The Experts below are selected from a list of 297 Experts worldwide ranked by ideXlab platform
Pedro Domingos - One of the best experts on this subject based on the ideXlab platform.
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probabilistic Theorem Proving
Communications of The ACM, 2016Co-Authors: Vibhav Gogate, Pedro DomingosAbstract:Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable elimination and belief propagation, neither of which take logical structure into account. We propose the first method that has the full power of both graphical model inference and first-order Theorem Proving (in finite domains with Herbrand interpretations). We first define probabilistic Theorem Proving (PTP), their generalization, as the problem of computing the probability of a logical formula given the probabilities or weights of a set of formulas. We then show how PTP can be reduced to the problem of lifted weighted model counting, and develop an efficient algorithm for the latter. We prove the correctness of this algorithm, investigate its properties, and show how it generalizes previous approaches. Experiments show that it greatly outperforms lifted variable elimination when logical structure is present. Finally, we propose an algorithm for approximate PTP, and show that it is superior to lifted belief propagation.
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Probabilistic Theorem Proving
arXiv: Artificial Intelligence, 2012Co-Authors: Vibhav Gogate, Pedro DomingosAbstract:Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable elimination and belief propagation, neither of which take logical structure into account. We propose the first method that has the full power of both graphical model inference and first-order Theorem Proving (in finite domains with Herbrand interpretations). We first define probabilistic Theorem Proving, their generalization, as the problem of computing the probability of a logical formula given the probabilities or weights of a set of formulas. We then show how this can be reduced to the problem of lifted weighted model counting, and develop an efficient algorithm for the latter. We prove the correctness of this algorithm, investigate its properties, and show how it generalizes previous approaches. Experiments show that it greatly outperforms lifted variable elimination when logical structure is present. Finally, we propose an algorithm for approximate probabilistic Theorem Proving, and show that it can greatly outperform lifted belief propagation.
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UAI - Probabilistic Theorem Proving
2011Co-Authors: Vibhav Gogate, Pedro DomingosAbstract:Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable elimination and belief propagation, neither of which take logical structure into account. We propose the first method that has the full power of both graphical model inference and first-order Theorem Proving (in finite domains with Herbrand interpretations). We first define probabilistic Theorem Proving, their generalization, as the problem of computing the probability of a logical formula given the probabilities or weights of a set of formulas. We then show how this can be reduced to the problem of lifted weighted model counting, and develop an efficient algorithm for the latter. We prove the correctness of this algorithm, investigate its properties, and show how it generalizes previous approaches. Experiments show that it greatly outperforms lifted variable elimination when logical structure is present. Finally, we propose an algorithm for approximate probabilistic Theorem Proving, and show that it can greatly outperform lifted belief propagation.
Vibhav Gogate - One of the best experts on this subject based on the ideXlab platform.
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probabilistic Theorem Proving
Communications of The ACM, 2016Co-Authors: Vibhav Gogate, Pedro DomingosAbstract:Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable elimination and belief propagation, neither of which take logical structure into account. We propose the first method that has the full power of both graphical model inference and first-order Theorem Proving (in finite domains with Herbrand interpretations). We first define probabilistic Theorem Proving (PTP), their generalization, as the problem of computing the probability of a logical formula given the probabilities or weights of a set of formulas. We then show how PTP can be reduced to the problem of lifted weighted model counting, and develop an efficient algorithm for the latter. We prove the correctness of this algorithm, investigate its properties, and show how it generalizes previous approaches. Experiments show that it greatly outperforms lifted variable elimination when logical structure is present. Finally, we propose an algorithm for approximate PTP, and show that it is superior to lifted belief propagation.
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Probabilistic Theorem Proving
arXiv: Artificial Intelligence, 2012Co-Authors: Vibhav Gogate, Pedro DomingosAbstract:Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable elimination and belief propagation, neither of which take logical structure into account. We propose the first method that has the full power of both graphical model inference and first-order Theorem Proving (in finite domains with Herbrand interpretations). We first define probabilistic Theorem Proving, their generalization, as the problem of computing the probability of a logical formula given the probabilities or weights of a set of formulas. We then show how this can be reduced to the problem of lifted weighted model counting, and develop an efficient algorithm for the latter. We prove the correctness of this algorithm, investigate its properties, and show how it generalizes previous approaches. Experiments show that it greatly outperforms lifted variable elimination when logical structure is present. Finally, we propose an algorithm for approximate probabilistic Theorem Proving, and show that it can greatly outperform lifted belief propagation.
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UAI - Probabilistic Theorem Proving
2011Co-Authors: Vibhav Gogate, Pedro DomingosAbstract:Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable elimination and belief propagation, neither of which take logical structure into account. We propose the first method that has the full power of both graphical model inference and first-order Theorem Proving (in finite domains with Herbrand interpretations). We first define probabilistic Theorem Proving, their generalization, as the problem of computing the probability of a logical formula given the probabilities or weights of a set of formulas. We then show how this can be reduced to the problem of lifted weighted model counting, and develop an efficient algorithm for the latter. We prove the correctness of this algorithm, investigate its properties, and show how it generalizes previous approaches. Experiments show that it greatly outperforms lifted variable elimination when logical structure is present. Finally, we propose an algorithm for approximate probabilistic Theorem Proving, and show that it can greatly outperform lifted belief propagation.
Geoff Sutcliffe - One of the best experts on this subject based on the ideXlab platform.
