D. Roth. Learning to reason: The non-monotonic case. In Proceedings of the International Joint Conference on Arti#cial Intelligence, pages 1178#1184, August 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....was true with high probability. We regard defaults as rules learned in this manner, where certain predicates are assumed to have value . Their validity arises from the fact that they had proved accurate in the past, or that they could be deduced from those that had. Further examples are given in [34, 41, 42]. 4.2 Robustness to Noise and Inconsistencies The two main methods of knowledge acquisition, inductive learning and programmed rules, will both need to cope with erroneous input data. Mechanisms are needed to make the system as robust as possible. For the case of inductive learning the issue of ....

D. Roth. Learning to reason: the non-monotonic case. Proc. Int. Joint Conf. Art. Intl., pages 1178--118, 1995.

....to the concepts of consistent and most robust extensions. The most robust extension is important in practice as it minimizes the number of corrected bits in order to have an extension. There are other possible treatments of missing bits appearing in the context of learning theory (see e.g. [6, 22, 24, 34, 36, 37, 39]) In this paper, we study the problems of deciding the existence of (and constructing) these extensions for various special classes of Boolean functions C, mainly from the view point of their computational complexity. We obtain computationally e#cient algorithms in some cases, and prove ....

D. Roth, Learning to reason: The non-monotonic case, Proceedings of IJCAI'95 (1995) 1178-1184.

....of strategies represented by rule based systems. In this model, the learner is given access to traces of behavior of another agent and using these traces it tries to reconstruct a strategy for behaving successfully in the same world. Following previous work on learning to reason (Khardon Roth, 1995, 1997) the formalization utilizes two general ideas. First, one can gain insights by focusing on learning that is done for the purpose of performing well in a particular task. Second, when coupling learning with the task, the competence required of the agent can be defined relative to its ....

....are represented by a set of n literals, X = x 1 ; x 2 ; x n , each taking a value in f0; 1; g. The value is intended to denote that the value of some variable is not known or has not been observed. No special semantics is given to partial assignments; instead we follow Valiant (1995) and Roth (1995) and simply consider the value as a third value an attribute can take. 2 The set f0; 1; g n is the domain of these measurements. For structural domains, as in work by Haussler (1989) the input is composed of a list of objects, and values of predicates instantiated with these objects. Namely, ....

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Roth, D. (1995). Learning to reason: The non-monotonic case. Proceedings of the International Joint Conference of Artificial Intelligence, pp. 1178--1184. Montreal, Canada: Morgan Kaufmann.

....for the latter. We regard defaults as rules where certain predicates are assumed to have the undetermined value in the precondition. Their validity arises from the fact that they had proved accurate in the past, or that they could be deduced from those that had. Further examples are given in [43, 52, 53]. 4.8 Reasoning Much effort has been put into seeing whether the various formalisms that have been suggested for reasoning in AI, at least those outside the probabilistic realm, can be formulated within predicate calculus. The general answer found to this question is in the affirmative, in the ....

D. Roth. Learning to reason: the non-monotonic case. Proc. Int. Joint Conf. Art. Intl., pages 1178--118, 1995.

....by rule based systems. In this model, the learner is given access to traces of behavior of another agent and using these traces it tries to reconstruct a strategy for behaving successfully in the same world. Following previous work on learning to reason (Khardon and Roth, 1994; Khardon and Roth, 1995) the formalization utilizes two general ideas. First, one can gain insights by focusing on learning that is done for the purpose of performing well in a particular task. Second, when coupling learning with the task, the competence required of the agent can be defined relative to its learning ....

....game. At each round, nature chooses an instance, x; g) such that x 2 f0; 1; g n and g 2 G. Then the agent is given some time, say N steps (where N is some fixed polynomial in the complexity parameters) to 3 Our treatment of partial assignments that include the value follows (Valiant, 1995; Roth, 1995) and simply considers the value as a third value. This is in contrast with previous work in (Khardon and Roth, 1995) where special a semantics is given to partial assignments. achieve the goal g starting with state x. In order to do this the learner has to apply its actions, one at a time, ....

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Roth, D. 1995. Learning to reason: The non-monotonic case. In Proceedings of the International Joint Conference of Artificial Intelligence, pages 1178--1184, August.

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D. Roth. Learning to reason: The non-monotonic case. In Proceedings of the International Joint Conference on Arti#cial Intelligence, pages 1178#1184, August 1995.

....been on the Inference with Classi ers paradigm. This is a concrete instantiation of our earlier work in the Learning to Reason framework an integrated theory of learning, knowledge representation and reasoning within a uni ed framework which uses learning to facilitate high level reasoning tasks [15, 23, 16, 24, 14]. Within the Inference with Classi ers paradigm we develop inference algorithms that take as input outcomes of classi ers. Our work in this area moves away from the study of single classi ers and studies ways to use classi ers in down stream inference processes [20, 22] Speci cally, we consider ....

