Showing papers in "Journal of Artificial Intelligence Research in 1999"
TL;DR: This work suggests that most of the gain in an ensemble's performance comes in the first few classifiers combined; however, relatively large gains can be seen up to 25 classifiers when Boosting decision trees.
Abstract: An ensemble consists of a set of individually trained classifiers (such as neural networks or decision trees) whose predictions are combined when classifying novel instances. Previous research has shown that an ensemble is often more accurate than any of the single classifiers in the ensemble. Bagging (Breiman, 1996c) and Boosting (Freund & Schapire, 1996; Schapire, 1990) are two relatively new but popular methods for producing ensembles. In this paper we evaluate these methods on 23 data sets using both neural networks and decision trees as our classification algorithm. Our results clearly indicate a number of conclusions. First, while Bagging is almost always more accurate than a single classifier, it is sometimes much less accurate than Boosting. On the other hand, Boosting can create ensembles that are less accurate than a single classifier - especially when using neural networks. Analysis indicates that the performance of the Boosting methods is dependent on the characteristics of the data set being examined. In fact, further results show that Boosting ensembles may overfit noisy data sets, thus decreasing its performance. Finally, consistent with previous studies, our work suggests that most of the gain in an ensemble's performance comes in the first few classifiers combined; however, relatively large gains can be seen up to 25 classifiers when Boosting decision trees.
2,672 citations
TL;DR: In this paper, a measure of semantic similarity in an IS-A taxonomy based on the notion of shared information content is presented, and experimental evaluation against a benchmark set of human similarity judgments demonstrates that the measure performs better than the traditional edge counting approach.
Abstract: This article presents a measure of semantic similarity in an IS-A taxonomy based on the notion of shared information content. Experimental evaluation against a benchmark set of human similarity judgments demonstrates that the measure performs better than the traditional edge-counting approach. The article presents algorithms that take advantage of taxonomic similarity in resolving syntactic and semantic ambiguity, along with experimental results demonstrating their effectiveness.
2,190 citations
TL;DR: In this article, the authors present an overview and synthesis of MDP-related methods, showing how they provide a unifying framework for modeling many classes of planning problems studied in AI.
Abstract: Planning under uncertainty is a central problem in the study of automated sequential decision making, and has been addressed by researchers in many different fields, including AI planning, decision analysis, operations research, control theory and economics. While the assumptions and perspectives adopted in these areas often differ in substantial ways, many planning problems of interest to researchers in these fields can be modeled as Markov decision processes (MDPs) and analyzed using the techniques of decision theory.
This paper presents an overview and synthesis of MDP-related methods, showing how they provide a unifying framework for modeling many classes of planning problems studied in AI. It also describes structural properties of MDPs that, when exhibited by particular classes of problems, can be exploited in the construction of optimal or approximately optimal policies or plans. Planning problems commonly possess structure in the reward and value functions used to describe performance criteria, in the functions used to describe state transitions and observations, and in the relationships among features used to describe states, actions, rewards, and observations.
Specialized representations, and algorithms employing these representations, can achieve computational leverage by exploiting these various forms of structure. Certain AI techniques-- in particular those based on the use of structured, intensional representations--can be viewed in this way. This paper surveys several types of representations for both classical and decision-theoretic planning problems, and planning algorithms that exploit these representations in a number of different ways to ease the computational burden of constructing policies or plans. It focuses primarily on abstraction, aggregation and decomposition techniques based on AI-style representations.
1,233 citations
TL;DR: A version of Markov localization which provides accurate position estimates and which is tailored towards dynamic environments, and includes a filtering technique which allows a mobile robot to reliably estimate its position even in densely populated environments in which crowds of people block the robot's sensors for extended periods of time.
