Above are papers related to the following paper: [Paper_ID] Paper #18785. 	[Title] On the Hardness of Approximate Reasoning [Abstract] Many AI problems, when formalized, reduce to evaluating the probability that a propositional expression is true. In this paper we show that this problem is computationally intractable even in surprisingly restricted cases and even if we settle for an approximation to this probability. We consider various methods used in approximate reasoning such as computing degree of belief and Bayesian belief networks, as well as reasoning techniques such as constraint satisfaction and knowledge compilation, that use approximation to avoid computational difficulties, and reduce them to model-counting problems over a propositional domain. We prove that counting satisfying assignments of propositional languages is intractable even for Horn and monotone formulae, and even when the size of clauses and number of occurrences of the variables are extremely limited. This should be contrasted with the case of deductive reasoning, where Horn theories and theories with binary clauses are distinguished by the existence of linear time satisfiability algorithms. What is even more surprising is that, as we show, even approximating the number of satisfying assignments (i.e., "approximating" approximate reasoning), is intractable for most of these restricted theories. We also identify some restricted classes of propositional formulae for which efficient algorithms for counting satisfying assignments can be given. fl Preliminary version of this paper appeared in the Proceedings of the 13th International Joint Conference on Artificial Intelligence, IJCAI93. y Supported by NSF grants CCR-89-02500 and CCR-92-00884 and by DARPA AFOSR-F4962-92-J-0466. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #86840. 	[Title] Learning Active Classifiers [Abstract] Many classification algorithms are "passive", in that they assign a class-label to each instance based only on the description given, even if that description is incomplete. In contrast, an active classifier can | at some cost | obtain the values of missing attributes, before deciding upon a class label. The expected utility of using an active classifier depends on both the cost required to obtain the additional attribute values and the penalty incurred if it outputs the wrong classification. This paper considers the problem of learning near-optimal active classifiers, using a variant of the probably-approximately-correct (PAC) model. After defining the framework | which is perhaps the main contribution of this paper | we describe a situation where this task can be achieved efficiently, but then show that the task is often intractable. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #18781. 	[Title] Learning to Reason with a Restricted View [Abstract] The Learning to Reason framework combines the study of Learning and Reasoning into a single task. Within it, learning is done specifically for the purpose of reasoning with the learned knowledge. Computational considerations show that this is a useful paradigm; in some cases learning and reasoning problems that are intractable when studied separately become tractable when performed as a task of Learning to Reason. In this paper we study Learning to Reason problems where the interaction with the world supplies the learner only partial information in the form of partial assignments. Several natural interpretations of partial assignments are considered and learning and reasoning algorithms using these are developed. The results presented exhibit a tradeoff between learnability, the strength of the oracles used in the interface, and the range of reasoning queries the learner is guaranteed to answer correctly. Please summarise all the given information.

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Paper #18785 has the title `On the Hardness of Approximate Reasoning  
` and the abstract `Many AI problems, when formalized, reduce to evaluating the probability that a propositional expression is true. In this paper we show that this problem is computationally intractable even in surprisingly restricted cases and even if we settle for an approximation to this probability. We consider various methods used in approximate reasoning such as computing degree of belief and Bayesian belief networks, as well as reasoning techniques such as constraint satisfaction and knowledge compilation, that use approximation to avoid computational difficulties, and reduce them to model-counting problems over a propositional domain. We prove that counting satisfying assignments of propositional languages is intractable even for Horn and monotone formulae, and even when the size of clauses and number of occurrences of the variables are extremely limited. This should be contrasted with the case of deductive reasoning, where Horn theories and theories with binary clauses are distinguished by the existence of linear time satisfiability algorithms. What is even more surprising is that, as we show, even approximating the number of satisfying assignments (i.e., "approximating" approximate reasoning), is intractable for most of these restricted theories. We also identify some restricted classes of propositional formulae for which efficient algorithms for counting satisfying assignments can be given. fl Preliminary version of this paper appeared in the Proceedings of the 13th International Joint Conference on Artificial Intelligence, IJCAI93. y Supported by NSF grants CCR-89-02500 and CCR-92-00884 and by DARPA AFOSR-F4962-92-J-0466. 
`.
Question: Which category should Paper #18785 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #18785 has the title `On the Hardness of Approximate Reasoning  
` and the abstract `Many AI problems, when formalized, reduce to evaluating the probability that a propositional expression is true. In this paper we show that this problem is computationally intractable even in surprisingly restricted cases and even if we settle for an approximation to this probability. We consider various methods used in approximate reasoning such as computing degree of belief and Bayesian belief networks, as well as reasoning techniques such as constraint satisfaction and knowledge compilation, that use approximation to avoid computational difficulties, and reduce them to model-counting problems over a propositional domain. We prove that counting satisfying assignments of propositional languages is intractable even for Horn and monotone formulae, and even when the size of clauses and number of occurrences of the variables are extremely limited. This should be contrasted with the case of deductive reasoning, where Horn theories and theories with binary clauses are distinguished by the existence of linear time satisfiability algorithms. What is even more surprising is that, as we show, even approximating the number of satisfying assignments (i.e., "approximating" approximate reasoning), is intractable for most of these restricted theories. We also identify some restricted classes of propositional formulae for which efficient algorithms for counting satisfying assignments can be given. fl Preliminary version of this paper appeared in the Proceedings of the 13th International Joint Conference on Artificial Intelligence, IJCAI93. y Supported by NSF grants CCR-89-02500 and CCR-92-00884 and by DARPA AFOSR-F4962-92-J-0466. 
`.
Question: Which category should Paper #18785 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Probabilistic_Methods