Description Logics for Modelling Dynamic Information
Federica MANDREOLI2002
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Abstract
In the first part of this Chapter we will introduce a general temporally enhanced conceptual data model able to represent time varying data, in the spirit of a temporally enhanced Entity-Relationship data model. In the second part, we will introduce an object-oriented conceptual data model enriched with schema change operators, which are able to represent the explicit temporal evolution of the schema while maintaining a consistent view on the (static) instantiated data. We will introduce a provably correct encoding of both conceptual data models and their inference problems in Description Logics. In this way, we study the properties of both the temporal conceptual data model and the object-oriented data model with schema change facilities.
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Description logics for modeling dynamic information
In the first part of this Chapter we will introduce a general temporally enhanced conceptual data model able to represent time varying data, in the spirit of a temporally enhanced Entity-Relationship data model. In the second part, we will introduce an object-oriented conceptual data model enriched with schema change operators, which are able to represent the explicit temporal evolution of the schema while maintaining a consistent view on the (static) instantiated data. We will introduce a provably correct encoding of both conceptual data models and their inference problems in Description Logics. In this way, we study the properties of both the temporal conceptual data model and the object-oriented data model with schema change facilities.
A Cookbook for Temporal Conceptual Data Modelling with Description Logics
ACM Transactions on Computational Logic, 2014
We design temporal description logics suitable for reasoning about temporal conceptual data models and investigate their computational complexity. Our formalisms are based on DL-Lite logics with three types of concept inclusions (ranging from atomic concept inclusions and disjointness to the full Booleans), as well as cardinality constraints and role inclusions. The logics are interpreted over the Cartesian products of object domains and the flow of time (Z, <), satisfying the constant domain assumption. Concept and role inclusions of the TBox hold at all moments of time (globally) and data assertions of the ABox hold at specified moments of time. To express temporal constraints of conceptual data models, the languages are equipped with flexible and rigid roles, standard future and past temporal operators on concepts and operators 'always' and 'sometime' on roles. The most expressive of our temporal description logics (which can capture lifespan cardinalities and either qualitative or quantitative evolution constraints) turns out to be undecidable. However, by omitting some of the temporal operators on concepts/roles or by restricting the form of concept inclusions we construct logics whose complexity ranges between NLOGSPACE and PSPACE. These positive results are obtained by reduction to various clausal fragments of propositional temporal logic, which opens a way to employ propositional or first-order temporal provers for reasoning about temporal data models. Zakharyaschev. 2014. A cookbook for temporal conceptual data modelling with description logics.
Tailoring Temporal Description Logics for Reasoning over Temporal Conceptual Models
Lecture Notes in Computer Science, 2011
Temporal data models have been used to describe how data can evolve in the context of temporal databases. Both the Extended Entity-Relationship (EER) model and the Unified Modelling Language (UML) have been temporally extended to design temporal databases. To automatically check quality properties of conceptual schemas various encoding to Description Logics (DLs) have been proposed in the literature. On the other hand, reasoning on temporally extended DLs turn out to be too complex for effective reasoning ranging from 2EXPTIME up to undecidable languages. We propose here to temporalize the 'light-weight' DL-Lite logics obtaining nice computational results while still being able to represent various constraints of temporal conceptual models. In particular, we consider temporal extensions of DL-Lite N bool , which was shown to be adequate for capturing non-temporal conceptual models without relationship inclusion, and its fragment DL-Lite N core with most primitive concept inclusions, which are nevertheless enough to represent almost all types of atemporal constraints (apart from covering).
A Temporal Description Logic for Reasoning over Conceptual Schemas and Queries
Lecture Notes in Computer Science, 2002
This paper introduces a new logical formalism, intended for temporal conceptual modelling, as a natural combination of the well-known description logic ÄÊ and point-based linear temporal logic with Since and Until. The expressive power of the resulting ÄÊÍË logic is illustrated by providing a characterisation of the most important temporal conceptual modelling constructs appeared in the literature. We define a query language (where queries are non-recursive Datalog programs and atoms are complex ÄÊÍË expressions) and investigate the problem of checking query containment under the constraints defined by ÄÊÍË conceptual schemas-i.e., ÄÊÍË knowledge bases-as well as the problems of schema satisfiability and logical implication. Although it is shown that reasoning in full ÄÊÍË is undecidable, we identify the decidable (in a sense, maximal) fragment ÄÊ ÍË by allowing applications of temporal operators to formulas and class expressions only (but not to relation expressions). We obtain the following hierarchy of complexity results: (a) reasoning in ÄÊ ÍË with atomic formulas is EXPTIME-complete, (b) satisfiability and logical implication of arbitrary ÄÊ ÍË formulas is EXPSPACE-complete, and (c) the problem of checking query containment of non-recursive Datalog queries under ÄÊ ÍË constraints is decidable in 2EXPTIME.