Abstract: Localization, that is the estimation of a robot's location from sensor data, is a fundamental problem in mobile robotics. This papers presents a version of Markov localization which provides accurate position estimates and which is tailored towards dynamic environments. The key idea of Markov localization is to maintain a probability density over the space of all locations of a robot in its environment. Our approach represents this space metrically, using a fine-grained grid to approximate densities. It is able to globally localize the robot from scratch and to recover from localization failures. It is robust to approximate models of the environment (such as occupancy grid maps) and noisy sensors (such as ultrasound sensors). Our approach also includes a filtering technique which allows a mobile robot to reliably estimate its position even in densely populated environments in which crowds of people block the robot's sensors for extended periods of time. The method described here has been implemented and tested in several real-world applications of mobile robots, including the deployments of two mobile robots as interactive museum tour-guides.
1,011 citations
TL;DR: This paper uses a set of learning algorithms to create classifiers that serve as noise filters for the training data and suggests that for situations in which there is a paucity of data, consensus filters are preferred, whereas majority vote filters are preferable for situations with an abundance of data.
Abstract: This paper presents a new approach to identifying and eliminating mislabeled training instances for supervised learning. The goal of this approach is to improve classification accuracies produced by learning algorithms by improving the quality of the training data. Our approach uses a set of learning algorithms to create classifiers that serve as noise filters for the training data. We evaluate single algorithm, majority vote and consensus filters on five datasets that are prone to labeling errors. Our experiments illustrate that filtering significantly improves classification accuracy for noise levels up to 30%. An analytical and empirical evaluation of the precision of our approach shows that consensus filters are conservative at throwing away good data at the expense of retaining bad data and that majority filters are better at detecting bad data at the expense of throwing away good data. This suggests that for situations in which there is a paucity of data, consensus filters are preferable, whereas majority vote filters are preferable for situations with an abundance of data.
877 citations
TL;DR: An on-line algorithm for learning preference functions that is based on Freund and Schapire's "Hedge" algorithm is considered, and it is shown that the problem of finding the ordering that agrees best with a learned preference function is NP-complete.
Abstract: There are many applications in which it is desirable to order rather than classify instances. Here we consider the problem of learning how to order instances given feedback in the form of preference judgments, i.e., statements to the effect that one instance should be ranked ahead of another. We outline a two-stage approach in which one first learns by conventional means a binary preference function indicating whether it is advisable to rank one instance before another. Here we consider an on-line algorithm for learning preference functions that is based on Freund and Schapire's "Hedge" algorithm. In the second stage, new instances are ordered so as to maximize agreement with the learned preference function. We show that the problem of finding the ordering that agrees best with a learned preference function is NP-complete. Nevertheless, we describe simple greedy algorithms that are guaranteed to find a good approximation. Finally, we show how metasearch can be formulated as an ordering problem, and present experimental results on learning a combination of "search experts," each of which is a domain-specific query expansion strategy for a web search engine.
779 citations
TL;DR: This paper addresses two crucial issues which have been considered to be a 'black art' in classification tasks ever since the introduction of stacked generalization: the type of generalizer that is suitable to derive the higher-level model, and the kind of attributes that should be used as its input.
Abstract: Stacked generalization is a general method of using a high-level model to combine lower-level models to achieve greater predictive accuracy In this paper we address two crucial issues which have been considered to be a 'black art' in classification tasks ever since the introduction of stacked generalization in 1992 by Wolpert: the type of generalizer that is suitable to derive the higher-level model, and the kind of attributes that should be used as its input We find that best results are obtained when the higher-level model combines the confidence (and not just the predictions) of the lower-level ones
We demonstrate the effectiveness of stacked generalization for combining three different types of learning algorithms for classification tasks We also compare the performance of stacked generalization with majority vote and published results of arcing and bagging
662 citations
TL;DR: Strengths and weaknesses of the evolutionary approach to reinforcement learning are presented, along with a survey of representative applications.
