Results 11  20
of
97
Logicbased ontology comparison and module extraction, with an application to DLLite
 ARTIFICIAL INTELLIGENCE
, 2010
"... We develop a formal framework for comparing different versions of DLLite ontologies. The main feature of our approach is that we take into account the vocabulary ( = signature) with respect to which one wants to compare ontologies. Five variants of difference and inseparability relations between on ..."
Abstract

Cited by 13 (6 self)
 Add to MetaCart
We develop a formal framework for comparing different versions of DLLite ontologies. The main feature of our approach is that we take into account the vocabulary ( = signature) with respect to which one wants to compare ontologies. Five variants of difference and inseparability relations between ontologies are introduced and their respective applications for ontology development and maintenance discussed. These variants are obtained by generalising the notion of conservative extension from mathematical logic and by distinguishing between differences that can be observed among concept inclusions, answers to queries over ABoxes, by taking into account additional context ontologies, and by considering a modeltheoretic, languageindependent notion of difference. We compare these variants, study their metaproperties, determine the computational complexity of the corresponding reasoning tasks, and present decision algorithms. Moreover, we show that checking inseparability can be automated by means of encoding into QBF satisfiability and using offtheshelf general purpose QBF solvers. Inseparability relations between ontologies are then used to develop a formal framework for (minimal) module extraction. We demonstrate that different types of minimal modules induced by these inseparability relations can be automatically extracted from realworld mediumsize DLLite ontologies by composing the tractable syntactic localitybased module extraction algorithm with nontractable extraction algorithms using the multiengine QBF solver aqme. Finally, we explore the relationship between uniform interpolation (or forgetting) and inseparability between ontologies.
Fast Approximate Search in Large Dictionaries
 COMPUTATIONAL LINGUISTICS
, 2004
"... The need to correct garbled strings arises in many areas of natural language processing. If a dictionary is available that covers all possible input tokens, a natural set of candidates for correcting an erroneous input P is the set of all words in the dictionary for which the Levenshtein distance to ..."
Abstract

Cited by 12 (3 self)
 Add to MetaCart
The need to correct garbled strings arises in many areas of natural language processing. If a dictionary is available that covers all possible input tokens, a natural set of candidates for correcting an erroneous input P is the set of all words in the dictionary for which the Levenshtein distance to P does not exceed a given (small) bound k. In this article we describe methods for efficiently selecting such candidate sets. After introducing as a starting point a basic correction method based on the concept of a "universal Levenshtein automaton," we show how two filtering methods known from the field of approximate text search can be used to improve the basic procedure in a significant way. The first method, which uses standard dictionaries plus dictionaries with reversed words, leads to very short correction times for most classes of input strings. Our evaluation results demonstrate that correction times for fixeddistance bounds depend on the expected number of correction candidates, which decreases for longer input words. Similarly the choice of an optimal filtering method depends on the length of the input words.
Probabilistic modal logic
 Proceedings of the 22nd AAAI Conference on Artificial Intelligence. (2007) 489
, 2007
"... A modal logic is any logic for handling modalities: concepts like possibility, necessity, and knowledge. Artificial intelligence uses modal logics most heavily to represent and reason about knowledge of agents about others ’ knowledge. This type of reasoning occurs in dialog, collaboration, and comp ..."
Abstract

Cited by 11 (2 self)
 Add to MetaCart
A modal logic is any logic for handling modalities: concepts like possibility, necessity, and knowledge. Artificial intelligence uses modal logics most heavily to represent and reason about knowledge of agents about others ’ knowledge. This type of reasoning occurs in dialog, collaboration, and competition. In many applications it is also important to be able to reason about the probability of beliefs and events. In this paper we provide a formal system that represents probabilistic knowledge about probabilistic knowledge. We also present exact and approximate algorithms for reasoning about the truth value of queries that are encoded as probabilistic modal logic formulas. We provide an exact algorithm which takes a probabilistic Kripke structure and answers probabilistic modal queries in polynomialtime in the size of the model. Then, we introduce an approximate method for applications in which we have very many or infinitely many states. Exact methods are impractical in these applications and we show that our method returns a close estimate efficiently. 1
Contrasting applications of logic in natural language syntactic description
 Logic, Methodology and Philosophy of Science: Proceedings of the Twelfth International Congress
, 2005
"... Abstract. Formal syntax has hitherto worked mostly with theoretical frameworks that take grammars to be generative, in Emil Post’s sense: they provide recursive enumerations of sets. This work has its origins in Post’s formalization of proof theory. There is an alternative, with roots in the semanti ..."
Abstract

