The Experts below are selected from a list of 25227 Experts worldwide ranked by ideXlab platform
Paul Wild - One of the best experts on this subject based on the ideXlab platform.
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a modal Characterization Theorem for a probabilistic fuzzy description logic
International Joint Conference on Artificial Intelligence, 2019Co-Authors: Paul Wild, Lutz Schroder, Dirk Pattinson, Barbara KonigAbstract:The fuzzy modality probably is interpreted over probabilistic type spaces by taking expected truth values. The arising probabilistic fuzzy description logic is invariant under probabilistic bisimilarity; more informatively, it is non-expansive wrt. a suitable notion of behavioural distance. In the present paper, we provide a Characterization of the expressive power of this logic based on this observation: We prove a probabilistic analogue of the classical van Benthem Theorem, which states that modal logic is precisely the bisimulation-invariant fragment of first-order logic. Specifically, we show that every formula in probabilistic fuzzy first-order logic that is non-expansive wrt. behavioural distance can be approximated by concepts of bounded rank in probabilistic fuzzy description logic.
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a modal Characterization Theorem for a probabilistic fuzzy description logic
arXiv: Logic in Computer Science, 2019Co-Authors: Paul Wild, Lutz Schroder, Dirk Pattinson, Barbara KonigAbstract:The fuzzy modality `probably` is interpreted over probabilistic type spaces by taking expected truth values. The arising probabilistic fuzzy description logic is invariant under probabilistic bisimilarity; more informatively, it is non-expansive wrt. a suitable notion of behavioural distance. In the present paper, we provide a Characterization of the expressive power of this logic based on this observation: We prove a probabilistic analogue of the classical van Benthem Theorem, which states that modal logic is precisely the bisimulation-invariant fragment of first-order logic. Specifically, we show that every formula in probabilistic fuzzy first-order logic that is non-expansive wrt. behavioural distance can be approximated by concepts of bounded rank in probabilistic fuzzy description logic. For a modal logic perspective on the same result, see arXiv:1810.04722.
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A Characterization Theorem for a Modal Description Logic
International Joint Conferences on Artificial Intelligence Organization, 2017Co-Authors: Paul Wild, Lutz SchroderAbstract:Modal description logics feature modalities that capture dependence of knowledge on parameters such as time, place, or the information state of agents. E.g., the logic S5-ALC combines the standard description logic ALC with an S5-modality that can be understood as an epistemic operator or as representing (undirected) change. This logic embeds into a corresponding modal first-order logic S5-FOL. We prove a modal Characterization Theorem for this embedding, in analogy to results by van Benthem and Rosen relating ALC to standard first-order logic: We show that S5-ALC with only local roles is, both over finite and over unrestricted models, precisely the bisimulation-invariant fragment of S5-FOL, thus giving an exact description of the expressive power of S5-ALC with only local roles.
Lutz Schroder - One of the best experts on this subject based on the ideXlab platform.
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a modal Characterization Theorem for a probabilistic fuzzy description logic
International Joint Conference on Artificial Intelligence, 2019Co-Authors: Paul Wild, Lutz Schroder, Dirk Pattinson, Barbara KonigAbstract:The fuzzy modality probably is interpreted over probabilistic type spaces by taking expected truth values. The arising probabilistic fuzzy description logic is invariant under probabilistic bisimilarity; more informatively, it is non-expansive wrt. a suitable notion of behavioural distance. In the present paper, we provide a Characterization of the expressive power of this logic based on this observation: We prove a probabilistic analogue of the classical van Benthem Theorem, which states that modal logic is precisely the bisimulation-invariant fragment of first-order logic. Specifically, we show that every formula in probabilistic fuzzy first-order logic that is non-expansive wrt. behavioural distance can be approximated by concepts of bounded rank in probabilistic fuzzy description logic.
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a modal Characterization Theorem for a probabilistic fuzzy description logic
arXiv: Logic in Computer Science, 2019Co-Authors: Paul Wild, Lutz Schroder, Dirk Pattinson, Barbara KonigAbstract:The fuzzy modality `probably` is interpreted over probabilistic type spaces by taking expected truth values. The arising probabilistic fuzzy description logic is invariant under probabilistic bisimilarity; more informatively, it is non-expansive wrt. a suitable notion of behavioural distance. In the present paper, we provide a Characterization of the expressive power of this logic based on this observation: We prove a probabilistic analogue of the classical van Benthem Theorem, which states that modal logic is precisely the bisimulation-invariant fragment of first-order logic. Specifically, we show that every formula in probabilistic fuzzy first-order logic that is non-expansive wrt. behavioural distance can be approximated by concepts of bounded rank in probabilistic fuzzy description logic. For a modal logic perspective on the same result, see arXiv:1810.04722.