Abstract: There are two distinct approaches to solving reinforcement learning problems, namely, searching in value function space and searching in policy space. Temporal difference methods and evolutionary algorithms are well-known examples of these approaches. Kaelbling, Littman and Moore recently provided an informative survey of temporal difference methods. This article focuses on the application of evolutionary algorithms to the reinforcement learning problem, emphasizing alternative policy representations, credit assignment methods, and problem-specific genetic operators. Strengths and weaknesses of the evolutionary approach to reinforcement learning are presented, along with a survey of representative applications.
351 citations
TL;DR: An ensemble consists of a set of individually trained classifiers (such as neural networks or decision trees) whose predictions are combined when classifying novel instances.
Abstract: An ensemble consists of a set of individually trained classifiers (such as neural networks or decision trees) whose predictions are combined when classifying novel instances. Previous research has ...
312 citations
TL;DR: This paper approaches conditional planning from a new viewpoint that is motivated by the use of satisfiability algorithms in classical planning and translates conditional planning to quantified Boolean formulae in the propositional logic.
Abstract: The research on conditional planning rejects the assumptions that there is no uncertainty or incompleteness of knowledge with respect to the state and changes of the system the plans operate on Without these assumptions the sequences of operations that achieve the goals depend on the initial state and the outcomes of nondeterministic changes in the system This setting raises the questions of how to represent the plans and how to perform plan search The answers are quite different from those in the simpler classical framework In this paper, we approach conditional planning from a new viewpoint that is motivated by the use of satisfiability algorithms in classical planning Translating conditional planning to formulae in the propositional logic is not feasible because of inherent computational limitations Instead, we translate conditional planning to quantified Boolean formulae We discuss three formalizations of conditional planning as quantified Boolean formulae, and present experimental results obtained with a theorem-prover
277 citations
TL;DR: In this paper, a greedy algorithm is used to construct a solution which is then analyzed to find the trouble spots, i.e., those elements, that, if improved, are likely to improve the objective function score.
Abstract: We describe a general approach to optimization which we term "Squeaky Wheel" Optimization (SWO). In SWO, a greedy algorithm is used to construct a solution which is then analyzed to find the trouble spots, i.e., those elements, that, if improved, are likely to improve the objective function score. The results of the analysis are used to generate new priorities that determine the order in which the greedy algorithm constructs the next solution. This Construct/Analyze/Prioritize cycle continues until some limit is reached, or an acceptable solution is found.
SWO can be viewed as operating on two search spaces: solutions and prioritizations. Successive solutions are only indirectly related, via the re-prioritization that results from analyzing the prior solution. Similarly, successive prioritizations are generated by constructing and analyzing solutions. This "coupled search" has some interesting properties, which we discuss.
We report encouraging experimental results on two domains, scheduling problems that arise in fiber-optic cable manufacturing, and graph coloring problems. The fact that these domains are very different supports our claim that SWO is a general technique for optimization.
TL;DR: It is argued that, by virtue of the high expressive power and of the associated reasoning capabilities on both unrestricted and finite models, the proposed logic provides a common core for class-based representation formalisms.
Abstract: The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases In this paper we study the basic issues underlying such representation formalisms and single out both their common characteristics and their distinguishing features Such investigation leads us to propose a unifying framework in which we are able to capture the fundamental aspects of several representation languages used in different contexts The proposed formalism is expressed in the style of description logics, which have been introduced in knowledge representation as a means to provide a semantically well-founded basis for the structural aspects of knowledge representation systems The description logic considered in this paper is a subset of first order logic with nice computational characteristics It is quite expressive and features a novel combination of constructs that has not been studied before The distinguishing constructs are number restrictions, which generalize existence and functional dependencies, inverse roles, which allow one to refer to the inverse of a relationship, and possibly cyclic assertions, which are necessary for capturing real world domains We are able to show that it is precisely such combination of constructs that makes our logic powerful enough to model the essential set of features for defining class structures that are common to frame systems, object-oriented database languages, and semantic data models As a consequence of the established correspondences, several significant extensions of each of the above formalisms become available The high expressiveness of the logic we propose and the need for capturing the reasoning in different contexts forces us to distinguish between unrestricted and finite model reasoning A notable feature of our proposal is that reasoning in both cases is decidable We argue that, by virtue of the high expressive power and of the associated reasoning capabilities on both unrestricted and finite models, our logic provides a common core for class-based representation formalisms
TL;DR: This work describes a variational approximation method for efficient inference in large-scale probabilistic models and evaluates the algorithm on a large set of diagnostic test cases, comparing the algorithm to a state-of-the-art stochastic sampling method.