Description Logics for Conceptual Data Modeling
inf.unibz.it, 1998
The article aims at establishing a logical approach to class-based data modeling. After a discussion on class-based formalisms for data modeling, we introduce a family of logics, called Description Logics, which stem from research on Knowledge Representation in Artificial Intelligence. The logics of this family are particularly well suited for specifying data classes and relationships among classes, and are equipped with both formal semantics and inference mechanisms. We demonstrate that several popular data modeling formalisms, including the Entity-Relationship Model, and the most common variants of object-oriented data models, can be expressed in terms of specific logics of the family. For this purpose we use a unifying Description Logic, which incorporates all the features needed for the logical reformulation of the data models used in the various contexts. We also discuss the problem of devising reasoning procedures for the unifying formalism, and show that they provide valuable supports for several important data modeling activities.
Applications of description logics: State of the art and research challenges
2005
Description Logics (DLs) are a family of class based knowledge representation formalisms characterised by the use of various constructors to build complex classes from simpler ones, and by an emphasis on the provision of sound, complete and (empirically) tractable reasoning services. They have a range of applications, but are mostly widely known as the basis for ontology languages such as OWL.
Happy Ever After: Temporally Attributed Description Logics
Description Logics, 2018
Knowledge graphs are based on graph models enriched with (sets of) attribute-value pairs, called annotations, attached to vertices and edges. Many application scenarios of knowledge graphs crucially rely on the frequent use of annotations related to time. Based on recently proposed attributed logics, we design description logics enriched with temporal annotations whose values are interpreted over discrete time. Investigating the complexity of reasoning in this new formalism, it turns out that reasoning in our temporally attributed description logic ALCH@ is highly undecidable; thus we establish restrictions where it becomes decidable, and even tractable.
A conceptual modelling formalism for temporal database applications
Information Systems, 1991
Arguably the most critical of all activities in the development of an information system is that of requirements modelling. The effectiveness of such a specification depends largely on the ability of the chosen conceptual model to represent the problem domain in such a way so as to permit natural and rigorous descriptions within a methodological framework. Recent years have witnessed an increased demand for information systems which cover a wide spectrum of application domains. This, inevitably, has had the effect of demanding conceptual models of enhanced functionality and expressive power than is currently possible in practice. This paper introduces the TEMPORA modelling paradigm for developing information system applications from a unified perspective which deals with definitional, intentional and constrain knowledge. The paper discusses in detail one of the components of the TEMPORA conceptual model, the entity-relationshiptime (ERT) model, which deals with structural aspects including time and complex objects modelling.
Temporalising Tractable Description Logics
14th International Symposium on Temporal Representation and Reasoning (TIME'07), 2007
It is known that for temporal languages, such as firstorder LT L, reasoning about constant (time-independent) relations is almost always undecidable. This applies to temporal description logics as well: constant binary relations together with general concept subsumptions in combinations of LT L and the basic description logic ALC cause undecidability. In this paper, we explore temporal extensions of two recently introduced families of 'weak' description logics known as DL-Lite and EL. Our results are twofold: temporalisations of even rather expressive variants of DL-Lite turn out to be decidable, while the temporalisation of EL with general concept subsumptions and constant relations is undecidable.
An Ontologically-Founded Reification Approach for Representing Temporally Changing Information in OWL
In this paper we present an approach for representing temporally changing information in OWL. This approach is based on a reification strategy founded on results from the philosophical discipline of Formal Ontology. These results grant ontological meaning to the reified individuals (intrinsic and relational properties) and provide an ontological semantics to the resulting specification. We also propose here some methodological guidelines for guiding the use of the proposed framework in supporting modeling decisions in OWL. By using the proposed framework, one can represent domain information regarding sources of temporal change such as the distinction between necessary versus contingent properties, or mutable versus immutable ones. Finally, we compare the proposed approach with another commonly used strategy for circumventing OWL ́s limitation w.r.t. temporally changing information.
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Toward Updates in Description Logics
The use of DL systems to add reasoning capabilities to database is now a major trend in convergence between knowledge base and database system but is still confronted with the issue of data update. DL systems provide fact additions and retractions but no real object update mechanisms. We present a semantics for update that favours attribute values to concept membership and deals with incomplete information. After relating our work to an existing previous one on update semantics we address implementation issues.
