1. Introduction

This paper is an extension of work originally presented in the Future Technologies Conference 2016 [1], where the use of ontologies in semantic web was established as an efficient and intelligent tool for managing timetabling knowledge [2]. Domain specific concepts and some complexities were presented in figures 2, 3(a) and 3(b) of the conference paper. The Allen’s interval-based temporal relations [3] were considered suitable and introduced for inferencing [4] in the sample rules used to describe possible resolutions to the highlighted complexities in the conference paper. Allen’s interval-based temporal relations were introduced to handle time durations and is adapted or reused for formal description of time periods for complex knowledge management as seen in the timetable domain. However, this paper extends works done in the conference paper as it aims at formalizing an ontology model for analyzing temporal scheduling complexities in an existing schedule and providing optimal possible time scheduling resolutions showing their reduction rate for efficient and intelligent knowledge management.

Ontologies exist in diverse forms – lexicons, dictionaries, thesauri, and logical models described in languages such as first order logic (FOL). Lexicons provide standard lists of words (vocabulary) in a language with corresponding knowledge of how each word is used.  Hence a lexicon can be seen as an index for mapping written form of a word with the information about that word [8]. Dictionaries can be organized to form hierarchies- taxonomies, meronomies, mereologies and merons, according to specific relations. Related terms, linguistics objects are added to any given collection of terms through thesauri. Ontologies provide standardization of the terms used to represent knowledge about a domain in any of these forms. They can as well support inference with FOL or its subset, by deriving new facts from a collection of facts and enforcement of consistency. It also allows for sharing common understanding of the structure of information among people or software agent; reuse of domain knowledge; making domain assumption explicit; separating domain knowledge from operational knowledge; and analyzing domain knowledge. These considerations are clearly useful for knowledge management, especially when large amounts of knowledge are being processed. Ontology is increasingly used in various fields such as Knowledge Engineering, Artificial Intelligence(AI) and computer science, in applications related to knowledge management (KM), natural language processing.  In recent years, the explicit formal specifications of terms in any given domain and relations among them have gradually moved from the realm of Artificial Intelligence (AI) laboratories to the desktops of domain experts. The representation of domain concepts in structural ways – definition of concepts (classes and properties) and mapping the relationships among the defined concepts, form the basis of Ontology [5]. From the computer science perspective, it is a formal naming and definition of the types, properties, and interrelationship of the entities that really or fundamentally exist for a particular domain of discourse [6] [7]. For example, in a lecture timetable domain, courses, timeslots, students, lecturers, venues and lectures are some of the concepts from which the timetabling application domain can be described. These concepts and their meanings together constitute ontology for timetable and can be used as common knowledge for communication among educational stakeholders and provides information for the development of a timetable information system.

KM involves the acquisition, creation, use, representation, organization and advancement of knowledge in its many forms. As a requirement for effective KM, an understanding of how individuals, groups and organizations use knowledge is needed. One major aspect of an organization that require effective management of knowledge is timetable scheduling. This is because an organization’s general timetable exhibit different levels of temporal scheduling complexities depending on the available resources. The threats posed by these complexities ranges from poor organization performance as seen in the domain of discourse (poor academic performance). Knowledge management is thereby required in attempt to reduce these complexities.  Automation of timetabling process as seen in existing systems [9] [10] [11] does not resolve these complexities. This paper demonstrates the application of ontologies in timetable KM. It is aimed at analyzing any existing temporal schedule to discover all complexities and providing possible temporal schedules with reduced complexities (in time and space requirement) that tends towards optimality. This is achieved by utilizing Allen’s temporal interval relations described in the following sections and evaluating the resulting optimal temporal schedule for proof and the need for adoption.