Abstract: We describe a variational approximation method for efficient inference in large-scale probabilistic models. Variational methods are deterministic procedures that provide approximations to marginal and conditional probabilities of interest. They provide alternatives to approximate inference methods based on stochastic sampling or search. We describe a variational approach to the problem of diagnostic inference in the "Quick Medical Reference" (QMR) network. The QMR network is a large-scale probabilistic graphical model built on statistical and expert knowledge. Exact probabilistic inference is infeasible in this model for all but a small set of cases. We evaluate our variational inference algorithm on a large set of diagnostic test cases, comparing the algorithm to a state-of-the-art stochastic sampling method.
TL;DR: In this paper, a family of empirical methods for committee-based sample selection in probabilistic classification models, which evaluate the informativeness of an example by measuring the degree of disagreement between several model variants, are drawn randomly from a probability distribution conditioned by the training set labeled so far.
Abstract: In many real-world learning tasks it is expensive to acquire a sufficient number of labeled examples for training This paper investigates methods for reducing annotation cost by sample selection In this approach, during training the learning program examines many unlabeled examples and selects for labeling only those that are most informative at each stage This avoids redundantly labeling examples that contribute little new information
Our work follows on previous research on Query By Committee, and extends the committee-based paradigm to the context of probabilistic classification We describe a family of empirical methods for committee-based sample selection in probabilistic classification models, which evaluate the informativeness of an example by measuring the degree of disagreement between several model variants These variants (the committee) are drawn randomly from a probability distribution conditioned by the training set labeled so far
The method was applied to the real-world natural language processing task of stochastic part-of-speech tagging We find that all variants of the method achieve a significant reduction in annotation cost, although their computational efficiency differs In particular, the simplest variant, a two member committee with no parameters to tune, gives excellent results We also show that sample selection yields a significant reduction in the size of the model used by the tagger
TL;DR: This article constructed and implemented a variety of market designs for climate control in large buildings, as well as different standard control engineering solutions, so as to learn about differences between standard versus agent approaches, and yielding new insights about benefits and limitations of computational markets.
Abstract: Multi-Agent Systems (MAS) promise to offer solutions to problems where established, older paradigms fall short. In order to validate such claims that are repeatedly made in software agent publications, empirical in-depth studies of advantages and weaknesses of multi-agent solutions versus conventional ones in practical applications are needed. Climate control in large buildings is one application area where multi-agent systems, and market-oriented programming in particular, have been reported to be very successful, although central control solutions are still the standard practice. We have therefore constructed and implemented a variety of market designs for this problem, as well as different standard control engineering solutions. This article gives a detailed analysis and comparison, so as to learn about differences between standard versus agent approaches, and yielding new insights about benefits and limitations of computational markets. An important outcome is that "local information plus market communication produces global control".
TL;DR: An algorithm is presented that computes the exact number of models of a propositional CNF or DNF formula F using the Davis-Putnam procedure and the practical performance of CDP has been estimated in a series of experiments on a wide variety of CNF formulas.
Abstract: As was shown recently, many important AI problems require counting the number of models of propositional formulas. The problem of counting models of such formulas is, according to present knowledge, computationally intractable in a worst case. Based on the Davis-Putnam procedure, we present an algorithm, CDP, that computes the exact number of models of a propositional CNF or DNF formula F. Let m and n be the number of clauses and variables of F, respectively, and let p denote the probability that a literal l of F occurs in a clause C of F, then the average running time of CDP is shown to be O(mdn), where d=[-1/log2(1-p)].The practical performance of CDP has been estimated in a series of experiments on a wide variety of CNF formulas.
