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- W2019062672 abstract "Kalicki [2] and Los [3] independently discovered essentially similar methods for determining effectively whether or not there are any tautologies according to an arbitrary matrix, and Kalicki took certain steps towards obtaining another such test by establishing: (K) If there exists a sequence of matrices 91, * *, 9NP such that 9N is cyclic, P.n= V and for all m < nf9Ym+i is either an extension or a repetition of 9JYtm, then 91 generates an empty set of tautologies. Kalicki [2] announced verification of the converse of (K) for all matrices with one, two and three elements, but reported that he had not succeeded in proving it generally. (K) together with its converse would of course provide an effective test for the existence of tautologies, but the purpose of this note is to show that no such test emerges. The matrix, 9N, set out in truth-table form below (i) generates an empty set of tautologies but (ii) is not obtainable from any cyclic matrix in the manner required by the converse of (K): For the proof of (i) consider the four matrices of which P is an extension:" @default.
- W2019062672 created "2016-06-24" @default.
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- W2019062672 date "1969-03-01" @default.
- W2019062672 modified "2023-09-26" @default.
- W2019062672 title "Solution to a problem posed by Kalicki" @default.
- W2019062672 cites W1994444284 @default.
- W2019062672 cites W2022239108 @default.
- W2019062672 doi "https://doi.org/10.1090/s0002-9939-1969-0243999-1" @default.
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