Upgrading a Multifuncoid

I define the concepts of multifuncoid (and completary multifuncoid) and upgrading. Then I conjecture that upgrading of certain multifuncoids are multifuncoids (and that upgrading certain completary multifuncoids are completary multifuncoids). I have proved the conjectures for n 6 2. The main conjecture from this article is now proved in the article “Multidimensional Funcoids“ This short article is the first my public writing where I introduce the concept of multidimensional funcoid which I am investigating now. Refer to this Web site for the theory which I now attempt to generalize. 1 Background 1.1 About some posets Let A is a poset that is a set partially ordered by a relation ≥. If A is a join-semilattice, I will denote a⊔ b join of its elements. (Dually for a meet-semilattice I will denote a ⊓ b meet of its elements.) If A = Ai∈n is a family of posets, then I will denote ∏ A the product order on A that is we have for every a, b ∈ ∏