2.       Formal Ontologies and Temporal Interval Relations

The time ontology has been considered by several authors with unique contributions to issues relating to temporal (time) representation and reasoning among others. Hobbs and Pan [12] considered temporal relations (TR) involving two subclasses of time— time instant and time interval. Allen’s interval relations [13, 3] centers on various time intervals and possible reasoning involving co-operating concepts. As proposed by Allen [3], a framework for temporal reasoning, and all the relations proposed dealt with the directionality of time. In his proposal, intervals are the only temporal primitives in the temporal logic. Allen aimed at illustrating natural language sentences and to represent plans. To achieve the thirteen (13) basic relations between time intervals, with six of the intervals being the inverse of the other six: before, after, finishes, finished-by, overlaps, overlapped-by, starts, started- by, during, contains, meets, met-by and equal [3]. The basic interval temporal relations (Figure 1). These temporal relations depict and relate the actions and plans described in this paper.

 

Figure 1: Allen’s interval based temporal relations

This paper is targeted at formalizing the basic temporal ontology model for reasoning and inference towards an optimal time scheduling, after an analysis of an existing timetable to unravel all the complexities and evaluating feasible solutions towards achieving optimality. An illustration of how moment and point works on interval-based temporal logic is given in “moment and point in an interval based temporal logic”. Moment is a non-decomposable period where the time is corresponding to instantaneous events while a point (a zero duration time) is where reasoning about the beginning and ending of event do arises. The axiomatization of the stated theory of time was done in terms of the simple relationship “meets” and subsumes the interval-based theory proposed in [3] thereby extending the theory to point-like time periods.

 

3.       Timetabling Complexities

Timetable analysis reveals the major concepts – departments, timeslots, courses, students, venue and lecturers as objects responsible for complexities in timetable implementations. Three categories of courses exist in any typical higher institution; departmental, faculty-based and university-based courses. This paper considers the complexities arising from their inter-dependencies in scheduling the intra-departmental and inter-departmental (faculty-based and university-based) courses. Amongst other timetabling competency questions, are the following in the optimization of the general temporal scheduling ontology. They include:

1. Is the course offered by other departments, other than the host department?
2. Are other courses for the same level in all cooperating departments allocated to the same time?

• Are students in higher levels in the cooperating departments also offering the course?

1. Is the course lecturer teaching another course allocated at the same time?
2. Is the venue for course far apart from venue of the preceding or succeeding courses (courses before or after)? That is, are the respective venue for teaching the courses on different campuses? or are they within the same campus but widely separated?

Each of these concepts has peculiar attributes. These concepts relate in diverse ways and some of the relations exist in reverse form. The relations include owns, has, can-be, offers, teaches, holds-in, lectures-in, and are-assigned-to. In consideration of the fact that most resources of the university (such as lecturer, venue, and courses) are shared and in some other cases limited, departments compete for these resources. A university has a given number of programmes running on specified number of campuses. Campuses or lecture venues widely separated far apart from each other will exhibit a high level of complexity with numerous inter-dependencies. A sample model in fig. 1 with the departmental general timetable ontology for each department was described in [1] and shown in the resulting ontograf (Figure 2) from protégé. Almost all the components of the ontology are shared, making it needful for interoperability amongst relating departments. An attempt to link the ontologies for all the relating departments will make the resulting ontology cumbersome and more complicated largely because components of the ontology are not owned by a department, the number of inter-dependencies will generate some form of conflict of interest.

Figure 2: An Ontograf of a Departmental Timetable Ontology

Suppose course c_i is to be taught by lecturer L_l, scheduled to hold at venue v₁ at time t_i and another course c_j to be taught be the same lecturer L_l at same time t_i in another venue v₂, exposes some form of complexities. Again, suppose c_i and c_j are both scheduled to hold at v₁ at the same time t_i bring to bear another level of complexity that is predominant in the domain. That is a groups of students offering a particular course holding at time t_1­ at campus U₁, and also offering another course c_j holding at time t₂ at campus U₂, where time t₁ meets time t₂. The meeting time does not give allowance for the participating students to travel from campus U₁ to campus U₂ (or from venue vi to venue v2 with campus U_i). A general model of these complexities is shown in Figure 3.

