Automatic Proofs and Counterexamples for Some Ortholattice Identities

Automatic Proofs and Counterexamples for Some Ortholattice Identities (1998)

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by William Mccune

Venue:	Information Processing Letters
Citations:	21 - 2 self

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TITLE	Automatic Proofs and Counterexamples for Some Ortholattice Identities	user correction - Legacy Corrections
AUTHOR NAME	William Mccune	SVM HeaderParse 0.1
AUTHOR AFFIL	Mathematics and Computer Science Division; Argonne National Laboratory	SVM HeaderParse 0.2
AUTHOR ADDR	Argonne, Illinois, 60439, U.S.A.	SVM HeaderParse 0.1
ABSTRACT	This note answers questions on whether three identities known to hold for orthomodular lattices are true also for ortholattices. One identity is shown to fail by MACE, a program that searches for counterexamples, an the other two are proved to hold by EQP, an equational theorem prover. The problems, from work in quantum logic, were given to us by Norman Megill. Keywords: Automatic theorem proving, ortholattice, quantum logic, theory of computation. 1 Introduction An ortholattice is an algebra with a binary operation (join) and a unary operation 0 (complement) satisfying the following (independent) set of identities. x y = (x 0 y 0 ) 0 (definition of meet) x y = y x (x y) z = x (y z) x (x y) = x x 00 = x x (y y 0 ) = y y 0 Supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Computational and Technology Research, U.S. Department of Energy, under Contract W-31-109-Eng-38. From these identities one can...	user correction - Legacy Corrections
YEAR	1998	INFERENCE
VENUE	Information Processing Letters	INFERENCE
VENUE TYPE	JOURNAL	INFERENCE
PAGES	285--291	INFERENCE
VOLUME	65	INFERENCE
CITATIONS	10 found	ParsCit 1.0