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A LogicalRelationship is a relationship (expressable as an AND/OR graph) between two or more Situations or entities (such as Goals) derived from Situations. WrappedSituation is an abstraction of Situation and these derived concepts (see below). A Situation is a macroscopic characteriation of the world state, and corresponds to set of (microscopic) world states, typically defined by some property that they all share. The familiar logic/set theory operators and relations (intersection/and, union/or, subset/implies) can be applied to Situations with a straight-forward semantic interpretation. The (meta-)relationships implies and decomposes are useful in providing a semantics for goal decomposition.
A subject Situation is said to imply an object Situation if the subject is a subset of the object. For example, if situationA is the set of states in which entity X has colour blue, and situationB is the set of states in which entity X has type car and colour blue, then situationB implies situationA. Note that situationB is a specialisation of situationA: its defining properties are obtained by adding to those of situationA. Thus isImpliedBy, the reverse reading of MESSAGE concept implies is a specialisation of the UML generalisation relationship.
Note that the conjunction (intersection) of set of Situations is itself a Situation (and it implies all the elements of the set). A set of Situations, S, is said to decompose situationA if the conjunction of S's elements is implied by situationA.
This means that LogicalRelationships can be used to show (logical) Goal and Task decomposition, graphs of Tasks achieving a Goal (plans), etc.