TL;DR: The implementation of STAN's plan graph is described and experimental results which demonstrate the circumstances under which advantages can be obtained from using this implementation are provided.
Abstract: STAN is a Graphplan-based planner, so-called because it uses a variety of STate ANalysis techniques to enhance its performance. STAN competed in the AIPS-98 planning competition where it compared well with the other competitors in terms of speed, finding solutions fastest to many of the problems posed. Although the domain analysis techniques STAN exploits are an important factor in its overall performance, we believe that the speed at which STAN solved the competition problems is largely due to the implementation of its plan graph. The implementation is based on two insights: that many of the graph construction operations can be implemented as bit-level logical operations on bit vectors, and that the graph should not be explicitly constructed beyond the fix point. This paper describes the implementation of STAN's plan graph and provides experimental results which demonstrate the circumstances under which advantages can be obtained from using this implementation.
TL;DR: In this paper, the problem of probabilistic deduction with conditional constraints over basic events is shown to be NP-hard, and a local approach is proposed to solve it in polynomial time in the size of the conditional constraint trees.
Abstract: We study the problem of probabilistic deduction with conditional constraints over basic events. We show that globally complete probabilistic deduction with conditional constraints over basic events is NP-hard. We then concentrate on the special case of probabilistic deduction in conditional constraint trees. We elaborate very efficient techniques for globally complete probabilistic deduction. In detail, for conditional constraint trees with point probabilities, we present a local approach to globally complete probabilistic deduction, which runs in linear time in the size of the conditional constraint trees. For conditional constraint trees with interval probabilities, we show that globally complete probabilistic deduction can be done in a global approach by solving nonlinear programs. We show how these nonlinear programs can be transformed into equivalent linear programs, which are solvable in polynomial time in the size of the conditional constraint trees.
TL;DR: Cox's well-known theorem justifying the use of probability is shown not to hold in finite domains and the counterexample suggests that Cox's assumptions are insufficient to prove the result even in infinite domains.
Abstract: Cox's well-known theorem justifying the use of probability is shown not to hold in finite domains The counterexample also suggests that Cox's assumptions are insufficient to prove the result even in infinite domains The same counterexample is used to disprove a result of Fine on comparative conditional probability
TL;DR: This paper shows how belief revision and belief update can be captured in a new framework to model belief change and shows that Katsuno and Mendelzon's notion of belief update depends on several strong assumptions that may limit its applicability in artificial intelligence.
Abstract: The study of belief change has been an active area in philosophy and AI. In recent years two special cases of belief change, belief revision and belief update, have been studied in detail. In a companion paper (Friedman & Halpern, 1997), we introduce a new framework to model belief change. This framework combines temporal and epistemic modalities with a notion of plausibility, allowing us to examine the change of beliefs over time. In this paper, we show how belief revision and belief update can be captured in our framework. This allows us to compare the assumptions made by each method, and to better understand the principles underlying them. In particular, it shows that Katsuno and Mendelzon's notion of belief update (Katsuno & Mendelzon, 1991a) depends on several strong assumptions that may limit its applicability in artificial intelligence. Finally, our analysis allow us to identify a notion of minimal change that underlies a broad range of belief change operations including revision and update.
TL;DR: Various sets of assumptions under which a Cox-style theorem can be proved are provided, although all are rather strong and, arguably, not natural.
Abstract: The assumptions needed to prove Cox's Theorem are discussed and examined. Various sets of assumptions under which a Cox-style theorem can be proved are provided, although all are rather strong and, arguably, not natural.
TL;DR: A measure of semantic similarity in an IS-A taxonomy based on the notion of shared information content is presented, and an experimental evaluation against a benchmark set of human similarity jud...
