

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




OFFSET

0,2


COMMENTS

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 valuemonotonic (if the relation holds, it is preserved with stronger premises and/or weaker conclusions). See reference below.
In nvalued 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 wellordered set of n elements.


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CROSSREFS



KEYWORD

nonn,more


AUTHOR



STATUS

approved