D. Roth. Learning to reason: The non-monotonic case. In Proc. of the International Joint Conference on Articial Intelligence, pages 1178-1184, 1995. 5

....: x n i is the index of the rst of these e i which evaluated to 1; hx 1 ; x 2 ; x n i) arg min i fe i (hx 1 ; x 2 ; x n i) 1g. Using this representation, we can then restrict each e i to belong to some speci ed collection of Boolean concepts E over f0; 1; g n ( a la [Rot95]) Although we do not do so in this paper, it would be interesting to investigate the connection between learnability of active classi ers thus speci ed, and standard PAC learnability of the classes E . 3 Why Should We Learn Active Classi ers The optimal active classi er is determined by the ....

D. Roth. Learning to reason: The non-monotonic case. In IJCAI-95, pages 1178{ 1184, 1995.

....is learnable from entailment. While in this paper we concentrate on deductive reasoning, the learning to reason approach should be seen in a more general context and can be applied for a variety of tasks. In particular, a different treatment of partial information is taken in (Valiant, 1995; Roth, 1995), where the effect of partially specified queries is discussed. A similar learning to reason approach is developed there, supporting several aspects of non monotonic reasoning (Reiter, 1987) which have proved difficult to capture in other frameworks. The Learning to Reason approach has also been ....

....be taken. Several other works (Ben David and Dichterman, 1993; Greiner, Grove, and Kogan, 1996; Schuurmans and Greiner, 1994) have studied partial assignments in different settings, mostly for learning to classify, and the models and results are incomparable with ours. The work in (Valiant, 1995; Roth, 1995) is closer in that it handles reasoning tasks. In contrast with the above interpretations they treat the unobserved value as a third valid value. This is used to show that several non monotonic reasoning phenomena can be explained through learning. 3.1 Reasoning in the Presence of Partial ....

Roth, D. 1995. Learning to reason: The non-monotonic case. In Proceedings of the International Joint Conference of Artificial Intelligence, pages 1178--1184, Montreal, Canada. Morgan Kaufmann.

....an intelligent agent constructs a representation of the world incrementally by pasting together many narrower views from different contexts. This intuitive idea is formalized in a more general setting in the Learning to Reason framework [10] and is also at the heart of the approach developed in [32, 25], where a different view on dealing with incomplete information is taken. We briefly discuss two results in the learning to reason framework that use model based representations in order to exploit the relevant information in the reasoning process. In particular, it has been shown, within the ....

D. Roth. Learning to reason: The non-monotonic case. In Proceedings of the International Joint Conference of Artificial Intelligence, pages 1178--1184, August 1995.

....truly gains additional reasoning power over what is possible in the traditional setting. In particular, reasoning problems that are provably intractable in the traditional approach are given efficient Learning to Reason algorithms. Previous works in the Learning to Reason framework [Khardonand Roth, 1994b; 1995b] have considered reasoning tasks whose functionality is well defined. This paper, on the other hand, considers tasks in which, in many cases, there is no agreement on what constitutes a plausible outcome. The disagreement, we believe, is justified. We argue here that commonsense reasoning, and ....

....efficiently from interaction with the environment, to yield efficient Learning to Reason algorithms. Later in the paper we discuss the relation of this work to the default reasoning literature. Now we briefly mention some works that are related to the approach presented here. In [Khardon and Roth, 1995b] a Learning to Reason approach that can deal with partial information is developed and shown to support efficient deduction. The interpretation taken there, however, is not expressive enough to support non monotonic reasoning. In [Khardon and Roth, 1995a] a solution to some restricted cases of ....

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D. Roth. Learning to reason: the non-monotonic case. 1995. Full Version. In Preparation.

....positive results that can be shown. While in this paper we concentrate on deductive reasoning, the learning to reason approach should be seen in a more general context and can be applied for a variety of tasks. In particular, a different treatment of partial information is taken in (Valiant, 1995; Roth, 1995), where the effect of partially specified queries is discussed. A similar learning to reason approach is developed there, supporting several aspects of non monotonic reasoning (Reiter, 1987) which have proved difficult to capture in other frameworks. The Learning to Reason approach has also been ....

....(Reiter, 1987) which have proved difficult to capture in other frameworks. The Learning to Reason approach has also been extended to consider several other tasks, including some forms of default reasoning, learning in order to act in the world, and learning of active classifiers (Khardon and Roth, 1995; Khardon, 1996; Greiner, Grove, and Roth, 1996) The rest of the paper is organized as follows. We start by presenting some preliminaries on reasoning in Section 2 and then introduce our notion of partial observations in Section 3. In Section 4 we formally define the Learning to Reason model. ....

[Article contains additional citation context not shown here]

Roth, D. 1995. Learning to reason: The non-monotonic case. In Proceedings of the International Joint Conference of Artificial Intelligence, pages 1178--1184, August.

