DL systems DL and the Web Ilie Savga [email protected]

• • • • Introduction DL systems: general overview - FaCT DL for the Semantic Web - DAML+OIL Conclusions

Content

Introduction

The main effort of research in knowledge representation is in providing theories and systems for expressing structured knowledge, for accessing it and reasoning with it in a principled way (Fensel et al).

DLs form an important and powerful class of logic-based KR languages.

DL systems: general overview

The investigation of the trade-off between the expressivity of DLs and the complexity of their inference problems - one of the most important issues in DL research.

This proccess has passed several phases.

DL systems: general overview

• Phase 1: First system implementations KL-ONE signaled the transition from semantic networks to DL. Introduced most of the key notions: concepts and roles, number and value restrictions, subsumption and classification, the distinction between TBox and ABox.

Its early descendants: BACK, LOOM, K-REP and others.

DL systems: general overview

• Phase 2: First complexity and undecidability results The structural subsumption algorithms used by the first systems turned to be quite efficient only for the very inexpressive DLs and undecidability problems were detected in some cases.

Two approaches: - call it a feature, not a bug (BACK, LOOM); - carefully restrict DL (CLASSIC);

DL systems: general overview

• Phase 3: Tableau algorithms for expressive DLs and thorough complexity analysis.

Tableau algorithms were developed - complete and of worst case complexity.

First DL systems (KRIS, CRACK) employing such algorithms demonstrated their acceptable behavior in practice.

Then the highly optimised systems (FaCT, DLP, Race) appeared with excellent benchmark results.

DL systems: general overview

• Algorithms and efficient systems for

very

expressive DLs.

Push further the decidability bound by implementing “practical” tableau algorithms for the very expressive DLs (e.g. DLs that do not have the finite model property).

DL systems: FaCT

FaCT (Fast Classification of Terminologies) is a DL classifier. • • • Its most interesting features: expressive logic - SHF resoner (ALC + transitive and functional roles and a role hierarchy) - SHIQ reasoner (SHF + inverse roles and qualified number restrictions) optimised tableaux implementation (become the standard for DL systems) CORBA client-server architecture

DL systems: FaCT

FaCT’s optimizations are specifically aimed at improving the system’s performance when classifying realistic ontologies. This results in performance improvements of several orders of magnitude when compared with older DL systems. It even solves the problems that are not-terminating for unoptimised systems.

FaCT checked and classified 2.740 classes from GALEN ontology in 60 sec. while KRIS gave up after several weeks of CPU time.

DL and WWW

It has long been realised that the web would benefit from some structure and explicit semantics for at least some of its content.

There are several possible directions DL can be applied to address the opened issues of WWW and the research just began !

Among the possible domains of interest are:

DL and WWW

• Structural modeling The possibility of viewing WWW as a semantic network has been considered since the advent of the Web itself.

The Untangle system is a DL system for representing bibliographic information.

It implements a hypertext view of the TBox and ABox semantic networks and uses nested bullet lists to view the concept taxonomy, with in-page cross references for concepts having multiple parents.

It is aimed to improve the accuracy and increase the throughput of classification.

DL and WWW

• Improving of information retrieval FindUR system allows for increasing of positive search results by query expansion.

It specifies the classification of sets of synonyms (and hyponyms). Wherever an input search query contains any term from the knowledge base, a new query is created by replacing the term with the disjunction of all the synonymous terms (and hyponyms).

DL and WWW

• Enabling the Semantic Web It is widely agreed that ontologies will play a key role in providing the web infrastructure in a machine understandable form. Hence, the ontology languages are of extreme importance for the Semantic Web.

While giving the clear and well defined semantics for ontology languages, DLs still allows for an efficient reasoning support.

This provides the basis for the machine processable interpretation of information, making possible the “Knowledgeable Web”.

DL and OIL

• • • OIL can be seen as a syntactic variant of the description logic SHIQ extended with simple concrete datatypes. Rather than providing the usual model theoretic semantics, OIL defines a translation function that maps an OIL ontology into an equivalent SHIQ(D) terminology. From this mapping, OIL derives both a clear semantics and a means to exploit the reasoning services of DL systems such as FaCT and Racer that implement (most of) SHIQ(D).

Mapping is trivial, exception - One-of constructor.

DL and DAML+OIL

DAML+OIL - a DL in RDF clothes.

RDFS is the only specification of the languages.

It improves the portability and re-use, but RDFS is not powerful enough to completely define the structure of the DAML+OIL.

Example: there is no way in RDFS to state that a restriction (slot constraint) should consist of exactly one property (slot) and one class.

Solution: to give a meaning to any (parts of) ontologies that conform to RDFS by defining the semantics of the language.

DL and DAML+OIL

• • • • • Several “unusual” features: no sense of a main definition of a class or individual: it is spread over the KB in form of RDF triples has two semantics: model-theoretic and an axiomatization (using KIF) allows named individuals to occur in concept definitions large collection of primitive datatypes from XML schema no way to capture the language constraint that cardinality constraints can only be applied to simple slots. Hence, DAML+OIL is teoretically undecidable !

DL and DAML+OIL

• • • All in one: “DAML+OIL is equivalent to a very expressive DL but … don’t tell anyone “ (Horrock) It is an extension of SHIQ DL by datatypes and nominals No reasoning algorithms proved and reasoning systems developed that support all the features of the language but… they are on their way ...

DL and DTD

• • The encoding of DTDs into DL is provided and can be exploited to verify inclusion, equivalence and disjointness between the sets of documents conforming respectively to two DTDs.

strong comparison considers both the document structure and the actual tag names structural comparison considers only the document structure

Conclusion

The well-defined semantics and efficient inference procedures of the Description Logics are crucial to the success of the Semantic Web.

Providing the formal basis for the important languages like OIL and DAML+OIL, DLs are of great importance on the way to the machine processable support in data, information and knowledge exchange.

With no doubt, new optimised algorithms and systems will be developed to improve the performance and to efficiently support the standards .

“The Semantic Web needs a logic on top” (Henry Thompson)