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The TPTP Problem Library
, 1999
"... This report provides a detailed description of the TPTP Problem Library for automated theorem proving systems. The library is available via Internet, and forms a common basis for development of and experimentation with automated theorem provers. This report provides: ffl the motivations for buildin ..."
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Cited by 100 (6 self)
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This report provides a detailed description of the TPTP Problem Library for automated theorem proving systems. The library is available via Internet, and forms a common basis for development of and experimentation with automated theorem provers. This report provides: ffl the motivations for building the library; ffl a discussion of the inadequacies of previous problem collections, and how these have been resolved in the TPTP; ffl a description of the library structure, including overview information; ffl descriptions of supplementary utility programs; ffl guidelines for obtaining and using the library; Contents 1 Introduction 2 1.1 Previous Problem Collections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 What is Required? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Inside the TPTP 6 2.1 The TPTP Domain Structure . . . . . . . . . . . . . . . . . . . . . ...
Optimizing proof search in model elimination
 13th International Conference on Automated Deduction, volume 1104 of Lecture Notes in Computer Science
, 1996
"... Many implementations of model elimination perform proof search by iteratively increasing a bound on the total size of the proof. We propose an optimized version of this search mode using a simple divideandconquer refinement. Optimized and unoptimized modes are compared, together with depthbounded ..."
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Cited by 20 (2 self)
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Many implementations of model elimination perform proof search by iteratively increasing a bound on the total size of the proof. We propose an optimized version of this search mode using a simple divideandconquer refinement. Optimized and unoptimized modes are compared, together with depthbounded and bestfirst search, over the entire TPTP problem library. The optimized sizebounded mode seems to be the overall winner, but for each strategy there are problems on which it performs best. Some attempt is made to analyze why. We emphasize that our optimization, and other implementation techniques like caching, are rather general: they are not dependent on the details of model elimination, or even that the search is concerned with theorem proving. As such, we believe that this study is a useful complement to research on extending the model elimination calculus.
A Connectionist Control Component for the Theorem Prover SETHEO
 In ECAI94 Workshop on Combining Symbolic and Connectionist Processing
, 1994
"... Today, the power of automated theorem provers is yet too weak for proving many challinging problems. However heuristics for guiding the proof search can dramatically improve the power of such provers. Since it is very difficult to develop heuristics by hand and since they have to be developed specif ..."
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Cited by 13 (9 self)
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Today, the power of automated theorem provers is yet too weak for proving many challinging problems. However heuristics for guiding the proof search can dramatically improve the power of such provers. Since it is very difficult to develop heuristics by hand and since they have to be developed specifically for each problem domain (theory), we decided to derive heuristics automatically using machine learning techniques. Especially neural networks seem to be very suitable for the representation of heuristics because of their ability to deal with incomplete and inconsistent knowledge. In the following paper we describe our experiences with a connectionist control component for the theorem prover SETHEO. As SETHEO is very closely related to the programming language Prolog, our work might be of interest for a greater public than just the theorem proving community. 1 Introduction In automated theorem proving the goal is to find a proof for a given theorem automatically, starting from a set o...
Computational Logic and Human Thinking: How to be Artificially Intelligent
, 2011
"... The mere possibility of Artificial Intelligence (AI) – of machines that can think and act as intelligently as humans – can generate strong emotions. While some enthusiasts are excited by the thought that one day machines may become more intelligent than people, many of its critics view such a prosp ..."
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Cited by 13 (7 self)
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The mere possibility of Artificial Intelligence (AI) – of machines that can think and act as intelligently as humans – can generate strong emotions. While some enthusiasts are excited by the thought that one day machines may become more intelligent than people, many of its critics view such a prospect with horror. Partly because these controversies attract so much attention, one of the most important accomplishments of AI has gone largely unnoticed: the fact that many of its advances can also be used directly by people, to improve their own human intelligence. Chief among these advances is Computational Logic. Computational Logic builds upon traditional logic, which was originally developed to help people think more effectively. It employs the techniques of symbolic logic, which has been used to build the foundations of mathematics and computing. However, compared with traditional logic, Computational Logic is much more powerful; and compared with symbolic logic, it is much simpler and more practical. Although the applications of Computational Logic in AI require the use of mathematical notation, its human applications do not. As a consequence, I have written the main part of this book informally, to reach as wide an audience as possible. Because human thinking is also the subject of study in many other fields, I have drawn upon related studies in Cognitive Psychology, Linguistics, Philosophy, Law, Management Science and English
Autarky pruning in propositional model elimination reduces failure redundancy
 Journal of Automated Reasoning
, 1999
"... Goalsensitive resolution methods, such as Model Elimination, have been observed to have a higher degree of search redundancy than modelsearch methods, Therefore, resolution methods have not been seen in high performance propositional satis ability testers. A method to reduce search redundancy in g ..."
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Cited by 12 (3 self)
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Goalsensitive resolution methods, such as Model Elimination, have been observed to have a higher degree of search redundancy than modelsearch methods, Therefore, resolution methods have not been seen in high performance propositional satis ability testers. A method to reduce search redundancy in goalsensitive resolution methods is introduced. The idea at the heart of the method is to attempt to construct a refutation and a model simultaneously and incrementally, based on subsearch outcomes. The method exploits the concept of \autarky", which can be informally described as a \selfsu cient " model for some clauses, but which does not a ect the remaining clauses of the formula. Incorporating this method into Model Elimination leads to an algorithm called Modoc. Modoc is shown, both analytically and experimentally, to be faster than Model Elimination by an exponential factor. Modoc, unlike Model Elimination, is able to nd a model if it fails to nd a refutation, essentially by combining autarkies. Unlike the pruning strategies of most re nements of resolution, autarkyrelated pruning does not prune any successful refutation; it only prunes attempts that ultimately will be unsuccessful; consequently, it will not force the underlying Modoc search to nd an unnecessarily long refutation. To prove correctness and other properties, a game characterization of refutation search isintroduced, which demonstrates
The HOL Light manual (1.1)
, 2000
"... ion is in a precise sense a converse operation to application. Given 49 50 CHAPTER 5. PRIMITIVE BASIS OF HOL LIGHT a variable x and a term t, which may or may not contain x, one can construct the socalled lambdaabstraction x: t, which means `the function of x that yields t'. (In HOL's ASCII concr ..."
