Evaluating Modelling Approaches for Medical Image Annotations

Information system designers face many challenges with regards to selecting appropriate semantic technologies and deciding on a modeling approach for their system. However, there is no clear methodology yet to evaluate “semantically enriched” information systems. In this paper we present a case study on different modeling approaches for annotating medical images and introduce a conceptual framework that can be used to analyze the fitness of information systems and help designers to spot the strengths and weaknesses of various modeling approaches as well as managing trade-offs between modeling effort and their potential benefits

Reasoning with Individuals for the Description Logic SHIQ

While there has been a great deal of work on the development of reasoning algorithms for expressive description logics, in most cases only Tbox reasoning is considered. In this paper we present an algorithm for combined Tbox and Abox reasoning in the SHIQ description logic. This algorithm is of particular interest as it can be used to decide the problem of (database) conjunctive query containment w.r.t. a schema. Moreover, the realisation of an efficient implementation should be relatively straightforward as it can be based on an existing highly optimised implementation of the Tbox algorithm in the FaCT system.Comment: To appear at CADE-1

Practical Reasoning for Very Expressive Description Logics

Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can be computationally problematical. We present an algorithm that decides satisfiability of the DL ALC extended with transitive and inverse roles and functional restrictions with respect to general concept inclusion axioms and role hierarchies; early experiments indicate that this algorithm is well-suited for implementation. Additionally, we show that ALC extended with just transitive and inverse roles is still in PSPACE. We investigate the limits of decidability for this family of DLs, showing that relaxing the constraints placed on the kinds of roles used in number restrictions leads to the undecidability of all inference problems. Finally, we describe a number of optimisation techniques that are crucial in obtaining implementations of the decision procedures, which, despite the worst-case complexity of the problem, exhibit good performance with real-life problems

Conjunctive Query Answering for the Description Logic SHIQ

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

Description Logics with Aggregates and Concrete Domains, Part II

We extend different Description Logics by concrete domains (such as integers and reals) and by aggregation functions over these domains (such as min,max,count,sum), which are usually available in database systems. We present decision procedures for the inference problems satisfiability for these Logics-provided that the concrete domain is not too expressive. An example of such a concrete domain is the set of (nonnegative) integers with comparisons (=,≤, ≤n, ...) and the aggregation functions min, max, count.This is a new, extended version of a report with the same number. An abridged version has appeared in the Proceedings of the European Conference on Artificial Intelligence, Brighton, UK, 1998

The modular structure of an ontology: Atomic decomposition

Extracting a subset of a given ontology that captures all the ontology’s knowledge about a specified set of terms is a well-understood task. This task can be based, for instance, on locality-based modules. However, a single module does not allow us to understand neither topicality, connectedness, structure, or superfluous parts of an ontology, nor agreement between actual and intended modeling. The strong logical properties of locality-based modules suggest that the family of all such modules of an ontology can support comprehension of the ontology as a whole. However, extracting that family is not feasible, since the number of localitybased modules of an ontology can be exponential w.r.t. its size. In this paper we report on a new approach that enables us to efficiently extract a polynomial representation of the family of all locality-based modules of an ontology. We also describe the fundamental algorithm to pursue this task, and report on experiments carried out and results obtained.

The Complexity of Reasoning with Boolean Modal Logics: Extended Version

Since Modal Logics are an extension of Propositional Logic, they provide Boolean operators for constructing complex formulae. However, most Modal Logics do not admit Boolean operators for constructing complex modal parameters to be used in the box and diamond operators. This asymmetry is not present in Boolean Modal Logics, in which box and diamond quantify over arbitrary Boolean combinations of atomic model parameters.This is an extended version of the article in: Advances in Modal Logic (AiML), Volume

Description Logics with Symbolic Number Restrictions

Aus der Einleitung: „Terminological knowledge representation systems (TKR systems) are powerful tools not only to represent but also to reason about the knowledge on the terminology of an application domain. Their particular power lie in their ability to infer implicit knowledge from the knowledge explicitly stored in a knowledge base. Mainly, a TKR system consists of three parts: First, a terminological knowledge base which contains the explicit description of the concepts relevant for the application domain. Second, an assertional knowledge base which contains the description of concrete individuals and their relations. This description of concrete individuals is realized using the terminology fixed in the terminological knowledge base. Third, a TKR system comprises an inference engine which is able to infer implicit properties of the defined concepts and individuals such as subclass/superclass relations amongst concepts (subsumption), the classifcation of all defned concepts with respect to the subclass/superclass relation. This yields the class taxonomy. whether there exists an interpretation of the terminology where a given concept has at least one instance (satisfiability), to enumerate all individuals that are instances of a given concept (retrieval), given a concrete individual, to enumerate the most specific concepts of the terminology this individual is an instance of.

A Description Logic with Transitive and Converse Roles, Role Hierarchies and Qualifying Number Restrictions

As widely argued [HG97; Sat96], transitive roles play an important role in the adequate representation of aggregated objects: they allow these objects to be described by referring to their parts without specifying a level of decomposition. In [HG97], the Description Logic (DL) ALCHR+ is presented, which extends ALC with transitive roles and a role hierarchy. It is argued in [Sat98] that ALCHR+ is well-suited to the representation of aggregated objects in applications that require various part-whole relations to be distinguished, some of which are transitive. However, ALCHR+ allows neither the description of parts by means of the whole to which they belong, or vice versa. To overcome this limitation, we present the DL SHI which allows the use of, for example, has part as well as is part of. To achieve this, ALCHR+ was extended with inverse roles. It could be argued that, instead of defining yet another DL, one could make use of the results presented in [DL96] and use ALC extended with role expressions which include transitive closure and inverse operators. The reason for not proceeding like this is the fact that transitive roles can be implemented more efficiently than the transitive closure of roles (see [HG97]), although they lead to the same complexity class (ExpTime-hard) when added, together with role hierarchies, to ALC. Furthermore, it is still an open question whether the transitive closure of roles together with inverse roles necessitates the use of the cut rule [DM98], and this rule leads to an algorithm with very bad behaviour. We will present an algorithm for SHI without such a rule. Furthermore, we enrich the language with functional restrictions and, finally, with qualifying number restrictions. We give sound and complete decision proceduresfor the resulting logics that are derived from the initial algorithm for SHI. The structure of this report is as follows: In Section 2, we introduce the DL SI and present a tableaux algorithm for satisfiability (and subsumption) of SI-concepts—in another report [HST98] we prove that this algorithm can be refined to run in polynomial space. In Section 3 we add role hierarchies to SI and show how the algorithm can be modified to handle this extension appropriately. Please note that this logic, namely SHI, allows for the internalisation of general concept inclusion axioms, one of the most general form of terminological axioms. In Section 4 we augment SHI with functional restrictions and, using the so-called pairwise-blocking technique, the algorithm can be adapted to this extension as well. Finally, in Section 5, we show that standard techniques for handling qualifying number restrictions [HB91;BBH96] together with the techniques described in previous sections can be used to decide satisfiability and subsumption for SHIQ, namely ALC extended with transitive and inverse roles, role hierarchies, and qualifying number restrictions. Although Section 5 heavily depends on the previous sections, we have made it self-contained, i.e. it contains all necessary definitions and proofs from scratch, for a better readability. Building on the previous sections, Section 6 presents an algorithm that decides the satisfiability of SHIQ-ABoxes