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31
Truth Maintenance
, 1990
"... General purpose truth maintenance systems have received considerable attention in the past few years. This paper discusses the functionality of truth maintenance systems and compares various existing algorithms. Applications and directions for future research are also discussed. Introduction In 197 ..."
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Cited by 110 (3 self)
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General purpose truth maintenance systems have received considerable attention in the past few years. This paper discusses the functionality of truth maintenance systems and compares various existing algorithms. Applications and directions for future research are also discussed. Introduction In 1978 Jon Doyle wrote a masters thesis at the MIT AI Laboratory entitled "Truth Maintenance Systems for Problem Solving" [ Doyle, 1979 ] . In this thesis Doyle described an independent module called a truth maintenance system, or TMS, which maintained beliefs for general problem solving systems. In the twelve years since the appearance of Doyle's TMS a large body of literature has accumulated on truth maintenance. The seminal idea appears not to have been any particular technical mechanism but rather the general concept of an independent module for truth (or belief) maintenance. All truth maintenance systems manipulate proposition symbols and relationships between proposition symbols. I will use...
Automatic Recognition of Tractability in Inference Relations
 Journal of the ACM
, 1990
"... This report describes research done at the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology. Support for the laboratory's artificial intelligence research is provided in part the National Science Foundation contract IRI8819624 and in part by the Advanced Research Proj ..."
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Cited by 61 (13 self)
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This report describes research done at the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology. Support for the laboratory's artificial intelligence research is provided in part the National Science Foundation contract IRI8819624 and in part by the Advanced Research Projects Agency of the Department of Defense under Office of Naval Research contract N0001486K0124
Inductive policy selection for firstorder MDPs
 In UAI
, 2002
"... We select policies for large Markov Decision Processes (MDPs) with compact firstorder representations. We find policies that generalize well as the number of objects in the domain grows, potentially without bound. Existing dynamicprogramming approaches based on flat, propositional, or firstorder ..."
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Cited by 39 (13 self)
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We select policies for large Markov Decision Processes (MDPs) with compact firstorder representations. We find policies that generalize well as the number of objects in the domain grows, potentially without bound. Existing dynamicprogramming approaches based on flat, propositional, or firstorder representations either are impractical here or do not naturally scale as the number of objects grows without bound. We implement and evaluate an alternative approach that induces firstorder policies using training data constructed by solving small problem instances using PGraphplan (Blum & Langford, 1999). Our policies are represented as ensembles of decision lists, using a taxonomic concept language. This approach extends the work of Martin and Geffner (2000) to stochastic domains, ensemble learning, and a wider variety of problems. Empirically, we find “good ” policies for several stochastic firstorder MDPs that are beyond the scope of previous approaches. We also discuss the application of this work to the relational reinforcementlearning problem. 1
On the Cubic Bottleneck in Subtyping and Flow Analysis
, 1997
"... A variety of program analysis methods have worst case time complexity that grows cubicly in the length of the program being analyzed. Cubic complexity typically arises in control flow analyses and the inference of recursive types (including object types). It is often said that such cubic performance ..."
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Cited by 32 (6 self)
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A variety of program analysis methods have worst case time complexity that grows cubicly in the length of the program being analyzed. Cubic complexity typically arises in control flow analyses and the inference of recursive types (including object types). It is often said that such cubic performance can not be improved because these analyses require "dynamic transitive closure". Here we prove linear time reductions from the problem of determining membership for languages defined by 2way nondeterministic pushdown automata (2NPDA) to problems of flow analysis and typability in the AmadioCardelli type system. An O(n 3 ) algorithm was given for 2NPDA acceptability in 1968 and is still the best known. The reductions are factored through the problem of "monotone closure" and we propose linear time reduction of the monotone closure as a method of establishing "monotone closure hardness" for program analysis problems. A subcubic procedure for a monotone closure hard problem would imply a ...
The Problem of LogicalForm Equivalence
 Computational Linguistics
, 1992
"... this paper, I review the problem, and attempt to highlight certain salient aspects of it that have been lost in the pursuing of solutions, in order to reconcile the apparently contradictory claims of the problem's intractability and its resolution. 2 Review of NaturalLanguage Generation ..."
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Cited by 30 (0 self)
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this paper, I review the problem, and attempt to highlight certain salient aspects of it that have been lost in the pursuing of solutions, in order to reconcile the apparently contradictory claims of the problem's intractability and its resolution. 2 Review of NaturalLanguage Generation
Tarskian Set Constraints
 IN PROCEEDINGS, 11 TH ANNUAL IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE
, 1996
"... We investigate set constraints over set expressions with Tarskian functional and relational operations. Unlike the Herbrand constructor symbols used in recent set constraint formalisms, the meaning of a Tarskian function symbol is interpreted in an arbitrary first order structure. We show that sat ..."
