

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 (ie values other than 0 and 1), which are truthfunctional, 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.


REFERENCES

E. Chemla, P. EgrÃ© and B. Spector (2016). Characterizing logical consequence in manyvalued logics. Ms. CNRS/ENS. J. of Logic and Computation, to appear (2016); http://semanticsarchive.net/Archive/GQzYTM4N/ChemlaEgreSpectorLCrelations.pdf


LINKS

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


CROSSREFS

Sequence in context: A301811 A216146 A111834 * A187587 A006471 A258391
Adjacent sequences: A271216 A271217 A271218 * A271220 A271221 A271222


KEYWORD

nonn,more


AUTHOR

Emmanuel Chemla, Apr 02 2016


STATUS

approved



