1. TOWARDS A FORMAL INTERVAL-BASED TEMPORAL ONTOLOGY FOR AN OPTIMIZED TIMETABLE MANAGEMENT
Patience U. Usip and Enobong Umoren
Computer Science Department, University of Uyo, Uyo, Nigeria.

2. INTRODUCTION
The effect of time in an organization; Conflict and Conflict resolution.
Timetabling in the University; an example of a scheduling problem.
The manual and automated system in existence.
The problems are found in the inter-departmental based courses and the faculty-based courses. For the conflict to be resolved, a common understanding of time management between the anchored and services department is required.
The ability to have common understanding demands that, the anchored and the services department should have a way of sharing the management process of time.
Ontology (an explicit formal specification of the terms in the domain and relation among them (Gruber, 1993)); that allows for sharing of common knowledge, among other functions, will help resolve the conflicts encountered between anchored department and services department.

3. Aims and Objective
This work is aimed at formalizing an interval-based temporal ontology for an optimized timetable management system. The paper hopes to achieve this by carefully analyzing the existing timetable production system of the university, formalizing the temporal ontology model for reasoning and inference.
The Objective includes;
To analyze the existing timetable production system.
To design a frame work that will produced an ontology model.
To formalize, using the interval based temporal relations.
In other to achieve the above aims and objectives, there are some competency questions that needs to be answered. (i.e the formalism, by way of management hopes to answer the following competency questions)

4. Competency Question
To design an interval-based temporal ontology that can help in managing conflicts such as that which arise in university timetabling, the following competency questions are taken into consideration.
Is this course offered by other department, other than the department that anchors it?
Is same level course in the services department allocated to the same time in which the course in question is fixed?
Are students in higher level in the affected departments also offering the course?
Is the lecturer for the course, teaching another course at that same time?
Is the venue for the lecture far apart, that is, on different campuses?

5. Other competency questions for the normal generation of a university timetable also include the following. (basics)
Is the lecture venue scheduled for the course also allocated for another course, either by the anchored department of serviced department?
Is the time allocated for the course, also scheduled for another course, either by the anchored department or serviced department?
Is the capacity of the lecture venue for the course smaller than the number of student offering that course?
Is the lecturer that will handle this course scheduled for another course in her department at same time?

6. RELATED WORKS
Timetabling belong to the general category of scheduling problem. In scheduling, resources are allocated to certain processes or object in a certain sequence. Examples of general scheduling problem are project schedules, bus scheduling, air flight schedules, making a duty roster, etc. (Modupe, Olusayo and Olatunde, 2014). Automated timetabling is a great task that serves a lot of man-hour work in an institution and other organization, and provides optimal solution with constraint satisfaction within minutes. Attempts made towards the realization of the automated timetable include several contributions from many researchers using different approaches.

7. Different Approaches used before now
YEAR
AUTHOUR
STRENGTH
WEAKNESS
Genetic Algorithm
2014
Modupe et al.
Has the capability of making random changes to their candidate solution and then uses the fitness function to determine whether those changes produce an improvement.
Despite its ability to manipulate many parameters simultaneously, premature convergence still arise.
Problem with “deceptive” fitness function where the location of improved points give misleading information about where the global optimum is likely to be found, occurs.
Simulated Annealing
1983,
1991
Kirkpatrick, Gelatt and Vecchi, 1983;
Abramson, D
SA is flexible and has the ability to approach global optimality.
SA can easily accommodate constraints because constraint values can easily be added onto the value evaluated at each move.
SA requires a lot of choices to obtain an algorithm.
The precision of the numbers used in implementation can have a significant effect upon the quality of the outcome.
Case-Based Reasoning
2002
Burke and Petrovic
It’s safes time, such that, a number of previously solved timetables are stored in the case-based and used in constructing a solution for a new timetabling problem by following the 4Rs of CBR: Retrieve, Reuse, Revise, and Retain.
CBR requires all the modification or alteration to be stored and this is prone to generate big data issues in future.

8. The Relevance of Time in Ontology Time is an important concept in semantic web with vision of creating a “meaningful” environment for programs and software agent to roam from pages to pages to carry out sophisticated task for user (Pan, 2007) and specification of temporal information is necessarily required to bring semantic web into reality. Ontology of time deals with some relevant temporal concept, as proposed by Hobbs and ‘Pan (2004) for describing the temporal content of web pages and the temporal properties of web services. The concept includes; the topological temporal relations, where two subclasses which are instant and interval are discussed. As proposed by Allen, a framework for temporal reasoning, and all the relations proposed dealt with the directionality to time. An instance of reasoning with these interval based logic was also demonstrated (Hemalatha, Uma and Aghila, 2012), meaning that intervals are important temporal primitives in temporal logic (Saleh, 2011).

9. METHODOLOGY Allen in 1993 proposed a work on “Temporal Reasoning”, which he defined the thirteen (13) basic relations between time intervals, though the basics of that work was not applied on Timetabling, but, in this paper work, the thirteen basics relations will be incorporated towards achieving an optimized timetable. The relations include before, after, finishes, finished-by, overlaps, overlapped-by, starts, started- by, during, contains, meets, met-by and equal (Allen, 1983). These temporal relations depict and relate the actions and plans. Out of these thirteen basic interval relations, six are the inverse of the other six. The thirteen (13) basic relations are illustrated in the next slide;

10. Figure 1 shows the representation o f the thirteen basic interval temporal relations. Fig. 1: Allen’s interval based temporal relations From the Allen’s temporal relations in figure 1, their relevance to the timetabling management system will be demonstrated in the following sections.

