ion and modularity D. Rouhling, A. Mahboubi & SGL axiomatised • the algebraic structure of constraints (some variant of meet-semilattice) • the specs of decision procedures called at leaves for the system to work (and to be equivalent to system w/o meta-variables) J-M Notin & SGL preparing PSYCHE 2.0 according to the above Backtrack mechanisms get tricky We also hope that this architecture can ...

Characterizations of the classes of all choice functions that select the cores or the externally stable cores induced by an underlying revealed dominance digraph are provided. Relying on such characterizations, the basic order-theoretic structure of the corresponding sets of revealed cores is also analyzed. In particular, it is shown that the poset of all revealed cores ordered by set inclusion...

For an abelian lattice ordered group G let convG be the system of all compatible convergences on G; this system is a meet semilattice but in general it fails to be a lattice. Let αnd be the convergence on G which is generated by the set of all nearly disjoint sequences in G, and let α be any element of convG. In the present paper we prove that the join αnd ∨ α does exist in convG.

A certain inequality is shown to hold for the values of the Möbius function of the poset obtained by attaching a maximum element to a lower Eulerian Cohen– Macaulay poset. In two important special cases, this inequality provides partial results supporting Stanley’s nonnegativity conjecture for the toric h-vector of a lower Eulerian Cohen–Macaulay meet-semilattice and Adin’s nonnegativity conjec...

The Abelian Sandpile Model is a diffusion process on (directed) graphs, studied, under various names, in statistical physics, discrete dynamical systems, theoretical computer science, algebraic graph theory, and other fields. The model takes a directed multigraph X with a sink accessible from all nodes; associates a configuration space with X and defines transition rules between the configurati...

A modular semilattice is a semilattice S in which w > a A ft implies that there exist i,jeS such that x > a. y > b and x A y = x A w. This is equivalent to modularity in a lattice and in the semilattice of ideals of the semilattice, and the condition implies the Kurosh-Ore replacement property for irreducible elements in a semilattice. The main results provide extensions of the classical charac...

Pseudo equality algebras were initially introduced by Jenei and Kóródi as a possible algebraic semantic for fuzzy type theory, and they have been revised by Dvurečenskij and Zahiri under the name of JK-algebras. The aim of this paper is to investigate the internal states and the state-morphisms on pseudo equality algebras. We define and study new classes of pseudo equality algebras, such as com...

This paper deals with maximization of set f'unctions delined as minimum values of monotone linkage functions. In previous research, it has been shown that such a set function can be maximized by a greedy type algorithm over a family of all subsets of a finite set. ln this paper, we extend this finding to meet-semilattices. We show that the class of functions defined as minimum values of monoton...

We prove that for every distributive ∨, 0-semilattice S, there are a meet-semilattice P with zero and a map µ : P × P → S such that µ(x, z) ≤ µ(x, y) ∨ µ(y, z) and x ≤ y implies that µ(x, y) = 0, for all x, y, z ∈ P , together with the following conditions: (P1) µ(v, u) = 0 implies that u = v, for all u ≤ v in P. (P2) For all u ≤ v in P and all a, b ∈ S, if µ(v, u) ≤ a ∨ b, then there are a pos...

We prove that for every distributive 〈∨, 0〉-semilattice S, there are a meet-semilattice P with zero and a map μ : P × P → S such that μ(x, z) ≤ μ(x, y)∨μ(y, z) and x ≤ y implies that μ(x, y) = 0, for all x, y, z ∈ P , together with the following conditions: (P1) μ(v, u) = 0 implies that u = v, for all u ≤ v in P . (P2) For all u ≤ v in P and all a,b ∈ S, if μ(v, u) ≤ a ∨ b, then there are a pos...