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Factored Models for Probabilistic Modal Logic
"... Modal logic represents knowledge that agents have about other agents ’ knowledge. Probabilistic modal logic further captures probabilistic beliefs about probabilistic beliefs. Models in those logics are useful for understanding and decision making in conversations, bargaining situations, and competi ..."
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Modal logic represents knowledge that agents have about other agents ’ knowledge. Probabilistic modal logic further captures probabilistic beliefs about probabilistic beliefs. Models in those logics are useful for understanding and decision making in conversations, bargaining situations, and competitions. Unfortunately, probabilistic modal structures are impractical for large real-world applications because they represent their state space explicitly. In this paper we scale up probabilistic modal structures by giving them a factored representation. This representation applies conditional independence for factoring the probabilistic aspect of the structure (as in Bayesian Networks (BN)). We also present two exact and one approximate algorithm for reasoning about the truth value of probabilistic modal logic queries over a model encoded in a factored form. The first exact algorithm applies inference in BNs to answer a limited class of queries. Our second exact method applies a variable elimination scheme and is applicable without restrictions. Our approximate algorithm uses sampling and can be used for applications with very large models. Given a query, it computes an answer and its confidence level efficiently. 1
Interactive dynamic influence diagrams
, 2006
"... This paper extends the framework of dynamic influence diagrams (DIDs) to the multi-agent setting. DIDs are computational representations of the Partially Observable Markov Decision Processes (POMDP), which are frameworks for sequential decision-making in single ..."
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Cited by 4 (0 self)
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This paper extends the framework of dynamic influence diagrams (DIDs) to the multi-agent setting. DIDs are computational representations of the Partially Observable Markov Decision Processes (POMDP), which are frameworks for sequential decision-making in single
doi:10.1017/S0266267110000386 TWO KINDS OF WE-REASONING
"... People sometimes think in terms of ‘we ’ referring to a group they belong to. When making decisions, they frame the decision problem as: ‘What should we do? ’ instead of ‘What should I do?’. We study one particular approach to such ‘we-reasoning’, economist Michael Bacharach’s theory of ‘team reason ..."
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People sometimes think in terms of ‘we ’ referring to a group they belong to. When making decisions, they frame the decision problem as: ‘What should we do? ’ instead of ‘What should I do?’. We study one particular approach to such ‘we-reasoning’, economist Michael Bacharach’s theory of ‘team reasoning’, and relate it to philosopher Raimo Tuomela’s distinction between ‘I-mode ’ reasoning and ‘we-mode ’ reasoning. We argue that these theories complement each other: Tuomela’s philosophical theory provides a conceptual framework augmenting Bacharach’s theory, and Bacharach’s mathematical results support Tuomela’s view on the irreducibility of the wemode to the I-mode. We-mode reasoning can explain some kinds of human cooperative behaviour left unexplained by standard game theory. Standard game theory is not well-equipped to deal with we-mode reasoning but it can be extended by the methods developed by Bacharach. However, we argue that both standard game theory and Bacharach’s theory require more attention to the information-sharing stages that precede actual decision making, and we describe a stage-based model of we-reasoning. 1.
Proceedings of the Twenty-Third AAAI Conference on Artificial Intelligence (2008) Factored Models for Probabilistic Modal Logic
"... Modal logic represents knowledge that agents have about other agents ’ knowledge. Probabilistic modal logic further captures probabilistic beliefs about probabilistic beliefs. Models in those logics are useful for understanding and decision making in conversations, bargaining situations, and competi ..."
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Modal logic represents knowledge that agents have about other agents ’ knowledge. Probabilistic modal logic further captures probabilistic beliefs about probabilistic beliefs. Models in those logics are useful for understanding and decision making in conversations, bargaining situations, and competitions. Unfortunately, probabilistic modal structures are impractical for large real-world applications because they represent their state space explicitly. In this paper we scale up probabilistic modal structures by giving them a factored representation. This representation applies conditional independence for factoring the probabilistic aspect of the structure (as in Bayesian Networks (BN)). We also present two exact and one approximate algorithm for reasoning about the truth value of probabilistic modal logic queries over a model encoded in a factored form. The first exact algorithm applies inference in BNs to answer a limited class of queries. Our second exact method applies a variable elimination scheme and is applicable without restrictions. Our approximate algorithm uses sampling and can be used for applications with very large models. Given a query, it computes an answer and its confidence level efficiently.
Hebrew University of
"... Market crash is usually considered an indication that the fundamentals of the economy have changed and recession is around the corner. This, however, need not be the case. For instance, in October 1987 Wall ..."
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Market crash is usually considered an indication that the fundamentals of the economy have changed and recession is around the corner. This, however, need not be the case. For instance, in October 1987 Wall
optimal proto–language
, 2006
"... Why evolution does not always lead to an optimal proto-language. An approach based on the replicator dynamics ..."
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Why evolution does not always lead to an optimal proto-language. An approach based on the replicator dynamics
