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17
On Generating Small Clause Normal Forms
, 1998
"... In this paper we focus on two powerful techniques to obtain compact clause normal forms: Renaming of formulae and refined Skolemization methods. We illustrate their effect on various examples. By an exhaustive experiment of all firstorder TPTP problems, it shows that our clause normal form tran ..."
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Cited by 90 (2 self)
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In this paper we focus on two powerful techniques to obtain compact clause normal forms: Renaming of formulae and refined Skolemization methods. We illustrate their effect on various examples. By an exhaustive experiment of all firstorder TPTP problems, it shows that our clause normal form transformation yields fewer clauses and fewer literals than the methods known and used so far. This often allows for exponentially shorter proofs and, in some cases, it makes it even possible for a theorem prover to find a proof where it was unable to do so with more standard clause normal form transformations. 1
Explaining ALC subsumption
 In Proc. of DL’99
, 1999
"... Abstract. Knowledge representation systems, including ones based on Description Logics (DLs), use explanation facilities to, among others, debug knowledge bases. Until now, such facilities were not available for expressive DLs, whose reasoning is an unnatural refutationbased tableau. We offer a so ..."
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Cited by 54 (15 self)
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Abstract. Knowledge representation systems, including ones based on Description Logics (DLs), use explanation facilities to, among others, debug knowledge bases. Until now, such facilities were not available for expressive DLs, whose reasoning is an unnatural refutationbased tableau. We offer a solution based on a sequent calculus that is closely related to the tableau implementation, exploiting its optimisations. The resulting proofs are pruned and then presented as simply as possible using templates. 1
AgentOriented Integration of Distributed Mathematical Services
 Journal of Universal Computer Science
, 1999
"... Realworld applications of automated theorem proving require modern software environments that enable modularisation, networked interoperability, robustness, and scalability. These requirements are met by the AgentOriented Programming paradigm of Distributed Artificial Intelligence. We argue that ..."
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Cited by 19 (10 self)
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Realworld applications of automated theorem proving require modern software environments that enable modularisation, networked interoperability, robustness, and scalability. These requirements are met by the AgentOriented Programming paradigm of Distributed Artificial Intelligence. We argue that a reasonable framework for automated theorem proving in the large regards typical mathematical services as autonomous agents that provide internal functionality to the outside and that, in turn, are able to access a variety of existing external services. This article describes...
Learning Search Control Knowledge for Equational Theorem Proving
 Fakultat fur Informatik, Technische Universitat Munchen
, 2001
"... One of the major problems in clausal theorem proving is the control of the proof search. In the presence of equality, this problem is particularly hard, since nearly all stateoftheart systems perform the proof search by saturating a mostly unstructured set of clauses. We describe an approach that ..."
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Cited by 19 (5 self)
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One of the major problems in clausal theorem proving is the control of the proof search. In the presence of equality, this problem is particularly hard, since nearly all stateoftheart systems perform the proof search by saturating a mostly unstructured set of clauses. We describe an approach that enables a superpositionbased prover to pick good clauses for generating inferences based on experiences from previous successful proof searches for other problems. Information about good and bad search decisions (useful and superfluous clauses) is automatically collected from search protocols and represented in the form of annotated clause patterns. At run time, new clauses are compared with stored patterns and evaluated according to the associated information found. We describe our implementation of the system. Experimental results demonstrate that a learned heuristic significantly outperforms the conventional base strategy, especially in domains where enough training examples are available.
Extending Sledgehammer with SMT Solvers
"... Abstract. Sledgehammer is a component of Isabelle/HOL that employs firstorder automatic theorem provers (ATPs) to discharge goals arising in interactive proofs. It heuristically selects relevant facts and, if an ATP is successful, produces a snippet that replays the proof in Isabelle. We extended Sl ..."
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Cited by 15 (6 self)
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Abstract. Sledgehammer is a component of Isabelle/HOL that employs firstorder automatic theorem provers (ATPs) to discharge goals arising in interactive proofs. It heuristically selects relevant facts and, if an ATP is successful, produces a snippet that replays the proof in Isabelle. We extended Sledgehammer to invoke satisfiability modulo theories (SMT) solvers as well, exploiting its relevance filter and parallel architecture. Isabelle users are now pleasantly surprised by SMT proofs for problems beyond the ATPs ’ reach. Remarkably, the best SMT solver performs better than the best ATP on most of our benchmarks. 1
Towards interoperable mechanized reasoning systems: the logic broker architecture
 AI*IATABOO Workshop `From Objects to Agents: Evolutionary Trends of Software Systems
, 2000
"... There is a growing interest in the integration of mechanized reasoning systems such as automated theorem provers, computer algebra systems, and model checkers. Stateoftheart reasoning systems are the result of many manyears of careful development and engineering, and usually they provide a high ..."
