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ABSTRACT: In this paper, we show how well-known graph-theoretic techniques can be successfully exploited to efficiently reason about
partially ordered events in Kowalski and Sergot's Event Calculus and in its skeptical and credulous modal variants. To overcome
the computational weakness of the traditional generate-and-test algorithm of (Modal) Event Calculus, we propose two alternative
graph-traversal algorithms that operate on the underlying directed acyclic graph of events representing ordering information.
The first algorithm pairs breadth-first and depth-first visits of such an event graph in a suitable way, while the second
one operates on its transitive closure and reduction. We prove the soundness and completeness of both algorithms, and thoroughly
analyze and compare their computational complexity.
Annals of Mathematics and Artificial Intelligence 04/2012; 30(1):93-118. · 0.36 Impact Factor
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ABSTRACT: In this paper, we describe a translation algorithm that maps spatio-temporal conceptual schemas into XML schemas expressed in the W3C XML Schema Language. Moreover, we extend the standard XML Schema validator with a Java library to check spatio-temporal constraints. The resulting framework allows one to validate XML documents containing spatio-temporal information with respect to spatio-temporal conceptual schemas.
Database and Expert Systems Applications, 2007. DEXA '07. 18th International Workshop on; 10/2007
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ABSTRACT: The eXtensible Markup Language (XML) was designed to describe the content of a document and its hierarchical structure, and the XML Path language (XPath) is a language for selecting elements from XML documents. There is a close connection between the query processing problem for XPath and the model checking problem for temporal logics. Both boil down to checking which nodes of a graph satisfy a property. We investigate the potential of a technique based on computation tree logic (CTL) model checking for evaluating queries expressed in (a subset of) XPath. To this aim, we isolate a simple fragment of XPath that is naturally embeddable into CTL. We report on experiments based on the model checker NuSMV, and compare our results with alternative academic XPath processors. We comment on the advantages and drawbacks of the application of our model checking-based approach to XPath processing.
Temporal Representation and Reasoning, 2004. TIME 2004. Proceedings. 11th International Symposium on; 08/2004
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ABSTRACT: Suitable extensions of the monadic second-order theory of k successors have been proposed in the literature to capture the notion of time granularity. In this paper, we provide the monadic second-order theories of downward unbounded layered structures, which are infinitely refinable structures consisting of a coarsest domain and an infinite number of finer and finer domains, and of upward unbounded layered structures, which consist of a finest domain and an infinite number of coarser and coarser domains, with expressively complete and elementarily decidable temporal logic counterparts. We obtain such a result in two steps. First, we define a new class of combined automata, called temporalized automata, which can be proved to be the automata-theoretic counterpart of temporalized logics, and show that relevant properties, such as closure under Boolean operations, decidability, and expressive equivalence with respect to temporal logics, transfer from component automata to temporalized ones. Then, we exploit the correspondence between temporalized logics and automata to reduce the task of finding the temporal logic counterparts of the given theories of time granularity to the easier one of finding temporalized automata counterparts of them.
12/2003;
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ABSTRACT: In this paper, we study the definability and decidability of binary predicates for time granularity with respect to monadic theories over finitely and infinitely layered structures. We focus our attention on the equi-level (resp. equi-column) predicate constraining two time points to belong to the same layer (resp. column) and on the horizontal (resp. vertical) successor predicate relating a time point to its successor within a given layer (resp. column). We give a number of positive and negative results by reduction to/from a wide spectrum of decidable/undecidable problems.
Temporal Representation and Reasoning, 2003 and Fourth International Conference on Temporal Logic. Proceedings. 10th International Symposium on; 08/2003
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ABSTRACT: We investigate expressivity and complexity of hybrid logics on linear structures. Hybrid logics are an enrichment of modal logics with certain first-order features which are algorithmically well behaved. Therefore, they are well suited for the specification of certain properties of computational systems. We show that hybrid logics are more expressive than usual modal and temporal logics on linear structures, and exhibit a hierarchy of hybrid languages. We determine the complexities of the satisfiability problem for these languages and define an existential fragment of hybrid logic for which satisfiability is still NP-complete. Finally, we examine the linear time model checking problem for hybrid logics and its complexity.
