The main effort of the research in knowledge representation is providing theories and systems for expressing structured knowledge and for accessing and reasoning with it in a principled way. Description Logics are considered the most important knowledge representation formalism unifying and giving a logical basis to the well known traditions of Frame-based systems, Semantic Networks and KL-ONE-like languages, Object-Oriented representations, Semantic data models, and Type systems.
This article surveys previous work on combining planning techniques with expressive representations of knowledge in description logics to reason about tasks, plans, and goals. Description logics can reason about the logical definition of a class and automatically infer class-subclass subsumption relations as well as classify instances into classes based on their definitions. Descriptions of actions, plans, and goals can be exploited during plan generation, plan recognition, or plan evaluation. These techniques should be of interest to planning practitioners working on knowledge-rich application domains. Another emerging use of these techniques is the semantic web, where current ontology languages based on description logics need to be extended to reason about goals and capabilities for web services and agents.
Data integration is the problem of combining data residing at different autonomous, heterogeneous sources and providing the client with a unified, reconciled global view of the data. We discuss dataintegration systems, taking the abstract viewpoint that the global view is an ontology expressed in a class-based formalism. We resort to an expressive description logic, ALCQI, that fully captures classbased representation formalisms, and we show that query answering in data integration, as well as all other relevant reasoning tasks, is decidable. However, when we have to deal with large amounts of data, the high computational complexity in the size of the data makes the use of a fullfledged expressive description logic infeasible in practice. This leads us to consider DL-Lite, a specifically tailored restriction of ALCQI that ensures tractability of query answering in data integration while keeping enough expressive power to capture the most relevant features of class-based formalisms.
Information incompleteness, or ignorance, is an issue that we have to consider in Semantic Web applications. Dempster-Shafer theory has been traditionally applied in information incompleteness situations. On the other hand, logic plays a major role in the Semantic Web community. In this paper, we propose a framework that applies Dempster-Shafer theory in a Description Logic Knowledge Base environment. We name our model a Dempster-Shafer DL Knowledge Base.
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.
Enrico Franconi's Course on Description Logics The material includes slides for 6 modules ( 320 slides): A review of Computational Logics, Structural Description Logics, Propositional Description Logics, Description Logics and Knowledge Bases, Description Logics and Logics, Description Logics and Databases. A web pointer to an online modified version of CRACK, allowing for tracing satisfiability proofs with tableaux, is provided. Pointers to relevant online literature are provided, too. Enrico Franconi's Course on Description Logics The material includes slides for 6 modules ( 320 slides): A review of Computational Logics, Structural Description Logics, Propositional Description Logics, Description Logics and Knowledge Bases, Description Logics and Logics, Description Logics and Databases. A web pointer to an online modified version of CRACK, allowing for tracing satisfiability proofs with tableaux, is provided.
Two essential tasks in managing description logic knowledge bases are eliminating problematic axioms and incorporating newly formed ones. Standard description logic semantics yields an infinite number of models for DL-Lite knowledge bases, thus it is difficult to develop algorithms for contraction and revision that involve DL models. It is more succinct and importantly, with a finite signature, the semantics always yields a finite number of models. We then define model-based contraction and revision functions for DL-Lite knowledge bases under type semantics and provide representation theorems for them.
Fuzzy Description Logics (DLs) are used to represent and reason about vague and imprecise knowledge that is inherent to many application domains. It was recently shown that the complexity of reasoning in finitely valued fuzzy DLs is often not higher than that of the underlying classical DL. We show that this does not hold for fuzzy extensions of the light-weight DL EL, which is used in many biomedical ontologies, under the Lukasiewicz semantics. The complexity of reasoning increases from PTime to ExpTime, even if only one additional truth value is introduced. The same lower bound holds also for infinitely valued Lukasiewicz extensions of EL.
Calvanese, Diego (Free University of Bozen-Bolzano) | Giacomo, Giuseppe De (Sapienza University of Rome) | Montali, Marco (Free University of Bozen-Bolzano) | Patrizi, Fabio (Free University of Bozen-Bolzano)
In this paper, we overview the recently introduced general framework of Description Logic Based Dynamic Systems, which leverages Levesque's functional approach to model systems that evolve the extensional part of a description logic knowledge base by means of actions. This framework is parametric w.r.t. the adopted description logic and the progression mechanism. In this setting, we discuss verification and adversarial synthesis for specifications expressed in a variant of first-order mu-calculus, with a controlled form of quantification across successive states, and present key decidability results under the natural assumption of state-boundedness.
Botoeva, Elena (Free University of Bozen-Bolzano) | Kontchakov, Roman (Birkbeck, University of London) | Ryzhikov, Vladislav (Free University of Bozen-Bolzano) | Wolter, Frank (University of Liverpool) | Zakharyaschev, Michael (Birkbeck, University of London)
Deciding inseparability of description logic knowledge bases (KBs) with respect to conjunctive queries is fundamental for many KB engineering and maintenance tasks including versioning, module extraction, knowledge exchange and forgetting. We study the combined and data complexity of this inseparability problem for fragments of Horn-ALCHI, including the description logics underpinning OWL 2 QL and OWL 2 EL.