11. Conceptualization of domain knowledge On considering the timetable domain, the major concepts include the department, student, course, venue, lecturer and time. Each of these concepts has unique attributes. Also, these concepts relate in diverse ways, some of the relations exist in reverse form while some do not. Some of the relations include owns, has, can be, offers, teaches, holds in, lectures in, and are assigned to. Note that, in a university where resources (such as lecturer, venue, and courses) are shared, there is bound to be competition. Each department is supposed to have the same working timetable ontology as shown in figure 2. Although almost all the components of the ontology are shared, showing the need for interoperability amongst relating departments. Hence, trying to link the ontologies for the relating departments will make the generalized ontology cumbersome and more complicated to handle. Since all these components are not owned by the department, there is certainly going to be some conflict of interest that is, some department will want to be given higher preferences.

12. Figure 2: A Departmental Timetable Ontology

13. On considering another domain concept, faculty, the ontology is expanded by mapping the various departmental timetable ontologies as shown in figure 3a. Again, another domain concept, university with all its faculties, needs to also map the various faculty timetable ontologies as modeled in the ontology in figure 3b. For instance, if one faculty having about eight departments will cause the ontology to have the representation in figure 3a and a university having more than three faculties is as depicted in figure 3b, then more complexities are envisaged. In other to manage such complexities, this paper proposes an optimized general timetable ontology with an allocation reasoner with interval-based temporal relations operating in-between the cooperating departmental timetable ontologies. The reasoner will help to manage the shared components of the proposed ontology without clashes or conflicts of interest.

14. (a) … Faculty 1st Department 2nd Department 3rd Department
8th Department

15. . . .
(b)
Figure 3: General timetable ontology showing complexity
An attempt to reduce these compounding complexities is the major focus of this work as demonstrated in the interval- based temporal relations that form part of the ontology in the following subsections.
University

16. Interval-Based Temporal Framework
Figure 4 presents the architecture of the proposed optimized general timetable ontology with the addition of the interval-based temporal components to the existing system.
Figure 4: Architecture of an interval-based temporal ontology

17. Formalizing the optimized timetable management system
From competency questions (i) to (v) identified in the previous section, the following rules can be written to address the conflicts.
R1: IF student offers course AND student is-owned-by dept AND dept NOT owns course THEN NOT (overlaps (course1, time1, course, time)).
R2: IF student offers course, student has level AND student1 offers course, student1 has level1 AND level1 > level THEN NOT during (course1, course)
R3: IF lecturer teaches course AND course holds-in venue, between time, time1 AND lectuer1 teaches course between time, time1 THEN NOT equal (lecturer1, lecturer)
R4: IF course holds venue AND course1 holds venue1AND distance (venue, venue1) is far apart THEN NOT meets (end-time, start-time)

18. Formalizing these rules in first-order logic, will facilitate explicit and expressive representation of the rules in the machine. For example, R1 can be formalized as shown in the following axiom.
 Student, Course, Dept,  Course1.
offers(Student, Course)  is-owned-by(Student, Dept)   owns(Dept, Course)
  overlaps(Course1, Time1, Course, Time).
As an interpretation of the axiom, let us read thus: For all student, course and dept, there exist another course1, such that student offers course and student is owned by dept and dept does not own course. Then it implies that time1 for course1 should not overlap with time for course.
From this formalism, the domain relations: offers, owns and a reverse relation to owns between Student and Dept. were explored. The power of Allen’s interval relation, overlaps, is also brought into consideration not forsaking the expressive tools in first-order logic. The use of the universal and the existential qualifiers gave life to the axiom. Putting all these together in Protégé ontology tool where the departmental timetable ontology have been developed and mapped together, reasoning to ensure that answers to the competency questions in section 3.1 is not a difficult task. Such a lecture time table is general and optimized.

19. Conclusion The temporal complexities in the mapped university ontology will be reduced with the use of the Allen’s interval relations. Ontology is a promising pathway towards solving the university timetable problems in universities. The interoperability and shared knowledge derived as benefits through the use of ontologies are common to the complexity reduction ability provided by the interval-based temporal relations brought into the timetable allocation reasoning process. This will yield the optimized general timetable ontology.

20. References
Allen, J Maintaining knowledge about temporal intervals. Communications of the ACM 26 (11):
Burke, E. K. and Petrovic, S. (2002). Recent Research directions in automated timetabling. European Journal of Operational Research
Modupe, A. O., Olusayo, O. E. and Olatunde, O. S. (2014). Development of a university lecture timetable using modified genetic Algorithm Approach. International Journal of Advance Research in Computer Science and Software Engineering
Hamalatha, M., Uma, V. and Aghila, G. (2012). Time Ontology with Reference Event based Temporal Relations (RETR). International Journal of Web and Semantic Technology (IJWSST). 3.
Hobb, J. R., and Pan, F. (2004). An ontology of Time for Semantic Web. Available in:
Pan, F. (2007). Representing Complex Temporal Phenomena for the Semantic Web and Natural Language. Available in:
Gruber, T. (1993). Ontology Development 101: A Guide to creating your first ontology.
Abramson, D. (1991). Constructing Scool Timetable using Simulated Annealing: sequential and parallel algorithm.
Kirtpatrick, S., Gelatt, C. D., and Vecchi, M. P. (1993). Optimization by Simulated Annealing, Science, New Series
Saleh, M. E. (2011). Semantic-Based Query in Relational Database using Ontology. Journal on Data and Knowledge Engineering. 2

21. THANK YOU