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O Kardaun - One of the best experts on this subject based on the ideXlab platform.
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On estimating the Epistemic Probability of realizing Q = Pfus/Paux larger than a specified lower bound in ITER
Nuclear Fusion, 2002Co-Authors: O KardaunAbstract:A simplified analysis is given of the problem of estimating the ‘Epistemic Probability’ for ITER to attain a power amplification factor Q larger than a certain lower bound. Attention is restricted to the parameters of ITER-FEAT and the 1998 ITER design. The probabilistic framework is briefly discussed and the distributional interval estimates for Q following from the interval estimates of the confinement time are derived (a) for ITER operation at constant fusion output power P fu s, and (b) for operation at a temperature that maximizes Q = P fu s/Paux. The second situation requires a radial integration of the flux surface averaged energy balance. Instead of a local transport model, a simple class of temperature profiles is used. The results are represented graphically. A generalization of the widely used fusion triple product plot against temperature is suggested. The analysis presupposes that at the reference operating point in situation (a), and in the range of operating temperatures projected to be achievable in situation (b), the conditions for reaching standard ELMy H mode in ITER are met. The practical conclusion of the article is that under this premise ITER-FEAT has a fairly large Epistemic Probability of obtaining plasma conditions with prevalent alpha particle heating.
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on estimating the Epistemic Probability of realizing q pfus paux larger than a specified lower bound in iter
Nuclear Fusion, 2002Co-Authors: O KardaunAbstract:A simplified analysis is given of the problem of estimating the ‘Epistemic Probability’ for ITER to attain a power amplification factor Q larger than a certain lower bound. Attention is restricted to the parameters of ITER-FEAT and the 1998 ITER design. The probabilistic framework is briefly discussed and the distributional interval estimates for Q following from the interval estimates of the confinement time are derived (a) for ITER operation at constant fusion output power P fu s, and (b) for operation at a temperature that maximizes Q = P fu s/Paux. The second situation requires a radial integration of the flux surface averaged energy balance. Instead of a local transport model, a simple class of temperature profiles is used. The results are represented graphically. A generalization of the widely used fusion triple product plot against temperature is suggested. The analysis presupposes that at the reference operating point in situation (a), and in the range of operating temperatures projected to be achievable in situation (b), the conditions for reaching standard ELMy H mode in ITER are met. The practical conclusion of the article is that under this premise ITER-FEAT has a fairly large Epistemic Probability of obtaining plasma conditions with prevalent alpha particle heating.
Francois Schwarzentruber - One of the best experts on this subject based on the ideXlab platform.
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Advances in Modal Logic - Epistemic Probability Logic Simplified
2020Co-Authors: Jan Van Eijck, Francois SchwarzentruberAbstract:We propose a simplified logic for reasoning about (multi-agent) Epistemic Probability models, and for Epistemic probabilistic model checking. Epistemic Probability models are multi-agent Kripke models that assign to each agent an equivalence relation on worlds, together with a function from worlds to positive rationals (a lottery). The difference with the usual approach is that Probability is linked to knowledge rather than belief, and that knowledge is equated with certainty. A first contribution of the paper is a comparison of a semantics for Epistemic Probability in terms of models with multiple lotteries and models with a single lottery. We give a proof that multiple lottery models can always be replaced by single lottery models. As multiple lotteries represent multiple subjective probabilities, our result connects subjective and intersubjective Probability. Next, we define an appropriate notion of bisimulation, and use it to prove an adaptation of the Hennessy-Milner Theorem and to prove that some finite multiple lottery models only have infinite single lottery counterparts. We then prove completeness, and state results about model checking complexity. In particular, we show the PSPACE-completeness of the model checking in the dynamic version with action models. The logic is designed with model checking for Epistemic Probability logic in mind; a prototype model checker for it exists. This program can be used to keep track of information flow about aleatory acts among multiple agents.
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Epistemic Probability logic simplified
Advances in Modal Logic, 2014Co-Authors: Jan Van Eijck, Francois SchwarzentruberAbstract:We propose a simplified logic for reasoning about (multi-agent) Epistemic Probability models, and for Epistemic probabilistic model checking. Epistemic Probability models are multi-agent Kripke models that assign to each agent an equivalence relation on worlds, together with a function from worlds to positive rationals (a lottery). The difference with the usual approach is that Probability is linked to knowledge rather than belief, and that knowledge is equated with certainty. A first contribution of the paper is a comparison of a semantics for Epistemic Probability in terms of models with multiple lotteries and models with a single lottery. We give a proof that multiple lottery models can always be replaced by single lottery models. As multiple lotteries represent multiple subjective probabilities, our result connects subjective and intersubjective Probability. Next, we define an appropriate notion of bisimulation, and use it to prove an adaptation of the Hennessy-Milner Theorem and to prove that some finite multiple lottery models only have infinite single lottery counterparts. We then prove completeness, and state results about model checking complexity. In particular, we show the PSPACE-completeness of the model checking in the dynamic version with action models. The logic is designed with model checking for Epistemic Probability logic in mind; a prototype model checker for it exists. This program can be used to keep track of information flow about aleatory acts among multiple agents.
