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The Common OrderTheoretic Structure of Version Spaces and ATMS's
 In Proceedings of the National Conference on Artificial Intelligence
, 1991
"... We demonstrate how ordertheoretic abstractions can be useful in identifying, formalizing, and exploiting relationships between seemingly dissimilar AI algorithms that perform computations on partiallyordered sets. In particular, we show how the ordertheoretic concept of an antichain can be used ..."
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We demonstrate how ordertheoretic abstractions can be useful in identifying, formalizing, and exploiting relationships between seemingly dissimilar AI algorithms that perform computations on partiallyordered sets. In particular, we show how the ordertheoretic concept of an antichain can be used to provide an efficient representation for such sets when they satisfy certain special properties. We use antichains to identify and analyze the basic operations and representation optimizations in the version space learning algorithm [10] and the assumptionbased truth maintenance system (ATMS) [2, 3]. Our analysis allows us to (1) extend the known theory [7, 10, 8] of admissibility of concept spaces for incremental version space merging, and (2) develop new, simpler labelupdate algorithms for ATMS's with DNF assumption formulas. Contents 1 Introduction 2 2 Representing Sets as AntiChains 4 3 Version Spaces 17 4 AssumptionBased Truth Maintenance Systems 32 5 Extended ATMS's 46 6 Ackno...
The Reference Argument of Epistemic must
 in Proceedings of the International Workshop on Computational Semantics
, 1994
"... e�mail � matthew�linc.cis.upenn.edu ..."
A Fixed Point Semantics for the ATMS
 Journal of Logic Computation
, 1993
"... In [CTW90], the ATMS resolution mechanisms have been formalized, using the concept of DKtree. We propose in this paper a new and simple approach based on the fixed point theory and an original demonstration of the completeness of these mechanisms. We first introduce the basic definitions of terms, ..."
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In [CTW90], the ATMS resolution mechanisms have been formalized, using the concept of DKtree. We propose in this paper a new and simple approach based on the fixed point theory and an original demonstration of the completeness of these mechanisms. We first introduce the basic definitions of terms, sets and functions which are used in the paper and build a lattice. Then, the basic formal tools to describe the ATMS mechanisms are introduced: The notion of DKClash (in fact, the inference rule), and a monotonic function, which represents the deduction process and whose least fixed point corresponds to the output of an ATMS. We prove the soundness and the completeness (for specific clauses) of these mechanisms. This demonstration brings to light an original and interesting property, whose applications are discussed at the end of the paper. Keywords : Assumption based Truth Maintenance System, propositional logic, fixed point theory, automatic theorem proving. Introduction Our purpose in...