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A Shortest 2Basis for Boolean Algebra in Terms of the Sheffer Stroke
 J. Automated Reasoning
, 2003
"... In this article, we present a short 2basis for Boolean algebra in terms of the Sheffer stroke and prove that no such 2basis can be shorter. We also prove that the new 2basis is unique (for its length) up to applications of commutativity. Our proof of the 2basis was found by using the method of p ..."
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In this article, we present a short 2basis for Boolean algebra in terms of the Sheffer stroke and prove that no such 2basis can be shorter. We also prove that the new 2basis is unique (for its length) up to applications of commutativity. Our proof of the 2basis was found by using the method of proof sketches and relied on the use of an automated reasoning program.
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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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
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, 2003
"... by The University of Chicago under contract W31109Eng38. ..."
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