Cited by 10 (1 self)
 Add to MetaCart
Abstract. Formal syntax has hitherto worked mostly with theoretical frameworks that take grammars to be generative, in Emil Post’s sense: they provide recursive enumerations of sets. This work has its origins in Post’s formalization of proof theory. There is an alternative, with roots in the semantic side of logic: modeltheoretic syntax (MTS). MTS takes grammars to be sets of statements of which (algebraically idealized) wellformed expressions are models. We clarify the difference between the two kinds of framework and review their separate histories, and then argue that the generative perspective has misled linguists concerning the properties of natural languages. We select two elementary facts about natural language phenomena for discussion: the gradient character of the property of being ungrammatical and the open nature of natural language lexicons. We claim that the MTS perspective on syntactic structure does much better on representing the facts in these two domains. We also examine the arguments linguists give for the infinitude of the class of all expressions in a natural language. These arguments turn out on examination to be either unsound or lacking in empirical content. We claim that infinitude is an unsupportable claim that is also unimportant. What is actually needed is a way of representing the structure of expressions in a natural language without assigning any importance to the notion of a unique set with definite cardinality that contains all and only the expressions in the language. MTS provides that.
A Kleene theorem for polynomial coalgebras
 In Foundations of Software Science and Computational Structures, 12th International Conference, FOSSACS 2009, volume 5504 of LNCS
, 2009
"... Abstract. For polynomial functors G, we show how to generalize the classical notion of regular expression to Gcoalgebras. We introduce a language of expressions for describing elements of the final Gcoalgebra and, analogously to Kleene’s theorem, we show the correspondence between expressions and ..."
Abstract

Cited by 10 (3 self)
 Add to MetaCart
Abstract. For polynomial functors G, we show how to generalize the classical notion of regular expression to Gcoalgebras. We introduce a language of expressions for describing elements of the final Gcoalgebra and, analogously to Kleene’s theorem, we show the correspondence between expressions and finite Gcoalgebras. 1
Closing the gap between runtime complexity and polytime computability
 In Proceedings of RTA 2010, volume 6 of LIPIcs
, 2010
"... Abstract. In earlier work, we have shown that for confluent term rewrite systems, innermost polynomial runtime complexity induces polytime computability of the functions defined. In this paper, we generalise this result to full rewriting. For that, we again exploit graph rewriting. We give a new pro ..."
Abstract

Cited by 9 (2 self)
 Add to MetaCart
Abstract. In earlier work, we have shown that for confluent term rewrite systems, innermost polynomial runtime complexity induces polytime computability of the functions defined. In this paper, we generalise this result to full rewriting. For that, we again exploit graph rewriting. We give a new proof of the adequacy of graph rewriting for full rewriting that allows for a precise control of the resources copied. In sum we completely describe an implementation of rewriting on a Turing machine. We show that the runtime complexity with respect to rewrite systems is polynomially related to the runtime complexity on a Turing machine. Our result strengthens the evidence that the complexity of a rewrite system is truthfully represented through the length of derivations. Moreover our result allows the classification of deterministic as well as nondeterministic polytimecomputation based on runtime complexity analysis of rewrite systems. 1.
Reuseware – adding modularity to your language of choice
 Proc. of TOOLS EUROPE 2007: Special Issue of the Journal of Object Technology
, 2007
"... The trend towards domainspecific languages leads to an evergrowing plethora of highly specialized languages. Developers of such languages focus on their specific domains rather than on technical challenges of language design. Generic features of languages are rarely included in specialpurpose lan ..."
Abstract

Cited by 8 (6 self)
 Add to MetaCart
The trend towards domainspecific languages leads to an evergrowing plethora of highly specialized languages. Developers of such languages focus on their specific domains rather than on technical challenges of language design. Generic features of languages are rarely included in specialpurpose languages. One very important feature is modularization, the ability to formulate partial programs in separate entities, composable into a complete program in a defined manner. This paper presents a generic approach for adding modularity to arbitrary languages, discussing the underlying concepts and presenting the Reuseware Composition Framework. We walk through an example based on Xcerpt, a Semantic Web query language. 1
The MyhillNerode Theorem based on Regular Expressions
 The Archive of Formal Proofs. http://afp.sourceforge.net/develentries/ MyhillNerode.shtml
, 2011
"... Abstract. There are numerous textbooks on regular languages. Nearly all of them introduce the subject by describing finite automata and only mentioning on the side a connection with regular expressions. Unfortunately, automata are difficult to formalise in HOLbased theorem provers. The reason is th ..."
Abstract

Cited by 8 (3 self)
 Add to MetaCart
Abstract. There are numerous textbooks on regular languages. Nearly all of them introduce the subject by describing finite automata and only mentioning on the side a connection with regular expressions. Unfortunately, automata are difficult to formalise in HOLbased theorem provers. The reason is that they need to be represented as graphs, matrices or functions, none of which are inductive datatypes. Also convenient operations for disjoint unions of graphs and functions are not easily formalisiable in HOL. In contrast, regular expressions can be defined conveniently as a datatype and a corresponding reasoning infrastructure comes for free. We show in this paper that a central result from formal language theory—the MyhillNerode theorem—can be recreated using only regular expressions. 1
Spatial Logics with Connectedness Predicates
 LOGICAL METHODS IN COMPUTER SCIENCE
, 2010
"... We consider quantifierfree spatial logics, designed for qualitative spatial representation and reasoning in AI, and extend them with the means to represent topological connectedness of regions and restrict the number of their connected components. We investigate the computational complexity of thes ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
We consider quantifierfree spatial logics, designed for qualitative spatial representation and reasoning in AI, and extend them with the means to represent topological connectedness of regions and restrict the number of their connected components. We investigate the computational complexity of these logics and show that the connectedness constraints can increase complexity from NP to PSpace, ExpTime and, if component counting is allowed, to NExpTime.