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Cited by 14 (1 self)
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There is a growing interest in the integration of mechanized reasoning systems such as automated theorem provers, computer algebra systems, and model checkers. Stateoftheart reasoning systems are the result of many manyears of careful development and engineering, and usually they provide a high degree of sophistication in their respective domain. Yet they often perform poorly when applied outside the domain they have been designed for. The problem of integrating mechanized reasoning systems is therefore being perceived as an important issue in automated reasoning. In this paper we present the Logic Broker Architecture, a framework which provides the needed infrastructure for making mechanized reasoning systems interoperate. The architecture provides location transparency, a way to forward requests for logical services to appropriate reasoning systems via a simple registration/subscription mechanism, and a translation mechanism which ensures the transparent and provably sound exchange of logical services. 1
PSETHEO: Strategy Parallel Automated Theorem Proving
 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX98
, 1998
"... One of the key issues in Automated Theorem Proving is the search for optimal proof strategies. Since there is not one uniform strategy which works optimal on all proof tasks, one is faced with the difficult problem of selecting a good strategy for a given task. In this paper, we discuss a way of cir ..."
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Cited by 10 (1 self)
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One of the key issues in Automated Theorem Proving is the search for optimal proof strategies. Since there is not one uniform strategy which works optimal on all proof tasks, one is faced with the difficult problem of selecting a good strategy for a given task. In this paper, we discuss a way of circumventing this strategy selection problem by using strategy parallelism. In this approach, a proof task is attempted in parallel by a set of uniform strategies while distributing the given amount of computing resources according to a certain schedule. We discuss important issues of strategy parallelism like search space partitioning, schedule computation, and scalability. In order to evaluate the potential of the method experimentally, we have implemented the strategy parallel theorem prover pSETHEO, which is also described in the paper. The experimental results obtained with the system justify our approach. 1 Introduction Automated Theorem Proving (ATP) is the subfield of theoretical co...
Verifying Intuition  ILF checks DAWN proofs
, 1999
"... The DAWN approach allows to model and verify distributed algorithms in an intuitive way. At a first glance, a DAWN proof may appear to be informal. In this paper, we argue that DAWN proofs are formal and can be checked for correctness fully automatically by automated theorem provers. The basic techn ..."
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Cited by 4 (4 self)
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The DAWN approach allows to model and verify distributed algorithms in an intuitive way. At a first glance, a DAWN proof may appear to be informal. In this paper, we argue that DAWN proofs are formal and can be checked for correctness fully automatically by automated theorem provers. The basic technique are proof rules which generate proof obligations. For the definition of the proof rules we adopt assertions and we introduce conflict formulas for algebraic Petri nets. Experiments show that the generated proof obligations can be automatically checked by theorem provers.
Integrating deduction techniques in a software reuse application
 J. UCS
, 1999
"... We investigate the application of automated deduction techniques to retrieve software components based on their formal specifications. The application profile has major impacts on the problem solving process and requires an open system architecture in which different deductive engines work in comb ..."
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Cited by 3 (1 self)
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We investigate the application of automated deduction techniques to retrieve software components based on their formal specifications. The application profile has major impacts on the problem solving process and requires an open system architecture in which different deductive engines work in combination because the proof problems are too difficult for a single monolithic system. We describe our system architecture, a pipeline of filters of increasing deductive strength, and concentrate on the final filter, in which theorem provers are applied. Here, we use the Ilfsystem as a control and integration shell to combine different provers. We support two different combination styles, competition and cooperation. Experiments confirm our approach. With moderate timeouts we already achieve an overall recall of approximately 80%.
Towards Concurrent Resource Managed Deduction
 UNIVERSITY OF BIRMINGHAM, SCHOOL OF COMPUTER SCIENCE. URL
, 1999
"... In this paper, we describe an architecture for resource guided concurrent mechanised deduction which is motivated by some findings in cognitive science. Its benefits are illustrated by comparing it with traditional proof search techniques. In particular, we introduce the notion of focused search ..."
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Cited by 3 (2 self)
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In this paper, we describe an architecture for resource guided concurrent mechanised deduction which is motivated by some findings in cognitive science. Its benefits are illustrated by comparing it with traditional proof search techniques. In particular, we introduce the notion of focused search and show that a reasoning system can be built as the cooperative collection of concurrently acting specialised problem solvers. These reasoners typically perform well in a particular problem domain. The system architecture that we describe assesses the subgoals of a theorem and distributes them to the specialised solvers that look the most promising. Furthermore it allocates resources (above all computation time and memory) to the specialised reasoners. This technique is referred to as resource management. Each reasoner terminates its search for a solution of a given subgoal when the solution is found or when it runs out of its assigned resources. We argue that the effect of resource ma...