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Cited by 25 (0 self)
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We investigate set constraints over set expressions with Tarskian functional and relational operations. Unlike the Herbrand constructor symbols used in recent set constraint formalisms, the meaning of a Tarskian function symbol is interpreted in an arbitrary first order structure. We show that satisfiability of Tarskian set constraints is decidable in nondeterministic doubly exponential time. We also consider various extensions of the basic language and show that: satisfiability of Tarskian set constraints with recursion (µsets) is undecidable but satisfiability for Tarskian set constraints with µsets but without function symbols is linear time equivalent to satisfiability in the propositional µcalculus and is therefore decidable in deterministic exponential time.
Birewriting, a Term Rewriting Technique for Monotonic Order Relations
 Rewriting Techniques and Applications, LNCS 690
, 1993
"... We propose an extension of rewriting techniques to derive inclusion relations $a \subseteq b$ between terms built from monotonic operators. Instead of using only a rewriting relation $\REa$ and rewriting $a$ to $b$, we use another rewriting relation $\REb$ as well and seek a common expression $c$ su ..."
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Cited by 22 (6 self)
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We propose an extension of rewriting techniques to derive inclusion relations $a \subseteq b$ between terms built from monotonic operators. Instead of using only a rewriting relation $\REa$ and rewriting $a$ to $b$, we use another rewriting relation $\REb$ as well and seek a common expression $c$ such that $a \REa^* c$ and $b \REb^* c$. Each component of the birewriting system $\pair{\REa}{\REb}$ is allowed to be a subset of the corresponding inclusion $\subseteq$ or $\superseteq$. In order to assure the decidability and completeness of the proof procedure we study the commutativity of $\REa$ and $\REb$. We also extend the existing techniques of rewriting modulo equalities to birewriting modulo a set of inclusions. We present the canonical birewriting system corresponding to the theory of nondistributive lattices.
Natural Language Based Inference Procedures applied to Schubert's Steamroller
 In AAAI91
, 1991
"... We have previously argued that the syntactic structure of natural language can be exploited to construct powerful polynomial time inference procedures. This paper supports the earlier arguments by demonstrating that a natural language based polynomial time procedure can solve Schubert's steamroller ..."
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Cited by 22 (8 self)
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We have previously argued that the syntactic structure of natural language can be exploited to construct powerful polynomial time inference procedures. This paper supports the earlier arguments by demonstrating that a natural language based polynomial time procedure can solve Schubert's steamroller in a single step. This report describes research done at the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology. Support for the work described in this paper was provided in part by Misubishi Electric Research Laboratories, Inc. Support for the laboratory's artificial intelligence research is provided in part by the Advanced Research Projects Agency of the Department of Defense under Office of Naval Research contract N0001485K0124. This paper appeared in AAAI91. A postscript electronic source for this paper can be found in ftp.ai.mit.edu:/pub/dam/aaaib.ps. A bibtex reference can be found in ftp.ai.mit.edu:/pub/dam/dam.bib. 1 Introduction Schubert's steamro...
AccessLimited Logic  A language for knowledgerepresentation
, 1990
"... AccessLimited Logic (ALL) is a language for knowledge representation which formalizes the access limitations inherent in a network structured knowledgebase. Where a deductive method such as resolution would retrieve all assertions that satisfy a given pattern, an accesslimited logic retrieves all ..."
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Cited by 16 (3 self)
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AccessLimited Logic (ALL) is a language for knowledge representation which formalizes the access limitations inherent in a network structured knowledgebase. Where a deductive method such as resolution would retrieve all assertions that satisfy a given pattern, an accesslimited logic retrieves all assertions reachable by following an available access path. The time complexity of inference is thus a polynomial function of the size of the accessible portion of the knowledgebase, rather than the size of the entire knowledgebase. AccessLimited Logic, though incomplete, still has a well defined semantics and a weakened form of completeness, Socratic Completeness, which guarantees that for any query which is a logical consequence of the knowledgebase, there exists a series of queries after which the original query will succeed. We have implemented ALL in Lisp and it has been used to build several nontrivial systems, including versions of Qualitative Process Theory and Pearl's probability networks. ALL is a step toward providing the properties clean semantics, efficient inference, expressive power which will be necessary to build large, effective knowledge
Natural Language Syntax and First Order Inference
 ARTIFICIAL INTELLIGENCE
, 1992
"... We have argued elsewhere that first order inference can be made more efficient by using nonstandard syntax for first order logic. In this paper we define a syntax for first order logic based on the structure of natural language under Montague semantics. We show that, for a certain fairly expressive ..."
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Cited by 16 (8 self)
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We have argued elsewhere that first order inference can be made more efficient by using nonstandard syntax for first order logic. In this paper we define a syntax for first order logic based on the structure of natural language under Montague semantics. We show that, for a certain fairly expressive fragment of this language, satisfiability is polynomial time decidable. The polynomial time decision procedure can be used as a subroutine in general purpose inference systems and seems to be more powerful than analogous procedures based on either classical or taxonomic syntax.