Resource Roles for Interfering Activities

Resource Roles for Interfering Actions

Extension Name: res_role.def

Primitive Lexicon: None

Defined Lexicon:

Relations:

Theories Required by this Extension: requires.th, act_occ.th, complex.th, atomic.th, subactivity.th, occtree.th, psl_core.th

Definitional Extensions Required by this Extension: None

An object is a resource only with respect to some activity which requires the resource. We are therefore not axiomatizing any other properties of resources, such as the issue of discrete vs continuous resources. Resource roles are one way of formalizing the way in which an activity requires the resource. The intuition behind the axiomatization of resource roles is the classification of interactions among activities with respect to the resources that they share. In particular, the set of resource roles defined in this note are a classification of interfering actions, that is, the effects of one action falsify the preconditions of another action.

Definitions

Definition 1 A resource ?r is reusable by an activity ?a if any other activity that also requires ?r is still possible to perform after ?a completes its occurrence, in every possible future.

An example of a reusable resource is a machine that does not require setup between activities. As soon as one activity occurs, it is always possible to perform the next activity. 

(forall (?r ?a1 ?a2 ?a ?occ2) (iff (reusable ?r ?a1)
        (if  (and	(common ?a1 ?a2 ?r)
			(subactivity ?a1 ?a)
			(subactivity ?a2 ?a)
                        (occurrence_of ?occ2 ?a1))
             (forall (?b ?occ3)
                        (if  (and  (subactivity_occurrence ?occ3 ?b)
				   (occurrence_of ?b ?a)
                                   (precedes ?occ2 ?occ3))
                             (poss ?a2 ?occ3))))))
Definition 2 A resource ?r is possibly reusable by an activity ?a iff for any other activity that also requires ?r is still possible to perform after ?a completes its occurrence, in some possible future situation.

An example of a possibly reusable is a machine that requires some setup between different activities. After the first activity occurs, it is possible for the other activity, but only if the setup activity occurs first. 


(forall (?r ?a1) (iff (possibly_reusable ?r ?a1)
(forall (?a2 ?occ2 ?a)
        (if  (and	(common ?a1 ?a2 ?r)
                        (subactivity ?a1 ?a)
                        (subactivity ?a2 ?a)
                        (occurrence_of ?occ2 ?a1))
             (exists (?b ?occ3)
                    (and    (subactivity_occurrence ?occ3 ?b)
		            (occurrence_of ?b ?a)
                            (precedes ?occ2 ?occ3)
                            (poss ?a2 ?occ3)))))))
Definition 3 A resource ?r is renewable with respect to an activity ?a iff for any other activity that also requires ?r is still possible to perform after ?a completes its occurrence, in every possible future situation unless it is prevented.

An example of a renewable resource is a solar-charged battery. Once it is depleted, there will always exist a future situation where the sun recharges the battery so that it can be used again. 


(forall (?r ?a1) (iff (renewable ?r ?a1)
(forall (?a ?a2 ?occ2)
        (if  (and	(common ?a1 ?a2 ?r)
			(subactivity ?a1 ?a)
			(subactivity ?a2 ?a)
                        (occurrence_of ?occ2 ?a1))
             (forall (?b)
                  (if  (occurrence_of ?b ?a)
		       (exists (?occ3)
                             (and    (subactivity_occurrence ?occ3 ?b)
                                     (precedes ?occ2 ?occ3)
                                     (poss ?a2 ?occ3)))))))))
Definition 4 A resource ?r is weakly reusable by an activity ?a iff for any other activity that also requires ?r is still possible to perform after ?a completes its occurrence, in every possible future situation unless it is prevented.

A weakly reusable resource is one where we can prevent the renewing of the resource. For example, a paintbrush is reusable only if we put it into varsol after use; otherwise, it is not reusable. 


