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Reasoning under the principle of maximum entropy for modal logics
 K45, KD45, and S5. In Theoretical Aspects of Rationality and Knowledge (TARK
, 2013
"... ABSTRACT We propose modal Markov logic as an extension of propositional Markov logic to reason under the principle of maximum entropy for modal logics K45, KD45, and S5. Analogous to propositional Markov logic, the knowledge base consists of weighted formulas, whose weights are learned from data. H ..."
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ABSTRACT We propose modal Markov logic as an extension of propositional Markov logic to reason under the principle of maximum entropy for modal logics K45, KD45, and S5. Analogous to propositional Markov logic, the knowledge base consists of weighted formulas, whose weights are learned from data. However, in contrast to Markov logic, in our framework we use the knowledge base to define a probability distribution over nonequivalent epistemic situations (pointed Kripke structures) rather than over atoms, and use this distribution to assign probabilities to modal formulas. As in all probabilistic representations, the central task in our framework is inference. Although the size of the state space grows doubly exponentially in the number of propositions in the domain, we provide an algorithm that scales only exponentially in the size of the knowledge base. Finally, we briefly discuss the case of languages with an infinite number of propositions.
A PartitionBased FirstOrder Probabilistic Logic to Represent Interactive Beliefs
"... Abstract. Being able to compactly represent large state spaces is crucial in solving a vast majority of practical stochastic planning problems. This requirement is even more stringent in the context of multiagent systems, in which the world to be modeled also includes the mental state of other age ..."
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Abstract. Being able to compactly represent large state spaces is crucial in solving a vast majority of practical stochastic planning problems. This requirement is even more stringent in the context of multiagent systems, in which the world to be modeled also includes the mental state of other agents. This leads to a hierarchy of beliefs that results in a continuous, unbounded set of possible interactive states, as in the case of Interactive POMDPs. In this paper, we describe a novel representation for interactive belief hierarchies that combines firstorder logic and probability. The semantics of this new formalism is based on recursively partitioning the belief space at each level of the hierarchy; in particular, the partitions of the belief simplex at one level constitute the vertices of the simplex at the next higher level. Since in general a set of probabilistic statements only partially specifies a probability distribution over the space of interest, we adopt the maximum entropy principle in order to convert it to a full specification.
Modal Markov Logic for Multiple Agents
"... Modal Markov Logic for a single agent has previously been proposed as an extension to propositional Markov logic. While the framework allowed reasoning under the principle of maximum entropy for various modal logics, it is not feasible to apply its counting based inference to reason about the belief ..."
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Modal Markov Logic for a single agent has previously been proposed as an extension to propositional Markov logic. While the framework allowed reasoning under the principle of maximum entropy for various modal logics, it is not feasible to apply its counting based inference to reason about the beliefs and knowledge of multiple agents due to magnitude of the numbers involved. We propose a modal extension of propositional Markov logic that avoids this problem by coarsening the state space. The problem stems from the fact that in the singleagent setting, the state space is only doubly exponential in the number of propositions in the domain, but the state space can potentially become infinite in the multiagent setting. In addition, the proposed framework adds only the overhead of deciding satisfiability for the chosen modal logic on the top of the complexity of exact inference in propositional Markov logic. The proposed framework allows one to find a distribution that matches probabilities of formulas obtained from training data (or provided by an expert). Finally, we show how one can compute lower and upper bounds on probabilities of arbitrary formulas. 1
Speculations on HumanAndroid Interaction in the Near and Distant Future
"... A psychologist and an AI researcher speculate on the future of social interaction between humans and androids (robots designed to look and act exactly like people). In reviewing the trajectory of currently developing robotics technologies, the level of android sophistication likely to be achieved in ..."
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A psychologist and an AI researcher speculate on the future of social interaction between humans and androids (robots designed to look and act exactly like people). In reviewing the trajectory of currently developing robotics technologies, the level of android sophistication likely to be achieved in fifty years time is assessed. On the basis of psychological research, obstacles to creating an android indistinguishable from humans are considered. Implications of humanandroid social interaction from the standpoint of current psychological and AI research are discussed, with speculation on novel psychological issues likely to arise from such interaction. The science of psychology will face a remarkable new set of challenges in grappling with humanandroid interaction.