....traditionally, as a CNF formula. the deductive case, the result obtained can be phrased as a Learning to Reason without Reasoning result. Default Reasoning As in the case of abductive reasoning, learnability results for model based representations, together with the results in (Khardon Roth 1995a) which show how model based representations can be used for efficient default reasoning, yield an algorithm for Learning to Reason with defaults. In particular, the results provide a Learning to Reason without Reasoning result to fragments of Reiter s default logic. Reasoning with Partial ....

....yield an algorithm for Learning to Reason with defaults. In particular, the results provide a Learning to Reason without Reasoning result to fragments of Reiter s default logic. Reasoning with Partial Assignments The deductive reasoning approach presented above has been extended in (Khardon Roth 1995b) to handle partial assignments in the input. Several interpretations for partial information in the interface with the environment are discussed there and the work on model based representations is extended to deal with partially observable worlds. Then, learning to reason algorithms that cope ....

[Article contains additional citation context not shown here]

Roth, D. 1995. Learning to reason: The nonmonotonic case. In Proceedings of the International Joint Conference of Artificial Intelligence, 1178--1184.

....which is a batch approach. the world, e.g. reading a sentence of text, is viewed as a positive example of a few of these items and a negative example for all the others. Each example is thus used once by all the items to learn and refine their definition in terms of the others [ Valiant, 1995; Roth, 1995 ] and is then discarded. Local learning algorithms are used at each node: a variant of Littlestone s Winnow algorithm [ Littlestone, 1988 ] is used by each node to learn its dependence on other nodes, but different members of a concept cloud run this algorithm with different parameters. A ....

D. Roth. Learning to reason: The non-monotonic case. In Proceedings of the International Joint Conference on Artificial Intelligence, pages 1178--1184, August 1995.

....context of the most basic reasoning task, namely deductive reasoning. The framework, however, should be seen in a more general context and can be applied for a variety of tasks. In particular, similar results have been recently developed for other, related, reasoning tasks within this framework [KR95a, Rot95, KR95b, Kha96, GGR96]. These include non monotonic reasoning, Learning to Reason with partial observations, Learning to Act in a dynamic world, and learning of active classifiers. 1.2 Comparison with Related Work The generally accepted framework for the study of reasoning in intelligent systems is the knowledgebased ....

....a result we suggest a new set of questions, oriented towards learning a functionality rather than learning a representation of the world. For the task of logical deduction we show cases where this is indeed useful. As mentioned above, similar results for other tasks have been recently obtained [KR95a, Rot95, KR95b, Kha96, GGR96]. ffl From the Knowledge Representation and Reasoning point of view the main contribution is the change of paradigm. We suggest that the reasoner interacts with the world and constructs a suitable knowledge representation. Consequently, the effectiveness of the knowledge representation depends on ....

[Article contains additional citation context not shown here]

D. Roth. Learning to reason: The non-monotonic case. In Proceedings of the International Joint Conference of Artificial Intelligence, pages 1178--1184, August 1995.

....k CNF is learnable from entailment. While in this paper we concentrate on deductive reasoning, the learning to reason approach should be seen in a more general context and can be applied for a variety of tasks. In particular, a di erent treatment of partial information is taken in (Valiant, 1995; Roth, 1995), where the e ect of partially speci ed queries is discussed. A similar learning to reason approach is developed there, supporting several aspects of non monotonic reasoning (Reiter, 1987) which have proved di cult to capture in other frameworks. The Learning to Reason approach has also been ....

....here. Several other works (Ben David and Dichterman, 1993; Greiner, Grove, and Kogan, 1996; Schuurmans and Greiner, 1994) have studied partial assignments in di erent settings, mostly for learning to classify, and the models and results are incomparable with ours. The work in (Valiant, 1995; Roth, 1995) is closer in that it handles reasoning tasks. In contrast with the above interpretations they treat the unobserved value as a third valid value. This is used to show that several non monotonic reasoning phenomena can be explained through learning. 3.1 Reasoning in the Presence of Partial ....

Roth, D. 1995. Learning to reason: The non-monotonic case. In Proc. of the International Joint Conference of Articial Intelligence, pages 1178-1184.

....the environment. Namely, the agent can incrementally construct a representation that is relevant to its environment, in the sense that it supports correct reasoning there. This intuitive idea is formalized in a more general setting in the Learning to Reason framework [7] and is discussed also in [31, 22, 8]. We discuss two results in the Learning to Reason framework that use model based representations in order to exploit the relevant information in the reasoning process. To summarize, this paper studies reasoning with model based representations, and further substantiates the claim regarding their ....

D. Roth. Learning to reason: The non-monotonic case. In Proc. of the International Joint Conference of Artificial Intelligence, pages 1178--1184, 1995.

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