 

A view of the various complexities based on the Allen’s interval relations results in the following temporal complexity types: overlapping time (which also includes starts, ends and during relations) for courses taught by same lecturers and offered by same level of students.  Meeting time complexity also results for courses offered by inter campus students. Other complexity types, not handled in this paper, include venue-clash and carrying capacity check.

Figure 3: A course allocation complexity model

where d is the department’s code, l is the level of students, t represents the timeslot, s is the lecturer, r the room number while U is the campus. i,j,n,m>0 are instances of the various objects

From the general course allocation complexity model in Figure 3, several levels of complexity are defined to include:

• Departmental Complexity (Regular)
• Departmental Complexity (Carryover)
• Faculty-Based (Inter-Departmental) Complexity (Regular)
• Faculty-Based (Inter-Departmental) Complexity (carryover)
• Inter-Faculty/Same Campus Complexities (Regular)
• Inter-Faculty/Same Campus Complexities (Carryover)
• Inter-Faculty/Inter-Campus Complexities

A generalized timetable ontology will expand the departmental timetable ontology is obtained from a mapped departmental timetable ontology as modeled in [1].  This require the mapping of domain resources ranging from, past results, course registration list, departmental brochure for details of all level courses and lecturers, campus location (or distance apart), etc.

Table 1 gives a justification of complexities in all the cases in consideration and the possible resolution based on interval temporal relations.

4.       System Framework

Figure 4 gives the architecture of the proposed Ontology-Based Temporal Scheduling Framework showing the relevant components for the achievement of its set goal of producing an optimal time schedule.

Table 1: Complexity description by type and possible time scheduling resolution

 

Case number	Case description	Complexity type	Resolution
1.	Carryover /repeating students in the host department.	Overlapping- Time	If carryover students are offering course ci at time t1, then time t2 for course cj (time for their level course should not overlap).
2.	Carryover / repeating students in the serviced department.	Overlapping- Time	If carryover students are offering course ci at time t1, then time t2 for course cj (time for their level course should not overlap).
3.	Regular students (students at that level) in the services department.	Meeting-Time	If course ci is scheduled at time t1 in campus U1, (for e.g 10-12) and course cj  is also scheduled at time t2 in campus U2, where the end-time of course1 ci meets with the start-time of course cj, the course should be rescheduled.
4.	Assigning the same lecturer to teach at different campuses, without giving sufficient time interval.	Meeting-Time	A lecturer assigned for course c1 at time t1 in campus U1, and also assigned for course cj at time t2 in campus U2, where the end-time of course ci meets with the start-time of course cj, should be rescheduled.
5.	students at same level and carryover/repeaters student in the services department.	Starts/ Finishes	If course ci and course cj  are of different department, then course cj  should not start at the same time with course1 and finishes after course ci
6.	Students in their regular year of studies and carryover student of different department, but the same faculty.	During	If course ci and course cj are of different department , di and dj  respectively, but of the same faculty, then course ci should not hold during  course cj
7.	Students (both regular students and carryover student) at another campus, offering a course holding at a different campus.	Location Campus location  (distance apart)	If course  ci is scheduled for time t1 in campus U1, and course cj  is also scheduled for time t2 in campus U2, then time t1 should not meet t2
8.	The class size and the carrying capacity of the lecture venue.	Space (carrying capacity)	If the number of students offering course ci is greater than the venue assigned, then course ci should be re-scheduled for a bigger venue.

    

 

Figure 4: Architecture of the Proposed Ontology-Based Time Scheduling System

The major components of the system as depicted in Figure 4, are described as follows:

• Universe of Discourse: the universe of discourse where the domain knowledge under consideration is obtained. It consists of all the domain concepts — courses, venues, universities, timeslots, lecturers, students, students’ status, departments, faculties, levels, campuses, locations, timetable and other aspects of the timetabling domain

 

• Fact Database: this includes the values and instances of the domain concepts, the resources, relations and a mapping of facts to concepts and resources. It also has the hard and soft constraints.

