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A271219 Number n of antichains of P(En) x En*, ordered by lexicographic order, with En a poset of n elements with no pair of elements ordered, and with En* that same set augmented with an (n+1)th element smaller than all others. 0
1, 5, 83, 28925, 7663696588 (list; graph; refs; listen; history; text; internal format)



This sequence is, more interestingly, the number of logical consequence relations in (n+2)-valued logic, with no order between intermediate values (ie values other than 0 and 1), which are truthfunctional, identical to the standard logical consequence relation on bivalent propositions and value-monotonic (if the relation holds, it is preserved with stronger premises and/or weaker conclusions). See reference below.

In n-valued logic with all truth values strictly ordered, the number of logical consequence relations with the same properties is more standard, it corresponds to: A030662. It satisfies the same definition as this sequence except that En should now be understood as a well-ordered set of n elements.


E. Chemla, P. Egré and B. Spector (2016). Characterizing logical consequence in many-valued logics. Ms. CNRS/ENS. J. of Logic and Computation, to appear (2016); http://semanticsarchive.net/Archive/GQzYTM4N/Chemla-Egre-Spector-LCrelations.pdf


Table of n, a(n) for n=0..4.


Sequence in context: A301811 A216146 A111834 * A187587 A006471 A258391

Adjacent sequences:  A271216 A271217 A271218 * A271220 A271221 A271222




Emmanuel Chemla, Apr 02 2016



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Last modified January 18 13:49 EST 2020. Contains 331010 sequences. (Running on oeis4.)