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System Description: IVY
 In Proc. 17th CADE, LNAI 1831
, 2000
"... . IVY is a verified theorem prover for firstorder logic with equality. It is coded in ACL2, and it makes calls to the theorem prover Otter to search for proofs and to the program MACE to search for countermodels. Verifications of Otter and MACE are not practical because they are coded in C. Ins ..."
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. IVY is a verified theorem prover for firstorder logic with equality. It is coded in ACL2, and it makes calls to the theorem prover Otter to search for proofs and to the program MACE to search for countermodels. Verifications of Otter and MACE are not practical because they are coded in C. Instead, Otter and MACE give detailed proofs and models that are checked by verified ACL2 programs. In addition, the initial conversion to clause form is done by verified ACL2 code. The verification is done with respect to finite interpretations. 1 Introduction Our theorem provers Otter [6, 7, 10] and EQP [4, 8] and our model searcher MACE [3, 5] are being used for practical work in several areas. Therefore, we wish to have very high confidence that the proofs and models they produce are correct. However, these are highperformance programs, coded in C, with many tricks, hacks, and optimizations, so formal verification of the programs is not practical. Instead, our approach is to have the...
Short equational bases for ortholattices
 Preprint ANL/MCSP10870903, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL
, 2004
"... Short single axioms for ortholattices, orthomodular lattices, and modular ortholattices are presented, all in terms of the Sheffer stroke. The ortholattice axiom is the shortest possible. Other equational bases in terms of the Sheffer stroke and in terms of join, meet, and complement are presented. ..."
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Short single axioms for ortholattices, orthomodular lattices, and modular ortholattices are presented, all in terms of the Sheffer stroke. The ortholattice axiom is the shortest possible. Other equational bases in terms of the Sheffer stroke and in terms of join, meet, and complement are presented. Proofs are omitted but are available in an associated technical report. Computers were used extensively to find candidates, reject candidates, and search for proofs that candidates are single axioms. The notion of computer proof is addressed. 1
A mechanized program verifier
 In IFIP Working Conference on the Program Verifier Challenge
, 2005
"... Abstract. In my view, the “verification problem ” is the theorem proving problem, restricted to a computational logic. My approach is: adopt a functional programming language, build a general purpose formal reasoning engine around it, integrate it into a program and proof development environment, an ..."
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Abstract. In my view, the “verification problem ” is the theorem proving problem, restricted to a computational logic. My approach is: adopt a functional programming language, build a general purpose formal reasoning engine around it, integrate it into a program and proof development environment, and apply it to model and verify a wide variety of computing artifacts, usually modeled operationally within the functional programming language. Everything done in this approach is software verification since the models are runnable programs in a subset of an ANSI standard programming language (Common Lisp). But this approach is of interest to proponents of other approaches (e.g., verification of procedural programs or synthesis) because of the nature of the mathematics of computing. I summarize the progress so far using this approach, sketch the key research challenges ahead and describe my vision of the role and shape of a useful verification system. 1
Initial Experiments with External Provers and Premise Selection on HOL Light Corpora
"... This paper reports our initial experiments with using external ATP and premise selection methods on some corpora built with the HOL Light system. The testing is done in three different settings, corresponding to those used earlier for evaluating such methods on the Mizar/MML corpus. This is intende ..."
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This paper reports our initial experiments with using external ATP and premise selection methods on some corpora built with the HOL Light system. The testing is done in three different settings, corresponding to those used earlier for evaluating such methods on the Mizar/MML corpus. This is intended to provide the first estimate about the usefulness of such external reasoning and AI systems for solving problems over HOL Light and its libraries. 1
Hammering towards QED
"... This paper surveys the emerging methods to automate reasoning over large libraries developed with formal proof assistants. We call these methods hammers. They give the authors of formal proofs a strong “onestroke ” tool for discharging difficult lemmas without the need for careful and detailed manu ..."
