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Axiomatizing the Skew Boolean Propositional Calculus
, 2007
"... Abstract. The skew Boolean propositional calculus (SBP C) is a generalization of the classical propositional calculus that arises naturally in the study of certain wellknown deductive systems. In this article, we consider a candidate presentation of SBP C and prove it constitutes a Hilbertstyle ax ..."
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Abstract. The skew Boolean propositional calculus (SBP C) is a generalization of the classical propositional calculus that arises naturally in the study of certain wellknown deductive systems. In this article, we consider a candidate presentation of SBP C and prove it constitutes a Hilbertstyle axiomatization. The problem reduces to establishing that the logic presented by the candidate axiomatization is algebraizable in the sense of Blok and Pigozzi. In turn, this is equivalent to verifying four particular formulas are derivable from the candidate presentation. Automated deduction methods played a central role in proving these four theorems. In particular, our approach relied heavily on the method of proof sketches. 1.
Automated discovery of single axioms for ortholattices
 Algebra Universalis
, 2005
"... Abstract. We present short single axioms for ortholattices, orthomodular lattices, and modular ortholattices, all in terms of the Sheffer stroke. The ortholattice axiom is the shortest possible. We also give multiequation bases in terms of the Sheffer stroke and in terms of join, meet, and complemen ..."
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Cited by 4 (1 self)
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Abstract. We present short single axioms for ortholattices, orthomodular lattices, and modular ortholattices, all in terms of the Sheffer stroke. The ortholattice axiom is the shortest possible. We also give multiequation bases in terms of the Sheffer stroke and in terms of join, meet, and complementation. Proofs are omitted but are available in an associated technical report and on the Web. We used computers extensively to find candidates, reject candidates, and search for proofs that candidates are single axioms. 1.
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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Cited by 3 (3 self)
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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
ANL/MCSTM265 Short Equational Bases for Ortholattices: Proofs and Countermodels
, 2003
"... Contract W31109ENG38. Argonne National Laboratory, with facilities in the states of Illinois and Idaho, is owned by the United States Government and operated by The University of Chicago under the provisions of a contract with the Department of Energy. DISCLAIMER This report was prepared as an a ..."
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Contract W31109ENG38. Argonne National Laboratory, with facilities in the states of Illinois and Idaho, is owned by the United States Government and operated by The University of Chicago under the provisions of a contract with the Department of Energy. DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor The University of Chicago, nor any of their employees or officers, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privatelyowned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of document authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof, Argonne National Laboratory, or The University of Chicago. ii
Preface
"... We proudly present the papers selected for the Fifth Workshop on the Implementation of Logics held in conjunction with the Eleventh International Conference on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2004), in Montevideo, Uruguay. We thank the authors who submitted their ..."
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We proudly present the papers selected for the Fifth Workshop on the Implementation of Logics held in conjunction with the Eleventh International Conference on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2004), in Montevideo, Uruguay. We thank the authors who submitted their highquality work and the program committee who performed the task of reviewing the submissions. We also thank the organisers of LPAR without whom this workshop would certainly not exist.
Lemma Management Techniques for Automated Theorem Proving
, 2005
"... Lemmas can provide valuable help for constructing a proof, by providing intermediate steps. However, not all the formulae supplied to an ATP system as lemmas are necessarily helpful. It is therefore necessary to develop lemma management techniques that use the right lemmas at the right time, to impr ..."
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Lemmas can provide valuable help for constructing a proof, by providing intermediate steps. However, not all the formulae supplied to an ATP system as lemmas are necessarily helpful. It is therefore necessary to develop lemma management techniques that use the right lemmas at the right time, to improve the problemsolving ability of ATP systems. This paper presents three lemma management techniques, reports on their implementation, and illustrates their potential with example problems.
The Use of Lemmas for Solving Hard Automated (May 2005)
, 2005
"... Thesis supervised by Professor Geoff Sutcliffe. No. of pages in text. (61) Using lemmas has been proved to be an effective approach to assisting ATP sytems to solve hard problems. Useful lemmas can provide valuable guidance in the proof search, and help construct the proof by filling in intermediate ..."
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Thesis supervised by Professor Geoff Sutcliffe. No. of pages in text. (61) Using lemmas has been proved to be an effective approach to assisting ATP sytems to solve hard problems. Useful lemmas can provide valuable guidance in the proof search, and help construct the proof by filling in intermediate steps. However, the formulae supplied to an ATP system as lemmas are not all necessarily useful. Unuseful lemmas act as noise, disturbing the search for the proof. It is therefore necessary to develop lemma management techniques that identify useful lemmas, and help an ATP system to use the useful lemmas to its advantage. This thesis presents three lemma management techniques. Their implementaton is reported. The potential of these techniques is illustrated with example problems. It has been shown that, with these three lemma management techniques, the problemsolving ability of an ATP system is improved. A recommendation for future work is enclosed. ACKNOWLEDGEMENTS I would like to thank my adviser, Professor Geoff Sutcliffe, for all the help and guidance he has given to me. He stimulated my interest in doing research and taught me how to think as a scientist. When I was stuck in my research, he was always patient and supportive. I feel so honored to have this excellent professor as my advisor. I would like to thank Professor Christian Duncan and Professor Miroslav Kubat for
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, 2003
"... by The University of Chicago under contract W31109Eng38. ..."
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