Jan Van Eijck - One of the best experts on this subject based on the ideXlab platform.
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Model Checking Uncertainty about Probability
2020Co-Authors: Jan Van EijckAbstract:This talk proposes a logic for reasoning about (multi-agent) Epistemic Probability models, and for Epistemic probabilistic model checking. Epistemic Probability models are multi-agent Kripke models that assign to each agent an equivalence relation on worlds and an equivalence relation on lotteries over worlds, where a lottery over (finite) world set W is a function from W to the positive rational numbers. Uncertainty about Probability is modelled as equivalence of lotteries. The difference with the usual approach is that Probability is linked to knowledge rather than belief, and that “agent A knows that φ” is equated with “agent A assigns Probability 1 to φ.” To motivate our approach, we formulate and prove a Certainty Theorem, stating that certainty in an Epistemic Probability model M corresponds to knowledge in the Epistemic model that results when all lottery information gets erased from M. It follows immediately from this that the certainty operator in Epistemic Probability logic is an S5 operator. We define a generic update mechanism for Epistemic Probability logic by means of update models that are like Epistemic Probability models, but with their valuations replaced by precondition/action pairs. The actions assign lotteries that are in turn used to recompute the lotteries of the input model. E.g., the act of drawing a marble from an urn containing m white and n black marbles is viewed as a lottery that assigns m to white and n to black. If there is time, we will end with an “oratio pro demo”, a short demonstration with PRODEMO, a model checker for Epistemic Probability logic that can be used to keep track of information flow about aleatory acts among multiple agents. Probability as a function of degree of information Dans les choses qui ne sont que vraisemblables, la difference des donnees que chaque homme a sur elles, est une des causes principales de la diversite des opinions que l’on voit regner sur les memes objects. Laplace [Lap14] Relation between Probability and Knowledge Agent a knows φ iff the Probability a assigns to φ equals 1. Let Paφ be the Probability that agent a assigns to φ. Certainty implies Truth Paφ = 1→ φ. Positive Introspection into Certainty Paφ = 1→ Pa(Paφ = 1) = 1. Negative Introspection into Certainty Paφ < 1→ Pa(Paφ < 1) = 1. Earlier proposals on combining knowledge and Probability [FH94, Koo03b, Koo03a, BGK09, BS08, Gie09], and many more. These proposals do not equate knowledge with certainty.
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Advances in Modal Logic - Epistemic Probability Logic Simplified
2020Co-Authors: Jan Van Eijck, Francois SchwarzentruberAbstract:We propose a simplified logic for reasoning about (multi-agent) Epistemic Probability models, and for Epistemic probabilistic model checking. Epistemic Probability models are multi-agent Kripke models that assign to each agent an equivalence relation on worlds, together with a function from worlds to positive rationals (a lottery). The difference with the usual approach is that Probability is linked to knowledge rather than belief, and that knowledge is equated with certainty. A first contribution of the paper is a comparison of a semantics for Epistemic Probability in terms of models with multiple lotteries and models with a single lottery. We give a proof that multiple lottery models can always be replaced by single lottery models. As multiple lotteries represent multiple subjective probabilities, our result connects subjective and intersubjective Probability. Next, we define an appropriate notion of bisimulation, and use it to prove an adaptation of the Hennessy-Milner Theorem and to prove that some finite multiple lottery models only have infinite single lottery counterparts. We then prove completeness, and state results about model checking complexity. In particular, we show the PSPACE-completeness of the model checking in the dynamic version with action models. The logic is designed with model checking for Epistemic Probability logic in mind; a prototype model checker for it exists. This program can be used to keep track of information flow about aleatory acts among multiple agents.
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Epistemic Probability logic simplified
Advances in Modal Logic, 2014Co-Authors: Jan Van Eijck, Francois SchwarzentruberAbstract:We propose a simplified logic for reasoning about (multi-agent) Epistemic Probability models, and for Epistemic probabilistic model checking. Epistemic Probability models are multi-agent Kripke models that assign to each agent an equivalence relation on worlds, together with a function from worlds to positive rationals (a lottery). The difference with the usual approach is that Probability is linked to knowledge rather than belief, and that knowledge is equated with certainty. A first contribution of the paper is a comparison of a semantics for Epistemic Probability in terms of models with multiple lotteries and models with a single lottery. We give a proof that multiple lottery models can always be replaced by single lottery models. As multiple lotteries represent multiple subjective probabilities, our result connects subjective and intersubjective Probability. Next, we define an appropriate notion of bisimulation, and use it to prove an adaptation of the Hennessy-Milner Theorem and to prove that some finite multiple lottery models only have infinite single lottery counterparts. We then prove completeness, and state results about model checking complexity. In particular, we show the PSPACE-completeness of the model checking in the dynamic version with action models. The logic is designed with model checking for Epistemic Probability logic in mind; a prototype model checker for it exists. This program can be used to keep track of information flow about aleatory acts among multiple agents.