 

• Time Ontology; this component stores the domain specific rule (owns, has, offers etc.) which will be considered while mapping the resources.

 

• Allocation Reasoner: this is where reasoning and inferencing take place based on the Allen’s interval-based temporal relations. The sets of rules arising from the competency questions and some already established constraints, are also part of this component. the Allocation Reasoner works in collaboration with the domain specific rules.

 

• Ontology Evaluation Approach: Criteria from the gold or golden ontology evaluation standard helps in assessing the set of feasibilities obtained from the Allocation Reasoner towards optimality of the timetable.

 

• Optimal Time Schedule: This gives the resulting possible time schedule showing the resolutions made towards optimality.

To manage the complexities called for the optimized general time schedule with an allocation reasoner with interval-based temporal relations operating in-between the cooperating departmental timetable ontologies. Shared components of the optimized general timetable ontology. The interval-based temporal relations/rules serve as the instrument for managing the identified complexities in the timetabling system. With the interval-based temporal relation allocation of courses to venues, allocation of courses to timeslots (time duration), and assignment of lecturers to courses/venues are efficiently done.

4.1  Proposed Complexity Reduction Rules

From competency questions (i) to (v) identified in section 3.0, rules R1 to R12 addresses the complexities as well as adopting the Allen’s interval relations in the proposed resolutions. It is assumed that all departments within the same faculties are domicile in the same geo-location:

R1:     IF student of department d_i offers course c_i AND department d_i NOT owns course c_i THEN time t₁ for course c_i NOT overlaps time t₂ for course c_j in department d₂.

R2:     IF course c_i holds at time t₁ and course c_j holds at time t₂ AND t₁ equals t₂ AND students offer c_i and c_j THEN t₁ and t₂ overlaps.

R3:     IF course c_i holds at time t₁ and course c_j holds at time t₂ AND time t₁ is during time t₂ AND students offer course c_i and course c_j THEN t₁ and t₂ overlaps.

R4:     IF course c_i holds at time t₁ and course c_j holds at time t₂ AND t₁ starts with t₂ AND students offer c_i and c_j THEN t₁ and t₂ overlaps.

R5:     IF course c_i holds at t₁ and course c_j holds at time c₂ AND t₁ finishes at t₂ AND students offer c_i and c_j THEN t₁ and t₂ overlaps.

R6:     IF c_i and c_j belongs to the same department, d₁, THEN scheduled c_j to t_i AND c_j to t_j such that t_i ¹ t_j (NOT overlaps).

R7:     IF c_i and c_j are of different department, d_i and d_j respectively, but of the same faculty, THEN time for c_i should NOT overlaps with c_j or c_i NOT during c_j.

R8:     IF t_i for c_i and t₂ for c_j meets, THEN t_j for c_j will be changed and scheduled for another time (NOT meets)

R9:     IF c_i and c_j are courses of different faculty, THEN their time NOT meets and NOT overlaps

R10:   IF time for c_i and c_j are equals AND venue assigned for c_i is the same venue assigned for c_j, THEN (c_i OR c_j ) should be rescheduled for different time.

R11:   IF time for c_i and c_j are equals or meets, AND the lecturer assigned for ci in campus U₁ is also assigned for c_j in U₂ within the time interval of one hour, THEN c_j should be re-scheduled for another time.

R12:   IF c_i is scheduled for t_i in U₁ AND c_j scheduled for t_j in U₂ THEN t_i NOT meets tj.

R13:   IF carryover/repeating students are offering c_i scheduled for time t_i THEN t_j, time for their level course, c_j NOT overlaps t_i.

R14:   IF c_i in campus U₁ and course c_j in U₂, THEN time t_i for c_i and t_j for c_j NOT meets or NOT overlaps.

R15:   IF number of students offering c_i is greater than the venue carrying capacity, THEN re-schedule c_i.