Base revision in description logics-preliminary results
Proc. of IWOD, 2007
Works on ontology versioning pay special attention to the logical analysis of ontology evolution. The paper considers extensible declarative approach to ontology change description. Metric temporal description logic with metric temporal modalities "future n" and "past n" and hybrid satisfaction operator @ is proposed as the logical basis for declarative ontology evolution analysis. Underlying time structure assumed to be linear and discrete, which is acceptable for modeling of ontology versions sequence. Introduced is OWL-MeT -metric extension of the Web ontology language OWL, which is supported with a reasoning engine under development on the basis of Pellet reasoner.
On the representation of temporally changing information in OWL
An important challenge in the Knowledge Representation area is on representing and reasoning over temporally changing information. Particularly, a number of authors have been investigating approaches to extend the expressivity beyond what is currently supported by the DL (Description Logics) based languages in order to address this issue, while maintaining compatibility with subclasses of DLs adopted in the Semantic Web. This is mainly due to the increasing popularity of the Semantic Web initiative as well as the role played by DL in that context. In this paper we defend the need of a higher-level foundational framework based on results coming from the discipline of Formal Ontology. We present two complementary proposals for modeling temporally changing information in OWL, based on the most discussed strategy in the literature to address this problem, namely, the use of a perdurantist (or 4D) view of domain entities. Moreover we compare the results with some related work and discuss its limitations and further improvements.
A Solution to the Ramification Problem Expressed in Temporal Description Logics
International Journal of Semantic Computing, 2014
The ramification problem in Artificial Intelligence is concerned with the indirect effects of an action. It has been shown in previous work that the ramification problem can be solved with the use of integrity constraints and actions representation. In this paper we begin with a quick review of the existing Description Logic Languages, and then we describe a Temporal Extension of Description Logics, able to represent integrity constraints, temporalized actions and non persistent effects. We describe a thorough solution to the ramification problem in Temporal Settings expressed in Temporal Description Logics. The solution also deals with the hard case, in which the effects of an action change the belief about the past.
Conceptual Modeling with Description Logics
Theory, Implementation and Applications, 2007
The purpose of the chapter is to help someone familiar with DLs to understand the issues involved in developing an ontology for some universe of discourse, which is to become a conceptual model or knowledge base represented and reasoned with using Description Logics. We briefly review the purposes and history of conceptual modeling, and then use the domain of a university library to illustrate an approach to conceptual modeling that combines general ideas of object-centered modeling with a look at special modeling/ontological problems, and DL-specific solutions to them. Among the ontological issues considered are the nature of individuals, concept specialization, non-binary relationships, materialization, aspects of part-whole relationships, and epistemic aspects of individual knowledge.
Temporally Attributed Description Logics
2019
Knowledge graphs are based on graph models enriched with (sets of) attribute-value pairs, called annotations, attached to vertices and edges. Many application scenarios of knowledge graphs crucially rely on the frequent use of annotations related to time. Building upon attributed logics, we design description logics enriched with temporal annotations whose values are interpreted over discrete time. Investigating the complexity of reasoning in this new formalism, it turns out that reasoning in our temporally attributed description logic \(\mathcal {ALCH} ^{\mathbb {T}}_@\) is highly undecidable; thus we establish restrictions where it becomes decidable, and even tractable.
The Description Logic Handbook
2007
Description logics are embodied in several knowledge-based systems and are used to develop various real-life applications. Now in paperback, The Description Logic Handbook provides a thorough account of the subject, covering all aspects of research in this field, namely: theory, implementation, and applications. Its appeal will be broad, ranging from more theoretically oriented readers, to those with more practically oriented interests who need a sound and modern understanding of knowledge representation systems based on description logics. As well as general revision throughout the book, this new edition presents a new chapter on ontology languages for the semantic web, an area of great importance for the future development of the web. In sum, the book will serve as a unique resource for the subject, and can also be used for self-study or as a reference for knowledge representation and artificial intelligence courses.
Definitorially Complete Description Logics
Principles of Knowledge Representation and Reasoning, 2006
The Terminology Box (TBox) of a Description Logic (DL) knowledge base is used to define new concepts in terms of primitive concepts and relations. The topic of this paper is the effect of the available operations in a DL on the length and the syntactic shape of definitions in a Terminology Box. Defining new concepts can be done in two
Description logics
2008
In this chapter we will introduce description logics, a family of logic-based knowledge representation languages that can be used to represent the terminological knowledge of an application domain in a structured way. We will first review their provenance and history, and show how the field has developed.
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