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the cade 23 automated Theorem Proving system competition casc 23
Ai Communications, 2012Co-Authors: Geoff SutcliffeAbstract:The CADE ATP System Competition (CASC) is an annual evaluation of fully automatic, classical logic Automated Theorem Proving (ATP) systems. CASC-23 was the sixteenth competition in the CASC series. Thirty-six ATP systems and system variants competed in the various competition and demonstration divisions. An outline of the competition design, and a commentated summary of the results, are presented.
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the 4th ijcar automated Theorem Proving system competition casc j4
Ai Communications, 2009Co-Authors: Geoff SutcliffeAbstract:The CADE ATP System Competition (CASC) is an annual evaluation of fully automatic, first order Automated Theorem Proving (ATP) systems. CASC-J4 was the thirteenth competition in the CASC series. Twenty-six ATP systems and system variants competed in the various competition and demonstration divisions. An outline of the competition design, and a commentated summary of the results, are presented.
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Discrete Event Calculus Deduction using First-Order Automated Theorem Proving
2008Co-Authors: Erik T Mueller, Geoff SutcliffeAbstract:Abstract. The event calculus is a powerful and highly usable formalism for reasoning about action and change. The discrete event calculus limits time to integers. This paper shows how discrete event calculus problems can be encoded in first-order logic, and solved using a first-order logic automated Theorem Proving system. The following techniques are discussed: reification is used to convert event and fluent atoms into first-order terms, uniqueness-of-names axioms are generated to ensure uniqueness of event and fluent terms, predicate completion is used to convert second-order circumscriptions into first-order formulae, and a limited first-order axiomatization of integer arithmetic is developed. The performance of first-order automated Theorem Proving is compared to that of satisfiability solving.
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tstp data exchange formats for automated Theorem Proving tools
2004Co-Authors: Geoff Sutcliffe, Jurgen Zimmer, Stephan SchulzAbstract:This paper describes two data-exchange formats for Automated Theorem Proving (ATP) tools. First, a language for writing the problems that are input to ATP systems, and for writing the solutions that are output from ATP systems, is described. Second, a hierarchy of values for specifying the logical status of an ATP problem, as may be established by an ATP system, is described. These data-exchange formats will support application and research in ATP, and will facilitate communication between ATP tools in distributed and embedded environments.
Cezary Kaliszyk - One of the best experts on this subject based on the ideXlab platform.
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reinforcement learning of Theorem Proving
Neural Information Processing Systems, 2018Co-Authors: Cezary Kaliszyk, Josef Urban, Henryk Michalewski, Miroslav OlsakAbstract:We introduce a Theorem Proving algorithm that uses practically no domain heuristics for guiding its connection-style proof search. Instead, it runs many Monte-Carlo simulations guided by reinforcement learning from previous proof attempts. We produce several versions of the prover, parameterized by different learning and guiding algorithms. The strongest version of the system is trained on a large corpus of mathematical problems and evaluated on previously unseen problems. The trained system solves within the same number of inferences over 40% more problems than a baseline prover, which is an unusually high improvement in this hard AI domain. To our knowledge this is the first time reinforcement learning has been convincingly applied to solving general mathematical problems on a large scale.
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HolStep: A Machine Learning Dataset for Higher-order Logic Theorem Proving
arXiv: Artificial Intelligence, 2017Co-Authors: Cezary Kaliszyk, François Chollet, Christian SzegedyAbstract:Large computer-understandable proofs consist of millions of intermediate logical steps. The vast majority of such steps originate from manually selected and manually guided heuristics applied to intermediate goals. So far, machine learning has generally not been used to filter or generate these steps. In this paper, we introduce a new dataset based on Higher-Order Logic (HOL) proofs, for the purpose of developing new machine learning-based Theorem-Proving strategies. We make this dataset publicly available under the BSD license. We propose various machine learning tasks that can be performed on this dataset, and discuss their significance for Theorem Proving. We also benchmark a set of simple baseline machine learning models suited for the tasks (including logistic regression, convolutional neural networks and recurrent neural networks). The results of our baseline models show the promise of applying machine learning to HOL Theorem Proving.
Joe Hurd - One of the best experts on this subject based on the ideXlab platform.
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TPHOLs - Applications of Polytypism in Theorem Proving
Lecture Notes in Computer Science, 2003Co-Authors: Konrad Slind, Joe HurdAbstract:Polytypic functions have mainly been studied in the context of functional programming languages. In that setting, applications of polytypism include elegant treatments of polymorphic equality, prettyprinting, and the encoding and decoding of high-level datatypes to and from low-level binary formats. In this paper, we discuss how polytypism supports some aspects of Theorem Proving: automated termination proofs of recursive functions, incorporation of the results of metalanguage evaluation, and equivalence-preserving translation to a low-level format suitable for propositional methods. The approach is based on an interpretation of higher order logic types as terms, and easily deals with mutual and nested recursive types.
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Applications of polytypism in Theorem Proving
Lecture Notes in Computer Science, 2003Co-Authors: Konrad Slind, Joe HurdAbstract:Polytypic functions have mainly been studied in the context of functional programming languages. In that setting, applications of polytypism include elegant treatments of polymorphic equality, prettyprinting, and the encoding and decoding of high-level datatypes to and from low-level binary formats. In this paper, we discuss how polytypism supports some aspects of Theorem Proving: automated termination proofs of recursive functions, incorporation of the results of metalanguage evaluation, and equivalence-preserving translation to a low-level format suitable for propositional methods. The approach is based on an interpretation of higher order logic types as terms, and easily deals with mutual and nested recursive types.
