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%I #20 Aug 27 2022 04:25:08
%S 1,5,83,28925,7663696588
%N 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.
%C This sequence is, more interestingly, the number of logical consequence relations in (n+2)-valued logic, with no order between intermediate values (i.e., values other than 0 and 1), which are truth functional, 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.
%C 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.
%H E. Chemla, P. Egré and B. Spector, <a href="http://semanticsarchive.net/Archive/GQzYTM4N/Chemla-Egre-Spector-LCrelations.pdf">Characterizing logical consequence in many-valued logics</a>, Ms. CNRS/ENS. J. of Logic and Computation, to appear (2016).
%K nonn,more
%O 0,2
%A _Emmanuel Chemla_, Apr 02 2016