Formally expressing the above rules in FOL results in axioms A1 to A15. Recalling from the conceptualization of the domain concepts: student, lecturer, time, venue and campus with domain-specific relations: owns, has, offers, holds and teaches does not resolve time scheduling complexities when considering inter-departmental course allocation. This called for the adoption of the Allen’s interval relations which includes temporal relations such as overlaps. meets, equals, during and their negations for a more explicit representation. Axioms A1 to A15 constitute the core of the ontology reasoner that results in the optimal time scheduling process.

A1:  “Student, Course1, Time1, Dept1 $ Course2, Time2, Dept2.

offers(Student, Course1) Ù owns(Dept1, Course1)

 Ù offers(Student, Course2)Ù owns(Dept2,Course2)

Þ cooperates(Dept1, Host,Dept2, Serviced).

A2:  “Student, Course1, Time1,Course2, Time2.

holds(Course1, Time1) Ù holds(Course2, Time2) Ù equals(Time1, Time2) Ù offers(Student, Course1) Ù offers(Student, Course2) Þ overlaps(Time1, Time2).

A3:  “Student, Course1, Time1, Course2, Time2.

holds(Course1, Time1) Ù holds(Course2, Time2) Ù during(Time1, Time2) Ùoffers(Student, Course1) Ù offers(Student, Course2) Þ overlaps(Time1, Time2).

A4:  “Student, Course1, Time1, Course2, Time2.

holds(Course1, Time1) Ù holds(Course2, Time2) Ù starts(Time1, Time2) Ùoffers(Student, Course1) Ù offers(Student, Course2)Þ overlaps(Time1, Time2).

A5:  “Student, Course1, Time1, Course2, Time2.

holds(Course1, Time1) Ù holds(Course2, Time2) Ù finishes(Time1, Time2) Ùoffers(Student, Course1) Ù offers(Student, Course2) Þ overlaps(Time1, Time2).

A6:  “ Course1, Time1, Dept1,Course2, Time2.

owns(Dept1, Course1) Ùowns(Dept1, Course2) Ùholds(Course1, Time1) Ù holds(Course2, Time2) Ùequals(Time1, Time2) Ùequals(Level1, Level2)

Þ Øoverlaps(Time1, Time2).

A7:  “ Course1, Time1, Dept1, Fac1, Course2, Time2, Dept2. Fac2.

owns(Dept1, Fac1, Course1) Ùowns(Dept2, Fac2, Course2)

Þ Øoverlaps(Time1,Time2) Ú Øduring(holds(Course1, Course2)) .

A8:  “ Course1, Time1, Course2, Time2, $ t.

holds(Course1, Time1) Ùholds(Course2, Time2) Ù finishes(Time1, t)Ù starts(Time2, t) Þ meets(Time1, Time2).

A9:  “ Course1, Time1, Dept1, Fac1, Course2, Time2, Dept2. Fac2.

owns(Dept1, Fac1, Course1) Ùowns(Dept2, Fac2, Course2) ÙØ equals (Fac1, Fac2)

Þ Ømeets(Time1, Time2)ÙØoverlaps(Time1, Time2).

A10: “ Course1, Time1, Venue1, Course2, Time2, Venue2.

holds(Course1, Time1) Ùholds(Course2, Time2) Ùequals (Venue1, Venue2) Þ Øequals(Time1, Time2).

A11: “ Course1, Time1, Let, Camp1, Course2, Time2, Camp2.

holds(Course1, Time1, Camp1) Ùholds(Course2, Time2, Camp2) Ùequals (Time1, Time2)Ùequals (Camp1, Camp2) Ùteaches (Let, Camp1)Ùteaches (Let, Camp2)

Þ Øoverlaps (Time1, Time2)ÚØmeets (Time1, Time2)

A12: “ Course1, Time1, Camp1, Course2, Time2, Camp2.

holds(Course1, Time1, Camp1) Ùholds(Course2, Time2, Camp2) Ùequals (Time1, Time2)Ù equals (Camp1, Camp2)

Þ Ø meets (Time1, Time2)

A13: “Student, Course1, Time1, Dept1, Course2, Time2.

offers(Student, Course1, Time1) Ùoffers(Student, Course2, Time2) Ùowns(Dept1, Course1) Ù equals(Time1, Time2) Ù equals(Level1, Level2) Þ Øoverlaps(Time1, Time2).