Temporal Representation and Reasoning, 2003 and Fourth International Conference on Temporal Logic. Proceedings. 10th International Symposium on; 08/2003
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ABSTRACT: We propose a logical approach to represent and reason about different time granularities. We identify a time granularity as a discrete infinite sequence of time points properly labelled with proposition symbols marking the starting and ending points of the corresponding granules, and we intensively model sets of granularities with linear time logic formulas. Some real-world granularities are provided to motivate and exemplify our approach. The proposed framework permits to algorithmically solve the consistency, the equivalence, and the classification problems in a uniform way, by reducing them to the validity problem for the considered linear time logic.
Temporal Representation and Reasoning, 2002. TIME 2002. Proceedings.Ninth International Symposium on; 02/2002
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ABSTRACT: We propose an original indexing by shape of image databases based
on extended grid files. We first introduce a recently developed shape
description method and tailor it to obtain suitable representation
structures for image databases. Then, in order to efficiently support
image retrieval, we define an indexing structure based on grid files,
since grid files were originally developed to speed up point (exact
match) and range (nearest neighbors within a threshold) queries on
multidimensional data with a fired number of attributes, we extend them
to cope with data provided with a varying number of attributes and to
deal with a new class of queries relevant to image databases, namely,
nearest neighbor queries. We give a detailed description of the proposed
search algorithms and a systematic analysis of their complexity, and
discuss the outcomes of some experimental tests on sample image
databases
Multimedia Computing and Systems, 1999. IEEE International Conference on; 08/1999
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ABSTRACT: We exploit graph-theoretic techniques to efficiently reason about
partially ordered events in the Event Calculus. We replace the
traditional generate-and-test reasoning strategy by a more efficient
generate-only one that operates on the underlying directed acyclic graph
of events representing ordering information by pairing breadth-first and
depth-first visits in a suitable way. We prove the soundness and
completeness of the proposed strategy, and thoroughly analyze its
computational complexity. Furthermore, we show how it can be generalized
to deal with the Modal Event Calculus, that provides a uniform modal
framework for the basic Event Calculus and its skeptical and credulous
variants
Temporal Representation and Reasoning, 1999. TIME-99. Proceedings. Sixth International Workshop on; 02/1999
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ABSTRACT: Kowalski and Sergot's (1986) Event Calculus (EC) is a simple
temporal formalism that, given a set of event occurrences, derives the
maximal validity intervals (MVIs) over which properties initiated or
terminated by these events hold. We extend this calculus to give a
semantic foundation to our Quantifiers and Connectives Event Calculus
(QCEC). In particular, we extend the range of queries accepted by EC,
which has so far been limited to Boolean combinations of MVI
verification or computation requests, to admit arbitrary quantification
over events and properties. We demonstrate the added expressive power by
encoding a medical diagnosis problem as a case study. Moreover, we give
a λProlog implementation of this formalism and analyze the
computational complexity of the extended calculus
Temporal Representation and Reasoning, 1998. Proceedings. Fifth International Workshop on; 06/1998
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ABSTRACT: Kowalski and Sergot's (1986) event calculus (EC) is a simple
temporal formalism that, given a set of event occurrences, allows the
derivation of the maximal validity intervals (MVIs) over which
properties initiated or terminated by those events hold. The limited
expressive power of EC is notably augmented by permitting events to
initiate or terminate a property only if a given set of preconditions
hold at their occurrence time. We define a semantic formalization of the
event calculus with preconditions. We gain further expressiveness by
considering modal variants of this formalism, and show how to adapt our
semantic characterization to encompass the additional operators. We
discuss the complexity of MVI validation and describe examples showing
that modal event calculi with preconditions can be successfully
exploited to deal with real-world applications
Temporal Representation and Reasoning, 1997. (TIME '97), Proceedings., Fourth International Workshop on; 06/1997
