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Determining whether a propositional theory is satissable is a prototypical example of an NP-complete problem. Further, a large number of problems that occur in knowledge-representation, learning, planning, and other ares of AI are essentially sat-issability problems. This paper reports on the most extensive set of experiments to date on the location and(More)
Many reasoning and optimization problems exhibit symmetries. Previous work has shown how special purpose algorithms can make use of these symmetries to simplify reasoning. We present a general scheme whereby symmetries are exploited by adding \symmetry-breaking" predicates to the theory. Our approach can be used on any propo-sitional satissability problem,(More)
Determining whether a propositional theory is satissable is a prototypical example of an NP-complete problem. Further, a large number of problems that occur in knowledge representation, learning, planning, and other areas of AI are essentially satissability problems. This paper reports on a series of experiments to determine the location of the crossover(More)
Considerable progress has been made in recent years in understanding and solving propositional satisfia-bilit y problems. Much of this work has been based on experiments on randomly generated 3SAT problems . One generally accepted shortcoming of this work is that it is not clear how the results and algorithms developed will carry over to " real "(More)
Qualitative reasoning can, and should, be decomposed into a model-building task, which creates a qualitative differential equation (QDE) as a model of a physical situation , and a qualitative simulation task, which starts with a QDE. and predicts the possible behaviors following from the model. In support of this claim, we present QPC, a model builder that(More)
Many classes of reasoning problems display a large amount of symmetry. In mathematical and common-sense reasoning, such symmetries are often used to reduce the diiculty of reasoning. In this paper we show how symmetries can be used in automated reasoning both to reduce or avoid case analysis, and to reduce the scope of existential quantiication. We show(More)
Access-Limited Logic (ALL) is a theory of knowledge representation which formalizes the access limitations inherent in a network structured knowledge-base. Where a deductive method such as resolution would retrieve all assertions that satisfy a given pattern, an access-limited logic retrieves only those assertions reachable by following an available access(More)
One of the fundamental problems in the theory of knowledge representation is the dii-culty of achieving both logical coherence and computational tractability. We present steps toward a theory of access-limited logic, in which access to assertions in the knowledge-base is constrained by semantic network style locality relations. Where a classical de-ductive(More)
The development of a formal logic for reasoning about change has proven to be surprisingly dif-cult. Furthermore, the logics that have been developed have found surprisingly little application in those elds, such as Qualitative Reasoning, that are concerned with building programs that emulate human common-sense reasoning about change. In this paper, we(More)