Riccardo Zese - One of the best experts on this subject based on the ideXlab platform.
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PAI - Semantics and Inference for Probabilistic Ontologies
2020Co-Authors: Fabrizio Riguzzi, Elena Bellodi, Evelina Lamma, Riccardo ZeseAbstract:We present BUNDLE, a reasoner able to perform reasoning on probabilistic knowledge bases according to the semantics DISPONTE. In DISPONTE the axioms of a probabilistic ontology can be annotated with an Epistemic or a statistical Probability. The Epistemic Probability represents a degree of confidence in the axiom, while the statistical Probability considers the populations to which the axiom is applied. BUNDLE exploits an underlying OWL DL reasoner, which is Pellet, that is able to return explanations for a query. However, it can work well with any reasoner able to return explanations for a query. The explanations are encoded in a Binary Decision Diagram from which the Probability of the query is computed.
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IJCAI - Inference and learning for probabilistic description logics
2015Co-Authors: Riccardo ZeseAbstract:The last years have seen an exponential increase in the interest for the development of methods for combining Probability with Description Logics (DLs). These methods are very useful to model real world domains, where incompleteness and uncertainty are common. This combination has become a fundamental component of the Semantic Web. Our work started with the development of a probabilistic semantics for DL, called DISPONTE (”DIstribution Semantics for Probabilistic ONTologiEs“, Spanish for ”get ready“). DISPONTE applies the distribution semantics [Sato, 1995] to DLs. The distribution semantics is one of the most effective approaches in logic programming and is exploited by many languages, such as Independent Choice Logic, Probabilistic Horn Abduction, PRISM, pD, Logic Programs with Annotated Disjunctions, CP-logic, and ProbLog. Under DISPONTE we annotate axioms of a theory with a Probability, that can be interpreted as an Epistemic Probability, i.e., as the degree of our belief in the corresponding axiom, and we assume that each axiom is independent of the others. DISPONTE, like the distribution semantics, defines a Probability distribution over regular knowledge bases (also called worlds). To create a world, we decide whether to include or not each probabilistic axiom, then we multiply the Probability of the choices done to compute the Probability of the world. The Probability of a query is then obtained from the joint Probability of the worlds and the query by marginalization. Consider the Knowledge Base (KB) below:
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URSW - Epistemic and statistical probabilistic ontologies
2012Co-Authors: Fabrizio Riguzzi, Elena Bellodi, Evelina Lamma, Riccardo ZeseAbstract:We present DISPONTE, a semantics for probabilistic ontologies that is based on the distribution semantics for probabilistic logic programs. In DISPONTE the axioms of a probabilistic ontology can be annotated with an Epistemic or a statistical Probability. The Epistemic Probability represents a degree of confidence in the axiom, while the statistical Probability considers the populations to which the axiom is applied.
Fabio Cuzzolin - One of the best experts on this subject based on the ideXlab platform.
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Belief Functions - Game-Theoretical Semantics of Epistemic Probability Transformations
Advances in Intelligent and Soft Computing, 2020Co-Authors: Fabio CuzzolinAbstract:Probability transformation of belief functions can be classified into different families, according to the operator they commute with. In particular, as they commute with Dempster’s rule, relative plausibility and belief transforms form one such “Epistemic” family, and possess natural rationales within Shafer’s formulation of the theory of evidence, while they are not consistent with the credal or Probability-bound semantic of belief functions. We prove here, however, that these transforms can be given in this latter case an interesting rationale in terms of optimal strategies in a non-cooperative game.
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game theoretical semantics of Epistemic Probability transformations
Belief Functions, 2012Co-Authors: Fabio CuzzolinAbstract:Probability transformation of belief functions can be classified into different families, according to the operator they commute with. In particular, as they commute with Dempster’s rule, relative plausibility and belief transforms form one such “Epistemic” family, and possess natural rationales within Shafer’s formulation of the theory of evidence, while they are not consistent with the credal or Probability-bound semantic of belief functions. We prove here, however, that these transforms can be given in this latter case an interesting rationale in terms of optimal strategies in a non-cooperative game.