Abstract: This article presents a measure of semantic similarity in an IS-A taxonomy based on the notion of shared information content. Experimental evaluation against a benchmark set of human similarity jud...
TL;DR: A novel algebra for reasoning about Spatial Congruence is introduced, it is shown that the satisfiability problem in the spatial algebra MC-4 is NP-complete, and a complete classification of tractability in the algebra is presented, based on the individuation of three maximal tractable subclasses, one containing the basic relations.
Abstract: In the recent literature of Artificial Intelligence, an intensive research effort has been spent, for various algebras of qualitative relations used in the representation of temporal and spatial knowledge, on the problem of classifying the computational complexity of reasoning problems for subsets of algebras. The main purpose of these researches is to describe a restricted set of maximal tractable subalgebras, ideally in an exhaustive fashion with respect to the hosting algebras.
In this paper we introduce a novel algebra for reasoning about Spatial Congruence, show that the satisfiability problem in the spatial algebra MC-4 is NP-complete, and present a complete classification of tractability in the algebra, based on the individuation of three maximal tractable subclasses, one containing the basic relations. The three algebras are formed by 14, 10 and 9 relations out of 16 which form the full algebra.
TL;DR: This paper presents a polynomial-time algorithm that can solve a set of constraints of the form "Points a and b are much closer together than points c and d", and proves that the first-order theory over such constraints is decidable.
Abstract: Order of magnitude reasoning -- reasoning by rough comparisons of the sizes of quantities -- is often called "back of the envelope calculation", with the implication that the calculations are quick though approximate. This paper exhibits an interesting class of constraint sets in which order of magnitude reasoning is demonstrably fast. Specifically, we present a polynomial-time algorithm that can solve a set of constraints of the form "Points a and b are much closer together than points c and d". We prove that this algorithm can be applied if "much closer together" is interpreted either as referring to an infinite difference in scale or as referring to a finite difference in scale, as long as the difference in scale is greater than the number of variables in the constraint set. We also prove that the first-order theory over such constraints is decidable.
TL;DR: In this paper, the authors investigate the problem of reasoning in the propositional fragment of MBNF, the logic of minimal belief and negation as failure introduced by Lifschitz, and provide algorithms for reasoning in propositional MBNF.
Abstract: We investigate the problem of reasoning in the propositional fragment of MBNF, the logic of minimal belief and negation as failure introduced by Lifschitz, which can be considered as a unifying framework for several nonmonotonic formalisms, including default logic, autoepistemic logic, circumscription, epistemic queries, and logic programming. We characterize the complexity and provide algorithms for reasoning in propositional MBNF. In particular, we show that skeptical entailment in propositional MBNF is Π3p-complete, hence it is harder than reasoning in all the above mentioned propositional formalisms for nonmonotonic reasoning. We also prove the exact correspondence between negation as failure in MBNF and negative introspection in Moore's autoepistemic logic.
TL;DR: Two algorithms for hypothesis ranking and their application for the probably approximately correct (PAC) and expected loss (EL) learning criteria are described and empirical results are provided to demonstrate the effectiveness of these ranking procedures on both synthetic and real-world datasets.
Abstract: This paper considers the problem of learning the ranking of a set of stochastic alternatives based upon incomplete information (i.e., a limited number of samples). We describe a system that, at each decision cycle, outputs either a complete ordering on the hypotheses or decides to gather additional information (i.e., observations) at some cost. The ranking problem is a generalization of the previously studied hypothesis selection problem -- in selection, an algorithm must select the single best hypothesis, while in ranking, an algorithm must order all the hypotheses.
The central problem we address is achieving the desired ranking quality while minimizing the cost of acquiring additional samples. We describe two algorithms for hypothesis ranking and their application for the probably approximately correct (PAC) and expected loss (EL) learning criteria. Empirical results are provided to demonstrate the effectiveness of these ranking procedures on both synthetic and real-world datasets.
