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.

1, 5, 83, 28925, 7663696588

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 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.

Links

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

E. Chemla, P. Egré and B. Spector, Characterizing logical consequence in many-valued logics, Ms. CNRS/ENS. J. of Logic and Computation, to appear (2016).

Crossrefs

Sequence in context: A301811 A216146 A111834 * A359110 A187587 A006471

Adjacent sequences: A271216 A271217 A271218 * A271220 A271221 A271222

Keyword

nonn,more

Author

Emmanuel Chemla, Apr 02 2016

Status

approved