2,858 research outputs found

    Crossing the Undecidability Border with Extensions of Propositional Neighborhood Logic over Natural Numbers

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    Propositional Neighborhood Logic (PNL) is an interval temporal logic featuring two modalities corresponding to the relations of right and left neighborhood between two intervals on a linear order (in terms of Allen's relations, meets and met by). Recently, it has been shown that PNL interpreted over several classes of linear orders, including natural numbers, is decidable (NEXPTIME-complete) and that some of its natural extensions preserve decidability. Most notably, this is the case with PNL over natural numbers extended with a limited form of metric constraints and with the future fragment of PNL extended with modal operators corresponding to Allen's relations begins, begun by, and before. This paper aims at demonstrating that PNL and its metric version MPNL, interpreted over natural numbers, are indeed very close to the border with undecidability, and even relatively weak extensions of them become undecidable. In particular, we show that (i) the addition of binders on integer variables ranging over interval lengths makes the resulting hybrid extension of MPNL undecidable, and (ii) a very weak first-order extension of the future fragment of PNL, obtained by replacing proposition letters by a restricted subclass of first-order formulae where only one variable is allowed, is undecidable (in contrast with the decidability of similar first-order extensions of point-based temporal logics)

    Complexity of ITL model checking: some well-behaved fragments of the interval logic HS

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    Model checking has been successfully used in many computer science fields, including artificial intelligence, theoretical computer science, and databases. Most of the proposed solutions make use of classical, point-based temporal logics, while little work has been done in the interval temporal logic setting. Recently, a non-elementary model checking algorithm for Halpern and Shoham's modal logic of time intervals HS over finite Kripke structures (under the homogeneity assumption) and an EXPSPACE model checking procedure for two meaningful fragments of it have been proposed. In this paper, we show that more efficient model checking procedures can be developed for some expressive enough fragments of HS

    How to use the Kohonen algorithm to simultaneously analyse individuals in a survey

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    The Kohonen algorithm (SOM, Kohonen,1984, 1995) is a very powerful tool for data analysis. It was originally designed to model organized connections between some biological neural networks. It was also immediately considered as a very good algorithm to realize vectorial quantization, and at the same time pertinent classification, with nice properties for visualization. If the individuals are described by quantitative variables (ratios, frequencies, measurements, amounts, etc.), the straightforward application of the original algorithm leads to build code vectors and to associate to each of them the class of all the individuals which are more similar to this code-vector than to the others. But, in case of individuals described by categorical (qualitative) variables having a finite number of modalities (like in a survey), it is necessary to define a specific algorithm. In this paper, we present a new algorithm inspired by the SOM algorithm, which provides a simultaneous classification of the individuals and of their modalities.Comment: Special issue ESANN 0

    Temporal Data Modeling and Reasoning for Information Systems

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    Temporal knowledge representation and reasoning is a major research field in Artificial Intelligence, in Database Systems, and in Web and Semantic Web research. The ability to model and process time and calendar data is essential for many applications like appointment scheduling, planning, Web services, temporal and active database systems, adaptive Web applications, and mobile computing applications. This article aims at three complementary goals. First, to provide with a general background in temporal data modeling and reasoning approaches. Second, to serve as an orientation guide for further specific reading. Third, to point to new application fields and research perspectives on temporal knowledge representation and reasoning in the Web and Semantic Web

    Gabbay Separation for the Duration Calculus

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