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This paper surveys the emerging methods to automate reasoning over large libraries developed with formal proof assistants. We call these methods hammers. They give the authors of formal proofs a strong “onestroke ” tool for discharging difficult lemmas without the need for careful and detailed manual programming of proof search. The main ingredients underlying this approach are efficient automatic theorem provers that can cope with hundreds of axioms, suitable translations of the proof assistant’s logic to the logic of the automatic provers, heuristic and learning methods that select relevant facts from large libraries, and methods that reconstruct the automatically found proofs inside the proof assistants. We outline the history of these methods, explain the main issues and techniques, and show their strength on several large benchmarks. We also discuss the relation of this technology to the QED Manifesto and consider its implications for QEDlike efforts. 1.
An Interface between Theorema and External Automated Deduction Systems
"... The interface between Theorema and external automated deduction systems implements a link providing a user with a tool for using external provers within a Theorema session in the same way as "internal " Theorema provers. Currently it supports 11 external systems, and support of links to ot ..."
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The interface between Theorema and external automated deduction systems implements a link providing a user with a tool for using external provers within a Theorema session in the same way as "internal " Theorema provers. Currently it supports 11 external systems, and support of links to other systems can be easily done. Also, the TPTP (Thousands of Problems of Theorem Provers − problem library) problem converter to Theorema format is described. This research is supported by the Autsrian Science Foundation (FWF) project FO−1302 (SFB). 1.
Using Theorem Proving and Algorithmic Decision Procedures for LargeScale System Verification
, 2005
"... To the few people who believed I could do it even when I myself didn’t Acknowledgments This dissertation has been shaped by many people, including my teachers, collaborators, friends, and family. I would like to take this opportunity to acknowledge the influence they have had in my development as a ..."
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To the few people who believed I could do it even when I myself didn’t Acknowledgments This dissertation has been shaped by many people, including my teachers, collaborators, friends, and family. I would like to take this opportunity to acknowledge the influence they have had in my development as a person and as a scientist. First and foremost, I wish to thank my advisor J Strother Moore. J is an amazing advisor, a marvellous collaborator, an insightful researcher, an empathetic teacher, and a truly great human being. He gave me just the right balance of freedom, encouragement, and direction to guide the course of this research. My stimulating discussions with him made the act of research an experience of pure enjoyment, and helped pull me out of many low ebbs. At one point I used to believe that whenever I was stuck with a problem one meeting with J would get me back on track. Furthermore, my times together with J and Jo during Thanksgivings and other occasions always made me feel part of his family. There was no problem, technical or otherwise, that I could not discuss with J, and there was no time when
Using a Bayesian Knowledge Base for Hint Selection on Domain Specific Problems
"... Abstract. A Bayesian Knowledge Base is a generalization of traditional Bayesian Networks where nodes or groups of nodes have independence. In this paper we describe a method of generating a Bayesian Knowledge Base from a corpus of student problem attempt data in order to automatically generate hints ..."
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Abstract. A Bayesian Knowledge Base is a generalization of traditional Bayesian Networks where nodes or groups of nodes have independence. In this paper we describe a method of generating a Bayesian Knowledge Base from a corpus of student problem attempt data in order to automatically generate hints for new students. We further show that using problem attempt data from systems used to teach propositional logic we could successfully use the created Bayesian Knowledge Base to solve other problems. Finally, we compare this method to our previous work using Markov Decision Processes to generate hints. 1
Proof Generation for Saturating FirstOrder Theorem Provers
"... Firstorder Automated Theorem Proving (ATP) is one of the oldest and most developed areas of automated reasoning. Today, the most widely used firstorder provers are fully automatic and process firstorder logic with equality. Many stateoftheart ATP systems consist of a clausifier, translating a ..."
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Firstorder Automated Theorem Proving (ATP) is one of the oldest and most developed areas of automated reasoning. Today, the most widely used firstorder provers are fully automatic and process firstorder logic with equality. Many stateoftheart ATP systems consist of a clausifier, translating a full firstorder