The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.


(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (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.
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).
Sequence in context: A301811 A216146 A111834 * A359110 A187587 A006471
Emmanuel Chemla, Apr 02 2016

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 13 22:21 EDT 2024. Contains 373391 sequences. (Running on oeis4.)