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Solution of the Robbins Problem
 Journal of Automated Reasoning
, 1997
"... . In this article we show that the three equations known as commutativity, associativity, and the Robbins equation are a basis for the variety of Boolean algebras. The problem was posed by Herbert Robbins in the 1930s. The proof was found automatically by EQP, a theoremproving program for equationa ..."
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. In this article we show that the three equations known as commutativity, associativity, and the Robbins equation are a basis for the variety of Boolean algebras. The problem was posed by Herbert Robbins in the 1930s. The proof was found automatically by EQP, a theoremproving program for equational logic. We present the proof and the search strategies that enabled the program to find the proof. Key words: Associativecommutative unification, Boolean algebra, EQP, equational logic, paramodulation, Robbins algebra, Robbins problem. 1. Introduction This article contains the answer to the Robbins question of whether all Robbins algebras are Boolean. The answer is yes, all Robbins algebras are Boolean. The proof that answers the question was found by EQP, an automated theoremproving program for equational logic. In 1933, E. V. Huntington presented the following three equations as a basis for Boolean algebra [6, 5]: x + y = y + x, (commutativity) (x + y) + z = x + (y + z), (associativit...
OTTER 3.3 Reference Manual
"... 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 a ..."
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Cited by 44 (5 self)
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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
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 36 (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...
Steps Toward a Computational Metaphysics
 JOURNAL OF PHILOSOPHICAL LOGIC
, 2007
"... In this paper, the authors describe their initial investigations in computational metaphysics. Our method is to implement axiomatic metaphysics in an automated reasoning system. In this objects is implemented in prover9 (a firstorder automated reasoning system which is the successor to otter). Afte ..."
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In this paper, the authors describe their initial investigations in computational metaphysics. Our method is to implement axiomatic metaphysics in an automated reasoning system. In this objects is implemented in prover9 (a firstorder automated reasoning system which is the successor to otter). After reviewing the secondorder, axiomatic theory of abstract objects, we show (1) how to represent a fragment of that theory in prover9’s firstorder syntax, and (2) how prover9 then finds proofs of interesting theorems of metaphysics, such as that every possible world is maximal. We conclude the paper by discussing some issues for further research.
Fitelson & Zalta Steps Toward a Computational Metaphysics 1
, 2003
"... Car si nous l’avions telle que je la conçois, nous pourrions raisonner en metaphysique et en morale à pue pres comme en Geometrie et en Analyse (Leibniz 1890, 21) If we had it [a characteristica universalis], we should be able to reason in metaphysics and morals in much the same way as in geometry a ..."
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Car si nous l’avions telle que je la conçois, nous pourrions raisonner en metaphysique et en morale à pue pres comme en Geometrie et en Analyse (Leibniz 1890, 21) If we had it [a characteristica universalis], we should be able to reason in metaphysics and morals in much the same way as in geometry and analysis. (Russell 1900, 169) Quo facto, quando orientur controversiae, non magis disputatione opus erit inter duos philosophos, quam inter duos Computistas. Sufficiet enim calamos in manus sumere sedereque ad abacos, et sibi mutuo... dicere: calculemus. (Leibniz 1890, 200) If controversies were to arise, there would be no more need of disputation between two philosophers than between two accountants. For it would suffice to take their pencils in their hands, to sit down to their slates, and to say to each other...: Let us calculate. (Russell 1900, 170)
ANL/MCSTM263 OTTER 3.3 Reference Manual
, 2003
"... 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 a ..."
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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