Terminology

The computation domain of Conjunto is finite so set domain and set term will stand respectively for finite set domain and finite set term in the following. Here are defined some of the terms mainly used in the predicate description.

Ground set

A known finite set containing only atoms from the Herbrand Universe or its powerset but without any variable.

Set domain

A discrete lattice or powerset D attached to a set variable S. D is defined by S in 2^lub_s | glb_s is_subseteq S under inclusion specified by the notation

Glb_s .. Lub_s. Glb_s and Lub_s represent respectively the intersection and union of elements of D. Thus they are both ground sets. S is then called a set domain variable.

Weighted set domain

A specific set domain WD attached to a set variable S where each element of WD is of the form e(s,w). s is a ground set representing a possible value of the set variable and w is the weight or cost associated to this value. e.g.

WD = {e(1,50),e({1,3},20)}..{e(1,50),e({1,3},20),e(f(a),100)}.

D would have been:

{1,{1,3}}..{1,{1,3},f(a)}.

Set expression

A composition of set domain variables or ground sets together with set operator symbols which are the standard ones coming from set theory.

S ::= S1 intersect S2 | S1 U S2 | S1 \ S2

Set term

Any term of the followings: (1) a ground set, (2) a set domain variable or (3) a set expression. All set built-in predicates deal with set terms thus with any of the three cases.