A14: “Student, Course1, Time1, Dept1, Course2, Time2.

offers(Student, Course2, Course2) Ù holds(Course1, Camp1) Ù holds(Course2, Camp2) Þ Ømeets(Time1, Time2)Ø overlaps (Time1, Time2).

A15: “Student, Course1,Venue1, Time1, nos, $ Venue2, ccap.

offers(Student, Course1, Venue1) Ù holds(Course1, Venue1, Time1) Ù (nos > ccap) Þ holds(Course1, Venue2)

4.2      Weighting of Complexities

The severity levels of complexities are denoted by 0%, 50% 70% and 100% respectively based on the sources of complexity (time, space and location).

1. Overlapping Time:

Overlapping time complexities includes five relations in Allen’s Interval-based Temporal Relations: starts, finishes, overlaps, during and equals. In this paper, these five temporal relations are classified into two levels of complexities namely complete and partial. Complete overlap occurs if two or more courses offered by a group of Students begins and ends at the same time (Equals Relation – See Table 2) or the Start and End times of these course is within the start and end time of c_j (During Relation – See Table 3), then a complete overlap of weight 100% has occurred. However, the During relation will not apply in this domain since the university system does not have 4-hour lecture period. For example, instances of equals and during relations are given in Tables 2 and 3 respectively.

 

Table 2:    equals Relation

8:00 – 9:00 AM	9:00 – 10:00 AM	10:00 – 11:00 AM	11:00–12:00 NOON
ci
cj

 

Table 3:    during Relation

8:00 – 9:00 AM	9:00 – 10:00 AM	10:00 – 11:00 AM	11:00– 12:00 NOON
ci
	cj

 

A partial overlap is described using Allen’s Interval-based Temporal Relations as follows; overlaps, starts and finishes shown in Tables 4, 5 and 6 respectively. These relations under partial overlap are assigned a complexity of 50%. Examples of partial overlaps are given in Tables 4, 5 and 6

 

Table 4:    overlaps Relation

8:00 – 9:00 AM	9:00 – 10:00 AM	10:00 – 11:00 AM	11:00– 12:00 NOON
ci
	cj

 

Table 5:    starts Relation

8:00 – 9:00 AM	9:00 – 10:00 AM	10:00 – 11:00 AM	11:00–12:00 NOON
ci
cj

 

Table 6:    finishes Relation

8:00 – 9:00 AM	9:00 – 10:00 AM	10:00 – 11:00 AM	11:00– 12:00 NOON
ci
	cj

In the resolved overlap, the desired Allen’s interval-based temporal relation for the resolution of overlapping time complexity is before in Table 7 and Table 8. When course c_i is before course c_j a 0% complexity is recorded.

 

Table 7:    before Relation (A)

8:00 – 9:00 AM	9:00 – 10:00 AM	10:00 – 11:00 AM	11:00– 12:00 NOON
ci
		cj

 

Table 8:    before Relation (B)

8:00 – 9:00 AM	9:00 – 10:00 AM	10:00 – 11:00 AM	11:00– 12:00 NOON
ci
			cj

 

2. Meeting Time Complexity

If courses c_i and c_j hold in geographically dispersed Venues (R_nU_m, R_n+1U_m+1) and it takes a student time t_n to move from venue R_nU_m to R_n+1U_m+1, there exist a time complexity if course c_j starts immediately course c_i ends as shown in Table 9.

