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Date created: 5/10/2003
Last updated: 2/17/2004
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PSL Core

The purpose of PSL-Core is to axiomatize a set of intuitive semantic primitives that is adequate for describing the fundamental concepts of manufacturing processes. Consequently, this characterization of basic processes makes few assumptions about their nature beyond what is needed for describing those processes, and the Core is therefore rather weak in terms of logical expressiveness.

The basic ontological commitments of PSL-Core are based on the following intuitions:

Intuition 1:

There are four kinds of entities required for reasoning about processes -- activities, activity occurrences, timepoints, and objects.

Intuition 2:

Activities may have multiple occurrences, or there may exist activities that do not occur at all.

Intuition 3:

Timepoints are linearly ordered, forwards into the future, and backwards into the past.

Intuition 4:

Activity occurrences and objects are associated with unique timepoints that mark the begin and end of the occurrence or object.


Informal Semantics for PSL-Core

(activity ?a) is TRUE in an interpretation of PSL-Core if and only if ?a is a member of the set of activities in the universe of discourse of the interpretation. Intuitively, activities can be considered to be reusable behaviors within the domain.

(activity_occurrence ?occ) is TRUE in an interpretation of PSL-Core if and only if ?occ is a member of the set of activity occurrences in the universe of discourse of the interpretation. An activity occurrence is associated with a unique activity and begins and ends at specific points in time. Although there may exist activities that have no activity occurrence, all activity occurrences must be associated with an activity

Activities are not classes within PSL; consequently, an activity occurrence is not an instance of an activity.

For example, the activity denoted by the term (paint House1 Paintcan1) is an instance of the class of Painting activities:
(Painting (paint House1 Paintcan1))
There may be multiple distinct occurrences of this instance:
(occurrence_of Occ1 (paint House1 Paintcan1))
(occurrence_of Occ2 (paint House1 Paintcan1))
(= (beginof Occ1) 1100)
(= (endof Occ1) 1200)
(= (beginof Occ2) 1500)
(= (endof Occ2) 1800)
There may be another instance of the class of Painting activities
(Painting (paint House1 Paintcan2))
that has no occurrences.

(timepoint ?t) is TRUE in an interpretation of PSL-Core if and only if ?t is a member of the set of timepoints in the universe of discourse of the interpretation. Timepoints form an infinite linear ordering with endpoints at infinity.

(object ?x) is TRUE in an interpretation of PSL-Core if and only if ?x is a member of the set of objects in the universe of discourse of the interpretation. An object is anything that is not a timepoint, nor an activity nor an activity-occurrence.

Intuitively, an object is a concrete or abstract thing that can participate in an activity. Objects can come into existence (be created) and go out of existence (be "used up" as a resource) at certain points in time. In such cases, an object has a begin and an end point. In some contexts it may be useful to consider some ordinary objects as having no such points either.

(= ?t inf-) is TRUE in an interpretation of PSL-Core if and only if ?t is the unique timepoint that is before all other timepoints in the linear ordering over timepoints in the universe of discourse of the interpretation.

inf- plays the role of negative infinity. It is needed to specify objects that have not been created.

(= ?t inf+) is TRUE in an interpretation of PSL-Core if and only if ?t is the unique timepoint that is after all other timepoints in the linear ordering over timepoints in the universe of discourse of the interpretation.

inf+ plays the role of positive infinity. It is needed to specify objects that are never destroyed.

(before ?t1 ?t2) is TRUE in an interpretation of PSL-Core if and only if the timepoint ?t1 is earlier than ?t2 in the linear ordering over timepoints in the interpretation.

In PSL-Core, the set of timepoints is not dense (between any two distinct timepoints there is a third timepoint), although in PSL-Core the set of timepoints is infinite. Denseness can be added by a user as an additional postulate. Time intervals are not included among the primitives of PSL-Core; intervals can be defined with respect to timepoints and activities.

(occurrence_of ?occ ?a) is TRUE in an interpretation of PSL-Core if and only if ?occ is a particular occurrence of the activity ?a. This is the basic relation between activities and activity occurrences. Every activity occurrence is associated with a unique activity. An activity may have no occurrences or multiple occurrences.

(participates_in ?x ?occ ?t) is TRUE in an interpretation of PSL-Core if and only if ?x plays some role in an occurrence of the activity occurrence ?occ at the timepoint ?t in the interpretation. An object can participate in an activity occurrence only at those timepoints at which both the object exists and the associated activity is occurring.

(= ?t (beginof ?occ)) is TRUE in an interpretation of PSL-Core if and only if ?t is the timepoint at which the activity occurrence ?occ begins.

(= ?t (beginof ?x)) is TRUE in an interpretation of PSL-Core if and only if ?t is the timepoint at which the object ?x becomes possible to participate in an activity.

(= ?t (endof ?occ)) is TRUE in an interpretation of PSL-Core if and only if ?t is the timepoint at which the activity occurrence ?occ ends.

(= ?t (endof ?x)) is TRUE in an interpretation of PSL-Core if and only if ?t is the timepoint at which the object ?x becomes no longer possible to participate in an activity.


Axioms of PSL-Core