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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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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.
System Description: TPS: A Theorem Proving System for Type Theory
, 2000
"... Introduction This is a brief update on the Tps automated theorem proving system for classical type theory, which was described in [3]. Manuals and information about obtaining Tps can be found at http://gtps.math.cmu.edu/tps.html. In Section 2 we discuss some examples of theorems which Tps can now ..."
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Introduction This is a brief update on the Tps automated theorem proving system for classical type theory, which was described in [3]. Manuals and information about obtaining Tps can be found at http://gtps.math.cmu.edu/tps.html. In Section 2 we discuss some examples of theorems which Tps can now prove automatically, and in Section 3 we discuss an example which illustrates one of the many challenges of theorem proving in higherorder logic. We rst provide a brief summary of the key features of Tps . Tps uses Church's type theory [8] (typed calculus) as its logical language. Ws are displayed on the screen and in printed proofs in the notation of this system of symbolic logic. One can use Tps in automatic, semiautomatic, or interactive mode to construct proofs in natural deduction style, and a mixture of these modes of operation is most useful fo
μJava: Embedding a Programming Language in a Theorem Prover
 Foundations of Secure Computation, volume 175 of NATO Science Series F: Computer and Systems Sciences
, 2000
"... . This paper introduces the subset Java of Java, essentially by omitting everything but classes. The type system and semantics of this language (and a corresponding abstract Machine JVM) are formalized in the theorem prover Isabelle/HOL. Type safety both of Java and the JVM are mechanically veri ..."
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Cited by 13 (0 self)
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. This paper introduces the subset Java of Java, essentially by omitting everything but classes. The type system and semantics of this language (and a corresponding abstract Machine JVM) are formalized in the theorem prover Isabelle/HOL. Type safety both of Java and the JVM are mechanically verified. To make the paper selfcontained, it begins with introductions to Isabelle/HOL and the art of embedding languages in theorem provers. 1 Introduction Embedding a programming language in a theorem prover means to describe (parts of) the language in the logic of the theorem prover, for example the abstract syntax, the semantics, the type system, a Hoare logic, a compiler, etc. One could call this applied machinechecked semantics. Why should we want to do this? We have to distinguish two possible applications: ffl Proving theorems about programs. This is usually called program analysis or verification and will not concern us very much in this paper. ffl Proving theorems about the pr...
ETPS: A System to Help Students Write Formal Proofs
 Journal of Automated Reasoning
, 2002
"... ETPS (Educational Theorem Proving System) is a program which logic students can use to write formal proofs in rstorder logic or higherorder logic. It enables students to concentrate on the essential logical problems involved in proving theorems, and automatically checks the proofs. ..."
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ETPS (Educational Theorem Proving System) is a program which logic students can use to write formal proofs in rstorder logic or higherorder logic. It enables students to concentrate on the essential logical problems involved in proving theorems, and automatically checks the proofs.
A survey of automated deduction
 EDINBURGH ARTI INTELLIGENCE RESEARCH PAPER 950
, 1999
"... We survey research in the automation of deductive inference, from its beginnings in the early history of computing to the present day. We identify and describe the major areas of research interest and their applications. The area is characterised by its wide variety of proof methods, forms of autom ..."
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We survey research in the automation of deductive inference, from its beginnings in the early history of computing to the present day. We identify and describe the major areas of research interest and their applications. The area is characterised by its wide variety of proof methods, forms of automated deduction and applications.
Extensional higherorder resolution
 In Kirchner and Kirchner [KK98
, 1998
"... Abstract. In this paper we present an extensional higherorder resolution calculus that is complete relative to Henkin model semantics. The treatment of the extensionality principles – necessary for the completeness result – by specialized (goaldirected) inference rules is of practical applicabilit ..."
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Abstract. In this paper we present an extensional higherorder resolution calculus that is complete relative to Henkin model semantics. The treatment of the extensionality principles – necessary for the completeness result – by specialized (goaldirected) inference rules is of practical applicability, as an implentation of the calculus in the LeoSystem shows. Furthermore, we prove the longstanding conjecture, that it is sufficient to restrict the order of primitive substitutions to the order of input formulae. 1
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
Multimodal and Intuitionistic Logics in Simple Type Theory
"... We study straightforward embeddings of propositional normal multimodal logic and propositional intuitionistic logic in simple type theory. The correctness of these embeddings is easily shown. We give examples to demonstrate that these embeddings provide an effective framework for computational inve ..."
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We study straightforward embeddings of propositional normal multimodal logic and propositional intuitionistic logic in simple type theory. The correctness of these embeddings is easily shown. We give examples to demonstrate that these embeddings provide an effective framework for computational investigations of various nonclassical logics. We report some experiments using the higherorder automated theorem prover LEOII.
LEO  A HigherOrder Theorem Prover
 In Proc. of CADE15, volume 1421 of LNAI
, 1998
"... this paper was supported by the Deutsche Forschungsgemeinschaft in grant HOTEL. EXT ..."
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Cited by 10 (7 self)
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this paper was supported by the Deutsche Forschungsgemeinschaft in grant HOTEL. EXT
Integrating TPS and ΩMEGA
 JOURNAL OF UNIVERSAL COMPUTER SCIENCE
, 1999
"... This paper reports on the integration of the higherorder theorem proving environment Tps [Andrews et al., 1996] into the mathematical assistant Ωmega [Benzmuller et al., 1997]. Tps can be called from mega either as a black box or as an interactive system. In black box mode, the user has control ov ..."
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Cited by 7 (4 self)
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This paper reports on the integration of the higherorder theorem proving environment Tps [Andrews et al., 1996] into the mathematical assistant Ωmega [Benzmuller et al., 1997]. Tps can be called from mega either as a black box or as an interactive system. In black box mode, the user has control over the parameters which control proof search in Tps; in interactive mode, all features of the Tpssystem are available to the user. If the subproblem which is passed to Tps contains concepts defined in Ωmega's database of mathematical theories, these definitions are not instantiated but are also passed to Tps. Using a special theory which contains proof tactics that model the NDcalculus variant of Tps within mega, any complete or partial proof generated in Tps can be translated one to one into an mega proof plan. Proof transformation is realised by proof plan expansion in Ωmega's 3dimensional proof data structure, and remains transparent to the user.