(forall (?r ?a1) (iff (weakly_reusable ?r ?a1)
(forall (?a ?a2 ?occ2)
        (if  (and	(common ?a1 ?a2 ?r)
			(subactivity ?a1 ?a)
			(subactivity ?a2 ?a)
                        (occurrence_of ?occ2 ?a1))
                  (exists (?b)
                        (and    (forall (?occ3)
                                        (if  (and	(subactivity_occurrence ?occ3 ?b)
							(occurrence_of ?b ?a)
                                                        (precedes ?occ2 ?occ3))
                                                  (poss ?a2 ?occ3)))))))))
Definition 5 A resource ?r is consumable by an activity ?a if any other activity that also requires ?r is not possible to perform after ?a completes its occurrence.

An example of a consumable resource is wood in a fire, or raw materials in a manufacturing production process. 

(forall (?r ?a1) (iff (consumable ?r ?a1)
(forall (?a ?a2 ?occ2)
        (if  (and	(common ?a1 ?a2 ?r)
			(subactivity ?a1 ?a)
			(subactivity ?a2 ?a)
                        (occurrence_of ?occ2 ?a1))
             (forall (?b ?occ3)
                  (if  (and  (subactivity_occurrence ?occ3 ?b)
			     (occurrence_of ?b ?a)
                             (precedes ?occ2 ?occ3))
                       (not (poss ?a2 ?occ3))))))))
Definition 6 A resource ?r is possibly consumable with respect to an activity ?a1 iff after the occurrence of ?a1, there exists a future situation in which any activity that requires ?r is no longer possible. 
(forall (?r ?a1) (iff (possibly_consumable ?r ?a1)
(forall (?a ?a2 ?occ2)
        (if  (and  	(common ?a1 ?a2 ?r)
			(subactivity ?a1 ?a)
			(subactivity ?a2 ?a)
                        (occurrence_of ?occ2 ?a1))
             (exists (?b ?occ3)
                   (and    (subactivity_occurrence ?occ3 ?b)
			   (occurrence_of ?b ?a)
                           (precedes ?occ2 ?occ3)
                           (not (poss ?a2 ?occ3))))))))
Definition 7 A resource ?r is weakly consumable with respect to an activity ?a1 iff after the occurrence of ?a1, there always exists a possible future along which any other activity that requires ?r will never be possible.

An example of a weakly consumable resource is a paintbrush; if we do put it into varsol after using it, then any activity that requires the brush will no longer be possible. 

(forall (?r ?a1) (iff (weakly_consumable ?r ?a1)
(forall (?a ?a2 ?occ2)
        (if  (and  	(common ?a1 ?a2 ?r)
			(subactivity ?a1 ?a)
			(subactivity ?a2 ?a)
                        (occurrence_of ?occ2 ?a1))
             (exists (?b)
                 (and    (occurrence_of ?b ?a)
			 (forall (?occ3)
                              (if  (and  (subactivity_occurrence ?occ3 ?b)
					 (occurrence_of ?b ?a)
                                         (precedes ?occ2 ?occ3))
                                   (not (poss ?a2 ?occ3))))))))))
Definition 8 A resource ?r is wearable with respect to an activity ?a1 iff after the occurrence of ?a1 there is always a situation in every possible future where any other activity that requires ?r is no longer possible.

An example of a wearable resource is a drill bit; in every possible future, there will exist a situation where the bt has worn down to the point where it can no longer be used. 

(forall (?r ?a1) (iff (wearable ?r ?a1)
(forall (?a ?a2 ?occ2)
        (if  (and  (common ?a1 ?a2 ?r)
			(subactivity ?a1 ?a)
			(subactivity ?a2 ?a)
                        (occurrence_of ?occ2 ?a1))
             (forall (?b)
                  (if  (occurrence_of ?b ?a)
		       (exists (?occ3)
                           (and    (subactivity_occurrence ?occ3 ?b)
                                   (precedes ?occ2 ?occ3)
                                   (not (poss ?a2 ?occ3))))))))))