly coupled disjunctive dl-programs, and we analyze the complexity of consistency checking and query processing for certain fuzzy dl-programs. Furthermore, the authors provide a special case of fuzzy dl-programs for which deciding consistency and query processing can both be done in polynomial time in the data complexity.

scholarly journals Signature-Based Abduction for Expressive Description Logics

2020 ◽  
Author(s):  
Patrick Koopmann ◽  
Warren Del-Pinto ◽  
Sophie Tourret ◽  
Renate A. Schmidt
Keyword(s):  
Description Logic ◽  
Description Logics ◽  
Background Knowledge ◽  
Knowledge Bases ◽  
Complete Set

Signature-based abduction aims at building hypotheses over a specified set of names, the signature, that explain an observation relative to some background knowledge. This type of abduction is useful for tasks such as diagnosis, where the vocab- ulary used for observed symptoms differs from the vocabulary expected to explain those symptoms. We present the first complete method solving signature-based abduction for observations expressed in the expressive description logic ALC, which can include TBox and ABox axioms. The method is guaranteed to compute a finite and complete set of hypotheses, and is evaluated on a set of realistic knowledge bases.

scholarly journals Loop formulas for description logic programs

2010 ◽  
Vol 10 (4-6) ◽  
pp. 531-545 ◽  
Author(s):  
YISONG WANG ◽  
JIA-HUAI YOU ◽  
LI YAN YUAN ◽  
YI-DONG SHEN
Keyword(s):  
Semantic Web ◽  
Description Logic ◽  
Description Logics ◽  
Answer Set Programming ◽  
Desirable Property ◽  
Logic Programs ◽  
Alternative Semantics ◽  
Answer Set Semantics ◽  
Answer Sets ◽  
Answer Set

AbstractDescription Logic Programs (dl-programs) proposed by Eiter et al. constitute an elegant yet powerful formalism for the integration of answer set programming with description logics, for the Semantic Web. In this paper, we generalize the notions of completion and loop formulas of logic programs to description logic programs and show that the answer sets of a dl-program can be precisely captured by the models of its completion and loop formulas. Furthermore, we propose a new, alternative semantics for dl-programs, called the canonical answer set semantics, which is defined by the models of completion that satisfy what are called canonical loop formulas. A desirable property of canonical answer sets is that they are free of circular justifications. Some properties of canonical answer sets are also explored.

scholarly journals Splitting and updating hybrid knowledge bases

2011 ◽  
Vol 11 (4-5) ◽  
pp. 801-819 ◽  
Author(s):  
MARTIN SLOTA ◽  
JOÃO LEITE ◽  
TERRANCE SWIFT
Keyword(s):  
Logic Programming ◽  
Description Logics ◽  
Expressive Power ◽  
Knowledge Bases ◽  
Theory And Practice ◽  
Useful Knowledge ◽  
Update Semantics ◽  
Closed World ◽  
Real World Applications ◽  
Hybrid Knowledge

AbstractOver the years, nonmonotonic rules have proven to be a very expressive and useful knowledge representation paradigm. They have recently been used to complement the expressive power of Description Logics (DLs), leading to the study of integrative formal frameworks, generally referred to ashybrid knowledge bases, where both DL axioms and rules can be used to represent knowledge. The need to use these hybrid knowledge bases in dynamic domains has called for the development of update operators, which, given the substantially different way DLs and rules are usually updated, has turned out to be an extremely difficult task. In Slota and Leite (2010b Towards Closed World Reasoning in Dynamic Open Worlds.Theory and Practice of Logic Programming, 26th Int'l. Conference on Logic Programming (ICLP'10) Special Issue10(4–6) (July), 547–564.), a first step towards addressing this problem was taken, and an update operator for hybrid knowledge bases was proposed. Despite its significance—not only for being the first update operator for hybrid knowledge bases in the literature, but also because it has some applications—this operator was defined for a restricted class of problems where only the ABox was allowed to change, which considerably diminished its applicability. Many applications that use hybrid knowledge bases in dynamic scenarios require both DL axioms and rules to be updated. In this paper, motivated by real world applications, we introduce an update operator for a large class of hybrid knowledge bases where both the DL component as well as the rule component are allowed to dynamically change. We introduce splitting sequences and splitting theorem for hybrid knowledge bases, use them to define a modular update semantics, investigate its basic properties, and illustrate its use on a realistic example about cargo imports.