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A Characterization Theorem for a Modal Description Logic
International Joint Conferences on Artificial Intelligence Organization, 2017Co-Authors: Paul Wild, Lutz SchroderAbstract:Modal description logics feature modalities that capture dependence of knowledge on parameters such as time, place, or the information state of agents. E.g., the logic S5-ALC combines the standard description logic ALC with an S5-modality that can be understood as an epistemic operator or as representing (undirected) change. This logic embeds into a corresponding modal first-order logic S5-FOL. We prove a modal Characterization Theorem for this embedding, in analogy to results by van Benthem and Rosen relating ALC to standard first-order logic: We show that S5-ALC with only local roles is, both over finite and over unrestricted models, precisely the bisimulation-invariant fragment of S5-FOL, thus giving an exact description of the expressive power of S5-ALC with only local roles.
Barbara Konig - One of the best experts on this subject based on the ideXlab platform.
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a modal Characterization Theorem for a probabilistic fuzzy description logic
International Joint Conference on Artificial Intelligence, 2019Co-Authors: Paul Wild, Lutz Schroder, Dirk Pattinson, Barbara KonigAbstract:The fuzzy modality probably is interpreted over probabilistic type spaces by taking expected truth values. The arising probabilistic fuzzy description logic is invariant under probabilistic bisimilarity; more informatively, it is non-expansive wrt. a suitable notion of behavioural distance. In the present paper, we provide a Characterization of the expressive power of this logic based on this observation: We prove a probabilistic analogue of the classical van Benthem Theorem, which states that modal logic is precisely the bisimulation-invariant fragment of first-order logic. Specifically, we show that every formula in probabilistic fuzzy first-order logic that is non-expansive wrt. behavioural distance can be approximated by concepts of bounded rank in probabilistic fuzzy description logic.
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a modal Characterization Theorem for a probabilistic fuzzy description logic
arXiv: Logic in Computer Science, 2019Co-Authors: Paul Wild, Lutz Schroder, Dirk Pattinson, Barbara KonigAbstract:The fuzzy modality `probably` is interpreted over probabilistic type spaces by taking expected truth values. The arising probabilistic fuzzy description logic is invariant under probabilistic bisimilarity; more informatively, it is non-expansive wrt. a suitable notion of behavioural distance. In the present paper, we provide a Characterization of the expressive power of this logic based on this observation: We prove a probabilistic analogue of the classical van Benthem Theorem, which states that modal logic is precisely the bisimulation-invariant fragment of first-order logic. Specifically, we show that every formula in probabilistic fuzzy first-order logic that is non-expansive wrt. behavioural distance can be approximated by concepts of bounded rank in probabilistic fuzzy description logic. For a modal logic perspective on the same result, see arXiv:1810.04722.
Karim Ivaz - One of the best experts on this subject based on the ideXlab platform.
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numerical solution of fuzzy differential equations under generalized differentiability
Nonlinear Analysis: Hybrid Systems, 2009Co-Authors: Juan J Nieto, Alireza Khastan, Karim IvazAbstract:Abstract In this paper, we interpret a fuzzy differential equation by using the strongly generalized differentiability concept. Utilizing the Generalized Characterization Theorem, we investigate the problem of finding a numerical approximation of solutions. Then we show that any suitable numerical method for ODEs can be applied to solve numerically fuzzy differential equations under generalized differentiability. The generalized Euler approximation method is implemented and its error analysis, which guarantees pointwise convergence, is given. The method’s applicability is illustrated by solving a linear first-order fuzzy differential equation.
Alireza Khastan - One of the best experts on this subject based on the ideXlab platform.
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numerical solution of fuzzy differential equations under generalized differentiability
Nonlinear Analysis: Hybrid Systems, 2009Co-Authors: Juan J Nieto, Alireza Khastan, Karim IvazAbstract:Abstract In this paper, we interpret a fuzzy differential equation by using the strongly generalized differentiability concept. Utilizing the Generalized Characterization Theorem, we investigate the problem of finding a numerical approximation of solutions. Then we show that any suitable numerical method for ODEs can be applied to solve numerically fuzzy differential equations under generalized differentiability. The generalized Euler approximation method is implemented and its error analysis, which guarantees pointwise convergence, is given. The method’s applicability is illustrated by solving a linear first-order fuzzy differential equation.
