Knowledge base exchange: the case of OWL 2 QL

In this article, we define and study the problem of exchanging knowledge between a source and a target knowledge base (KB), connected through mappings. Differently from the traditional database exchange setting, which considers only the exchange of data, we are interested in exchanging implicit knowledge. As representation formalism we use Description Logics (DLs), thus assuming that the source and target KBs are given as a DL TBox+ABox, while the mappings have the form of DL TBox assertions. We define a general framework of KB exchange, and study the problem of translating the knowledge in the source KB according to the mappings expressed in OWL 2 QL, the profile of the standard Web Ontology Language OWL 2 based on the description logic DL-LiteR. We develop novel game- and automata-theoretic techniques, and we provide complexity results that range from NLogSpace to ExpTim

Metamathematics Of Contexts

In this paper we investigate the simple logical properties of contexts. We describe both the syntax and semantics of a general propositional language of context, and we give a Hilbert style proof system for this language. A propositional logic of context extends classical propositional logic in two ways. Firstly, a new modality, ist(; OE), is introduced. It is used to express that the sentence, OE, holds in the context, . Secondly, each context has its own vocabulary, i.e. a set of propositional atoms which are defined or meaningful in that context. The main results of this paper are the soundness and completeness of this Hilbert style proof system. We also provide soundness and completeness results (i.e., correspondence theory) for various extensions of the general system. Finally, we prove that our logic is decidable, and give a brief comparison of our semantics to Kripke semantics. 1 Introduction In this paper we investigate the simple logical properties of contexts. Contexts were..

The Semantics of Propositional Contexts

. In this paper we investigate the semantic properties of contexts. We describe the syntax and semantics of the propositional logic of context. This logic extends classical propositional logic in two ways. Firstly, a new modality, ist(; OE), is introduced. It is used to express that the sentence, OE, holds in the context . Secondly, each context has its own vocabulary, i.e. a set of propositional atoms which are defined or meaningful in that context. The main results of this paper are a proof that our logic is decidable and comparison of our semantics to Kripke semantics. 1 Introduction In this paper we investigate the semantic properties of contexts as they appear in declarative AI. Contexts were first suggested in McCarthy's Turing Award Paper, [5], as a possible solution to the problem of generality in AI. Our main motivation for formalizing contexts is to solve this problem. We want to be able to make AI systems which are never permanently stuck with the concepts they use at a gi..

Metamathematics Of Contexts

In this paper we investigate the simple logical properties of contexts. We describe both the syntax and semantics of a general propositional language of context, and we give a Hilbert style proof system for this language. A propositional logic of context extends classical propositional logic in two ways. Firstly, a new modality, ist(; OE), is introduced. It is used to express that the sentence, OE, holds in the context, . Secondly, each context has its own vocabulary, i.e. a set of propositional atoms which are defined or meaningful in that context. The main results of this paper are the soundness and completeness of this Hilbert style proof system. We also provide soundness and completeness results (i.e., correspondence theory) for various extensions of the general system. Finally, we prove that our logic is decidable, and give a brief comparison of our semantics to Kripke semantics. 1 Introduction In this paper we investigate the simple logical properties of contexts. Contexts were..

Formalizing Context (Expanded Notes)

These notes discuss formalizing contexts as first class objects. The basic relationships are: ist(c,p) meaning that the proposition p is true in the context c, and value(c,p) designating the value of the term e in the context c Besides these, there are lifting formulas that relate the propositions and terms in subcontexts to possibly more general propositions and terms in the outer context. Subcontextx are often specialised with regard to time, place and terminology. Introducing contexts as formal objects will permit axiomatizations in limited contexts to be expanded to transcend the original limitations. This seems necessary to provide AI programs using logic with certain capabilities that human fact representation and human reasoning possess. Fully implementing transcendence seems to require further extensions to mathematical logic, ie. beyond the nonmonotonic inference methods first invented in AI and now studied as a new domain of logic

Quantificational Logic of Context

In this paper we extend the Propositional Logic of Context, (Buvac & Mason 1993; Buvac, Buvac, & Mason 1995), to the quantificational (predicate calculus) case. This extension is important in the declarative representation of knowledge for two reasons. Firstly, since contexts are objects in the semantics which can be denoted by terms in the language and which can be quantified over, the extension enables us to express arbitrary first-order properties of contexts. Secondly, since the extended language is no longer only propositional, we can express that an arbitrary predicate calculus formula is true in a context. The paper describes the syntax and the semantics of a quantificational language of context, gives a Hilbert style formal system, and outlines a proof of the system's completeness. Introduction Contexts first appeared in declarative AI when they were presented as a possible solution to the problem of generality in McCarthy's Turing Award Paper, (McCarthy 1987). ..

Decidability of Contextual Reasoning

this paper is to show that propositional contextual reasoning is decidable. Propositional logic of context extends classical propositional logic with a new modality, ist(c; OE), used to express that the sentence, OE, is true in the contex