TL;DR: A perturbational approach in the form of a cumulant expansion which, to lowest order, recovers the standdard Kullback-Leibler variational bound, which is demonstrated on a particular class of undirected graphical models, Boltzmann machines, to confirm improved accuracy and enhanced stability during learning.
Abstract: Intractable distributions present a common difficulty in inference within the probabilistic knowledge representation framework and variational methods have recently been popular in providing an approximate solution In this article, we describe a perturbational approach in the form of a cumulant expansion which, to lowest order, recovers the standdard Kullback-Leibler variational bound Higher-order terms describe corrections on the variational approach without incurring much further computational cost The relationship to other perturbational approaches such as TAP is also elucidated We demonstrate the method on a particular class of undirected graphical models, Boltzmann machines, for which our simulation results confirm improved accuracy and enhanced stability during learning
PARC1
TL;DR: A previously developed quantum search algorithm for solving 1-SAT problems in a single step is generalized to apply to a range of highly constrained k-S AT problems, identifying a bound on the number of clauses in satisfiahility problems for which the generalized algorithm can find a solution in a constant number of steps as theNumber of variables increases.
Abstract: A previously developed quantum search algorithm for solving 1-SAT problems in a single step is generalized to apply to a range of highly constrained k-SAT problems. We identify a bound on the number of clauses in satisfiahility problems for which the generalized algorithm can find a solution in a constant number of steps as the number of variables increases. This performance contrasts with the linear growth in the number of steps required by the best classical algorithms, and the exponential number required by classical and quantum methods that ignore the problem structure. In some cases, the algorithm can also guarantee that insoluble problems in fact have no solutions, unlike previously proposed quantum search algorithms.
TL;DR: In this paper, the authors propose an approach to extensible knowledge representation and reasoning for the Description Logic family of formalisms based on the notion of adding new concept constructors, and include a heuristic methodology for specifying the desired extensions, as well as a modularized software architecture that supports implementing extensions.
Abstract: This paper offers an approach to extensible knowledge representation and reasoning for the Description Logic family of formalisms. The approach is based on the notion of adding new concept constructors, and includes a heuristic methodology for specifying the desired extensions, as well as a modularized software architecture that supports implementing extensions. The architecture detailed here falls in the normalize-compared paradigm, and supports both intentional reasoning (subsumption) involving concepts, and extensional reasoning involving individuals after incremental updates to the knowledge base.
The resulting approach can be used to extend the reasoner with specialized notions that are motivated by specific problems or application areas, such as reasoning about dates, plans, etc. In addition, it provides an opportunity to implement constructors that are not currently yet sufficiently well understood theoretically, but are needed in practice. Also, for constructors that are provably hard to reason with (e.g., ones whose presence would lead to undecidability), it allows the implementation of incomplete reasoners where the incompleteness is tailored to be acceptable for the application at hand.
TL;DR: In order to identify subgoal clauses and lemmas which are actually relevant for the proof task, the ability of the techniques to shorten proofs as well as to reorder the search space in an appropriate manner is discussed.
Abstract: Top-down and bottom-up theorem proving approaches each have specific advantages and disadvantages Bottom-up provers profit from strong redundancy control but suffer from the lack of goal-orientation, whereas top-down provers are goal-oriented but often have weak calculi when their proof lengths are considered In order to integrate both approaches, we try to achieve cooperation between a top-down and a bottom-up prover in two different ways: The first technique aims at supporting a bottom-up with a top-down prover A top-down prover generates subgoal clauses, they are then processed by a bottom-up prover The second technique deals with the use of bottom-up generated lemmas in a top-down prover We apply our concept to the areas of model elimination and superposition We discuss the ability of our techniques to shorten proofs as well as to reorder the search space in an appropriate manner Furthermore, in order to identify subgoal clauses and lemmas which are actually relevant for the proof task, we develop methods for a relevancy-based filtering Experiments with the provers SETHEO and SPASS performed in the problem library TPTP reveal the high potential of our cooperation approaches