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...

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 IRI-8819624 and in part by the Advanced Research Projects Agency of the Department of Defense under Office of Naval Research contract N00014-86-K-0124

We select policies for large Markov Decision Processes (MDPs) with compact first-order representations. We find policies that generalize well as the number of objects in the domain grows, potentially without bound. Existing dynamic-programming approaches based on flat, propositional, or first-order 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 first-order 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 first-order MDPs that are beyond the scope of previous approaches. We also discuss the application of this work to the relational reinforcement-learning problem. 1

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 2-way nondeterministic pushdown automata (2NPDA) to problems of flow analysis and typability in the Amadio-Cardelli 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 sub-cubic procedure for a monotone closure hard problem would imply a ...

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 Natural-Language Generation

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 N00014-85-K-0124. This paper appeared in AAAI-91. 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...

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 (µ-sets) is undecidable but satisfiability for Tarskian set constraints with µ-sets but without function symbols is linear time equivalent to satisfiability in the propositional µ-calculus and is therefore decidable in deterministic exponential time.

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 bi-rewriting 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 bi-rewriting modulo a set of inclusions. We present the canonical bi-rewriting system corresponding to the theory of non-distributive lattices.

We have argued elsewhere that first order inference can be made more efficient by using non-standard 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.

Access-Limited Logic (ALL) is a language for 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 all assertions reachable by following an available access path. In this paper, we extend previous work to include negation, disjunction, and the ability to make assumptions and reason by contradiction. We show that the extended ALL neg remains Socratically Complete (thus guaranteeing that for any fact which is a logical consequence of the knowledgebase, there exists a series of preliminary queries and assumptions after which a query of the fact will succeed) and computationally tractable. We show further that the key factor determining the computational difficulty of finding such a series of preliminary queries and assumptions is the depth of assumption nesting. We thus demonstrate the existenc...