scholarly journals Building Rules on Top of Ontologies for the Semantic Web with Inductive Logic Programming

2008 ◽  
Vol 8 (3) ◽  
pp. 271-300 ◽  
Author(s):  
FRANCESCA A. LISI
Keyword(s):  
Semantic Web ◽  
Logic Programming ◽  
Inductive Logic Programming ◽  
Description Logic ◽  
Ad Hoc ◽  
Inductive Logic ◽  
Knowledge Representation And Reasoning ◽  
Reasoning Systems ◽  
Hybrid Knowledge ◽  
Deductive Power

AbstractBuilding rules on top of ontologies is the ultimate goal of the logical layer of the Semantic Web. To this aim, an ad-hoc markup language for this layer is currently under discussion. It is intended to follow the tradition of hybrid knowledge representation and reasoning systems, such as$\mathcal{AL}$-log that integrates the description logic$\mathcal{ALC}$and the function-free Horn clausal languageDatalog. In this paper, we consider the problem of automating the acquisition of these rules for the Semantic Web. We propose a general framework for rule induction that adopts the methodological apparatus of Inductive Logic Programming and relies on the expressive and deductive power of$\mathcal{AL}$-log. The framework is valid whatever the scope of induction (description versus prediction) is. Yet, for illustrative purposes, we also discuss an instantiation of the framework which aims at description and turns out to be useful in Ontology Refinement.

Two results for prioritized logic programming

2003 ◽  
Vol 3 (2) ◽  
pp. 223-242 ◽  
Author(s):  
YAN ZHANG
Keyword(s):  
Knowledge Representation ◽  
Logic Programming ◽  
Logic Program ◽  
Default Reasoning ◽  
Knowledge Representation And Reasoning ◽  
Logic Programs ◽  
Splitting Technique ◽  
Close Relationship ◽  
Answer Set Semantics ◽  
Answer Set

Prioritized default reasoning has illustrated its rich expressiveness and flexibility in knowledge representation and reasoning. However, many important aspects of prioritized default reasoning have yet to be thoroughly explored. In this paper, we investigate two properties of prioritized logic programs in the context of answer set semantics. Specifically, we reveal a close relationship between mutual defeasibility and uniqueness of the answer set for a prioritized logic program. We then explore how the splitting technique for extended logic programs can be extended to prioritized logic programs. We prove splitting theorems that can be used to simplify the evaluation of a prioritized logic program under certain conditions.

scholarly journals Nominals, Inverses, Counting, and Conjunctive Queries or: Why Infinity is your Friend!

2010 ◽  
Vol 39 ◽  
pp. 429-481 ◽  
Author(s):  
S. Rudolph ◽  
B. Glimm
Keyword(s):  
Knowledge Representation ◽  
Description Logic ◽  
Query Language ◽  
Description Logics ◽  
Knowledge Bases ◽  
Conjunctive Query ◽  
Conjunctive Queries ◽  
Decidability Result ◽  
Wide Range ◽  
Significant Attention

Description Logics are knowledge representation formalisms that provide, for example, the logical underpinning of the W3C OWL standards. Conjunctive queries, the standard query language in databases, have recently gained significant attention as an expressive formalism for querying Description Logic knowledge bases. Several different techniques for deciding conjunctive query entailment are available for a wide range of DLs. Nevertheless, the combination of nominals, inverse roles, and number restrictions in OWL 1 and OWL 2 DL causes unsolvable problems for the techniques hitherto available. We tackle this problem and present a decidability result for entailment of unions of conjunctive queries in the DL ALCHOIQb that contains all three problematic constructors simultaneously. Provided that queries contain only simple roles, our result also shows decidability of entailment of (unions of) conjunctive queries in the logic that underpins OWL 1 DL and we believe that the presented results will pave the way for further progress towards conjunctive query entailment decision procedures for the Description Logics underlying the OWL standards.

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