![]() ![]() The Subsume strategy asks if the user is interested in finding out more about the item, it then waits for a response – any response –and then proceeds to output a short text about the item.Īpproach 1: Extend the Private Company Alternative to Subsume Certain CRis and all NCAs into Goodwill c.Ĭomputation Time of the Overall Approach The strategy tries to broaden the user’s goal from obtaining a specific piece of in- formation to just hearing some general interesting information about the piece.The second strategy is Subsume Split, which is similar to Subsume but gives the user a choice of what subsuming information they prefer. Plotkin, in 1970.Approach 1: Extend the Private Company Alternative to Subsume Certain CRIs and all NCAs into Goodwillb.Īpproach 1: Extend the Private Company Alternative to Subsume Certain CRIs and all NCAs into goodwillWhile this approach would align the guidance for private companies and not-for-profit entities with the guidance for PBEs, we do not support optionality for PBEs, consistent with the findings in the Pozen Committee Report. Therefore, every sublattice of the lattice of linear terms that does not contain Ω is isomorphic to a set lattice, and hence distributive (see Pic. 5).Īpparently, the subsumption lattice was first investigated by Gordon D. their anti-unification and unification, corresponds to intersection and union of their path sets, respectively. Join and meet of two proper linear terms, i.e. As the join operations do not in general agree, the linear terms lattice is not properly speaking a sublattice of the all terms lattice. The join operation in the all terms lattice yields always an instance of the join in the linear terms lattice for example, the (ground) terms f( a, a) and f( b, b) have the join f( x, x) and f( x, y) in the all terms lattice and in the linear terms lattice, respectively. The meet operation yields always the same result in the lattice of all terms as in the lattice of linear terms. This lattice, too, includes N 5 and the minimal non-distributive lattice M 3 as sublattices (see Pic. 3 and Pic. 4) and is hence not modular, let alone distributive. The set of linear terms, that is of terms without multiple occurrences of a variable, is a sub-poset of the subsumption lattice, and is itself a lattice. if t is the join of t 1 and t 2, then Gnd( t) ⊇ Gnd( t 1) ∪ Gnd( t 2).if t is the meet of t 1 and t 2, then Gnd( t) = Gnd( t 1) ∩ Gnd( t 2),.terms with the same set of ground instances are equal modulo renaming,.t 1 is an instance of t 2 if and only if Gnd( t 1) ⊆ Gnd( t 2),.t equals the join of all members of Gnd( t), modulo renaming,.The set of terms unifiable with a given term need not be closed with respect to meet Pic. 2 shows a counter-example.ĭenoting by Gnd( t) the set of all ground instances of a term t, the following properties hold: If f is a binary function symbol, g is a unary function symbol, and x and y denote variables, then the terms f( x, y), f( g( x), y), f( g( x), g( y)), f( x, x), and f( g( x), g( x)) form the minimal non-modular lattice N 5 (see Pic. 1) its appearance prevents the subsumption lattice from being modular and hence also from being distributive. The lattice has infinite descending chains, e.g. each term without variables, is an atom of the lattice. A variable x and the artificial element Ω are the top and the bottom element of the lattice, respectively. The join and the meet operation in this lattice are called anti-unification and unification, respectively. Pic. 2: Part of the subsumption lattice showing that the terms f( a, x), f( x, x), and f( x, c) are pairwise unifiable, but not simultaneously. ![]()
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