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Cited by 6 (0 self)
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ion is in a precise sense a converse operation to application. Given 49 50 CHAPTER 5. PRIMITIVE BASIS OF HOL LIGHT a variable x and a term t, which may or may not contain x, one can construct the socalled lambdaabstraction x: t, which means `the function of x that yields t'. (In HOL's ASCII concrete syntax the backslash is used, e.g. \x. t.) For example, x: x + 1 is the function that adds one to its argument. Abstractions are not often seen in informal mathematics, but they have at least two merits. First, they allow one to write anonymous functionvalued expressions without naming them (occasionally one sees x 7! t[x] used for this purpose), and since our logic is avowedly higher order, it's desirable to place functions on an equal footing with rstorder objects in this way. Secondly, they make variable dependencies and binding explicit; by contrast in informal mathematics one often writes f(x) in situations where one really means x: f(x). We should give some idea of how ordina...
Cooperation Between TopDown and BottomUp Theorem Provers by Subgoal Clause Transfer
 JOURNAL OF ARTIFICIAL INTELLIGENCE RESEARCH
, 1998
"... Topdown and bottomup theorem proving approaches have each specific advantages and disadvantages. Bottomup provers profit from strong redundancy control and su#er from the lack of goalorientation, whereas topdown provers are goaloriented but have weak calculi when their proof lengths are con ..."
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Cited by 4 (2 self)
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Topdown and bottomup theorem proving approaches have each specific advantages and disadvantages. Bottomup provers profit from strong redundancy control and su#er from the lack of goalorientation, whereas topdown provers are goaloriented but have weak calculi when their proof lengths are considered. In order to integrate both approaches our method is to achieve cooperation between a topdown and a bottomup prover: the topdown prover generates subgoal clauses, then they are processed by a bottomup prover. We discuss theoretic aspects of this methodology and we introduce techniques for a relevancybased filtering of generated subgoal clauses. Experiments with a model elimination and a superposition prover reveal the high potential of our approach.
HEUROPA: Heuristic Optimization of Parallel Computations
 In !EuroARCH '93
, 1993
"... . The performance of almost all parallel algorithms and systems can be improved by the use of heuristics that affect the parallel execution. However, since optimal guidance usually depends on many different influences, establishing such heuristics is often difficult. Due to the importance of heurist ..."
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Cited by 2 (2 self)
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. The performance of almost all parallel algorithms and systems can be improved by the use of heuristics that affect the parallel execution. However, since optimal guidance usually depends on many different influences, establishing such heuristics is often difficult. Due to the importance of heuristics for optimizing parallel execution, and the similarity of the problems that arise for establishing such heuristics, the HEUROPA activity was founded to attack these problems in a uniform way. To overcome the difficulties of specifying heuristics by hand, machine learning techniques have been employed to obtain heuristics automatically. This paper presents the general approach used for learning heuristics, describes the applications arising in the various subprojects, and provides a detailed case study using the approach for a particular application. 1 Introduction Parallel algorithms represent complex software, with a large number of parameters that need to be adjusted for optimal perfor...
Persistent and QuasiPersistent Lemmas in Propositional Model Elimination
 IN (ELECTRONIC) PROC. 6TH INT’L SYMPOSIUM ON ARTIFICIAL INTELLIGENCE AND MATHEMATICS
, 2000
"... Model elimination is a backchaining strategy to search for and construct resolution refutations. Many formulas can be refuted more succinctly by recording certain derived clauses, called lemmas, then using them where a clause of the original formula would normally be required. However, recording ..."
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Cited by 1 (0 self)
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Model elimination is a backchaining strategy to search for and construct resolution refutations. Many formulas can be refuted more succinctly by recording certain derived clauses, called lemmas, then using them where a clause of the original formula would normally be required. However, recording too many lemmas overwhelms the proof search.
The HOL Light manual (1.0)
, 1998
"... ion is in a precise sense a converse operation to application. Given 49 50 CHAPTER 5. PRIMITIVE BASIS OF HOL LIGHT a variable x and a term t, which may or may not contain x, one can construct the socalled lambdaabstraction x: t, which means `the function of x that yields t'. (In HOL's ASCII concr ..."
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Cited by 1 (0 self)
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ion is in a precise sense a converse operation to application. Given 49 50 CHAPTER 5. PRIMITIVE BASIS OF HOL LIGHT a variable x and a term t, which may or may not contain x, one can construct the socalled lambdaabstraction x: t, which means `the function of x that yields t'. (In HOL's ASCII concrete syntax the backslash is used, e.g. "x. t.) For example, x: x + 1 is the function that adds one to its argument. Abstractions are not often seen in informal mathematics, but they have at least two merits. First, they allow one to write anonymous functionvalued expressions without naming them (occasionally one sees x 7! t[x] used for this purpose), and since our logic is avowedly higher order, it's desirable to place functions on an equal footing with firstorder objects in this way. Secondly, they make variable dependencies and binding explicit; by contrast in informal mathematics one often writes f(x) in situations where one really means x: f(x). We should give some idea of how ordinary...