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33
E  A Brainiac Theorem Prover
, 2002
"... We describe the superpositionbased theorem prover E. E is a sound and complete... ..."
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Cited by 128 (18 self)
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We describe the superpositionbased theorem prover E. E is a sound and complete...
Lava: Hardware Design in Haskell
, 1998
"... Lava is a tool to assist circuit designers in specifying, designing, verifying and implementing hardware. It is a collection of Haskell modules. The system design exploits functional programming language features, such as monads and type classes, to provide multiple interpretations of circuit descri ..."
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Cited by 116 (7 self)
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Lava is a tool to assist circuit designers in specifying, designing, verifying and implementing hardware. It is a collection of Haskell modules. The system design exploits functional programming language features, such as monads and type classes, to provide multiple interpretations of circuit descriptions. These interpretations implement standard circuit analyses such as simulation, formal veri#cation and the generation of code for the production of real circuits.
User Interaction with the Matita Proof Assistant
 Journal of Automated Reasoning, Special
, 2006
"... Abstract. Matita is a new, documentcentric, tacticbased interactive theorem prover. This paper focuses on some of the distinctive features of the user interaction with Matita, mostly characterized by the organization of the library as a searchable knowledge base, the emphasis on a highquality not ..."
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Cited by 48 (14 self)
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Abstract. Matita is a new, documentcentric, tacticbased interactive theorem prover. This paper focuses on some of the distinctive features of the user interaction with Matita, mostly characterized by the organization of the library as a searchable knowledge base, the emphasis on a highquality notational rendering, and the complex interplay between syntax, presentation, and semantics.
Ivy: A Preprocessor And Proof Checker For FirstOrder Logic
, 1999
"... This case study shows how nonACL2 programs can be combined with ACL2 functions in such a way that useful properties can be proved about the composite programs. Nothing is proved about the nonACL2 programs. Instead, the results of the nonACL2 programs are checked at run time by ACL2 functions, and ..."
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Cited by 29 (10 self)
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This case study shows how nonACL2 programs can be combined with ACL2 functions in such a way that useful properties can be proved about the composite programs. Nothing is proved about the nonACL2 programs. Instead, the results of the nonACL2 programs are checked at run time by ACL2 functions, and properties of these checker functions are proved. The application is resolution/paramodulation automated theorem proving for firstorder logic. The top ACL2 function takes a conjecture, preprocesses the conjecture, and calls a nonACL2 program to search for a proof or countermodel. If the nonACL2 program succeeds, ACL2 functions check the proof or countermodel. The top ACL2 function is proved sound with respect to finite interpretations. Introduction Our ACL2 project arose from a different kind of automated theorem proving. We work with fully automatic resolution/paramodulation theo This work was supported by the Mathematical, Information, and Computational Sciences Division subprogram...
Automatic Proofs and Counterexamples for Some Ortholattice Identities
 Information Processing Letters
, 1998
"... This note answers questions on whether three identities known to hold for orthomodular lattices are true also for ortholattices. One identity is shown to fail by MACE, a program that searches for counterexamples, an the other two are proved to hold by EQP, an equational theorem prover. The problems, ..."
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Cited by 22 (2 self)
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This note answers questions on whether three identities known to hold for orthomodular lattices are true also for ortholattices. One identity is shown to fail by MACE, a program that searches for counterexamples, an the other two are proved to hold by EQP, an equational theorem prover. The problems, from work in quantum logic, were given to us by Norman Megill. Keywords: Automatic theorem proving, ortholattice, quantum logic, theory of computation. 1 Introduction An ortholattice is an algebra with a binary operation (join) and a unary operation 0 (complement) satisfying the following (independent) set of identities. x y = (x 0 y 0 ) 0 (definition of meet) x y = y x (x y) z = x (y z) x (x y) = x x 00 = x x (y y 0 ) = y y 0 Supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Computational and Technology Research, U.S. Department of Energy, under Contract W31109Eng38. From these identities one can...
MetiTarski: An Automatic Theorem Prover for RealValued Special Functions
"... Abstract Many theorems involving special functions such as ln, exp and sin can be proved automatically by MetiTarski: a resolution theorem prover modified to call a decision procedure for the theory of real closed fields. Special functions are approximated by upper and lower bounds, which are typica ..."
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Cited by 20 (4 self)
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Abstract Many theorems involving special functions such as ln, exp and sin can be proved automatically by MetiTarski: a resolution theorem prover modified to call a decision procedure for the theory of real closed fields. Special functions are approximated by upper and lower bounds, which are typically rational functions derived from Taylor or continued fraction expansions. The decision procedure simplifies clauses by deleting literals that are inconsistent with other algebraic facts. MetiTarski simplifies arithmetic expressions by conversion to a recursive representation, followed by flattening of nested quotients. Applications include verifying hybrid and control systems.
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 20 (6 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.
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...
Critical Agents Supporting Interactive Theorem Proving
 PROC. OF EPIA99, LNAI 1695
, 1999
"... We introduce a resource adaptive agent mechanism which supports the user of an interactive theorem proving system. The mechanism, an extension of [4], uses a two layered architecture of agent societies to suggest applicable commands together with appropriate command argument instantiations. Exp ..."
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Cited by 14 (12 self)
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We introduce a resource adaptive agent mechanism which supports the user of an interactive theorem proving system. The mechanism, an extension of [4], uses a two layered architecture of agent societies to suggest applicable commands together with appropriate command argument instantiations. Experiments with this approach show that its effectiveness can be further improved by introducing a resource concept. In this paper we provide an abstract view on the overall mechanism, motivate the necessity of an appropriate resource concept and discuss its realization within the agent architecture.
Knowledge Representation and Classical Logic
, 2007
"... Mathematical logicians had developed the art of formalizing declarative knowledge long before the advent of the computer age. But they were interested primarily in formalizing mathematics. Because of the important role of nonmathematical knowledge in AI, their emphasis was too narrow from the perspe ..."
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Cited by 11 (4 self)
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Mathematical logicians had developed the art of formalizing declarative knowledge long before the advent of the computer age. But they were interested primarily in formalizing mathematics. Because of the important role of nonmathematical knowledge in AI, their emphasis was too narrow from the perspective of knowledge representation, their formal languages were not sufficiently expressive. On the other hand, most logicians were not concerned about the possibility of automated reasoning; from the perspective of knowledge representation, they were often too generous in the choice of syntactic constructs. In spite of these differences, classical mathematical logic has exerted significant influence on knowledge representation research, and it is appropriate to begin this handbook with a discussion of the relationship between these fields. The language of classical logic that is most widely used in the theory of knowledge representation is the language of firstorder (predicate) formulas. These are the formulas that John McCarthy proposed to use for representing declarative knowledge in his advice taker paper [176], and Alan Robinson proposed to prove automatically using resolution [236]. Propositional logic is, of course, the most important subset of firstorder logic; recent