Table 9: Meeting Time Complexity (100%)

8:00 – 9:00 AM	9:00 – 10:00 AM	10:00 – 11:00 AM	11:00 – 12:00 NOON
ci
		cj

The 70% is for time to reach the venue and 100% is if there is additional time for the student to settle in the class before the actual lecture start time, an additional 30% weight is added. A 70% and a 100% resolution of the Meeting time complexity is as shown in Tables 10 and 11

 

Table 10: 70% Resolved Meeting Time Complexity

8:00 – 9:00 AM	9:00 – 10:00 AM	10:00 – 11:00 AM		11:00 – 12:00 NOON
ci
				cj

 

Table 11: 100% Resolved Meeting Time Complexity

8:00 – 9:00 AM	9:00 – 10:00 AM	10:00 – 11:00 AM	11:00 – 12:00 NOON
ci
			cj

 

5. Implementation Results and Discussions

The timetable showing schedules for two departments located at different campuses are used for the implementation of the proposed system.

These two departments offer common courses — CSC 211, STA 211, CSC 111. The natures of complexity are (meeting and overlapping times) clearly. Analysis of existing system shows the course under study, CSC 211 with Geo-informatics students in 300 level, who may be carrying over the course. It also handles the distance apart between the two campuses, being the venue for these two courses. Another case considers a complete overlap where CSC 211 and STA 211 from two different departments at two different venues, though in the same campus. Here, students of both departments are offering CSC 211. The analysis of these complexity levels with given assigned weights on the identified complexities is as shown in Table 12.

 

Table 12: Complexity weights of the existing time schedules

Case No	Complexity Type	Complexity Weight (%)
1	Meeting Time	100
2.	Overlapping Time (equals)	100

Figure. 5: Active Resolution of Meeting Time Complexity.

• Resolutions with proposed Time Scheduling system

To resolve the time schedules, the complexity weights of the two cases should be 30% and 0% for meeting time and overlapping time respectively. The screen shots in Figure 5 gives the resolution of the meeting time complexity for the scheduled GEO 211 and CSC 211. The screen shot also shows a prompt to reschedule the STA 212 course as shown on the white pop-up window.  That is the overlapping time complexity resolution, where the prompt calls for the relocation of the statistics (STA) course resulted. This is because CSC 211 is offered by many other departments, thereby having increased level of inter-dependency than the STA 212 course.

 

6. Conclusion

The proposed optimized time scheduling system analyzes any given existing time schedule and identifies the complexity types in existence. It provides the users the window to reschedule any time with identified complexity to obtain an optimized time schedule as shown in this paper. The rules in the reasoner are based on Allen’s interval-based temporal relations as well the domain specific relations. Knowledge management as seen in the university timetabling complexities is possible with the mapping of the departmental timetable ontologies shown in the ontograf with all other required resources in the databases of fact. As a further work, the formal model that describes how the embedded semantics in the given rules are used for inferencing will be implemented on the ontology.

1. P. U. Usip and M. M. Ntekop. “The use of ontologies as efficient and intelligent knowledge management tool”, In Proceedings of Future Technologies Conference. 6-7 December 2016, San Francisco. pp 626-631. DOI: 10.1109/FTC.2016.7821671
2. M. E. Saleh. Semantic-based query in relational database using ontology. Journal on Data and Knowledge Engineering. 2011.
3. J. Allen. Maintaining knowledge about temporal intervals. Communications of the ACM 26. 1983. (11): 832-843.
4. P. U. Usip and E. Umoren. Towards a formal interval-based temporal ontology for an optimized timetable management. In Proceedings of Transition from Observation to Knowledge to Intelligence Conference (TOKI 2016), Lagos. pp. 293-304
5. K. H. Shafa’amri and J. O. Atoum. A framework for improving the performance of ontology matching techniques in semantic web. International Journal of Advanced Computer Science and Applications, 2012. 3(1) 8-14.
6. B. Coppin. Artificial Intelligence Illuminated. Jones and Bartlett Publishers, Inc., 2004. Sudbury
7. D. Waltz. Artificial Intelligence: realizing the ultimate promises of computing, AI magazine. 1997) 18, 49–52
8. I. M. Jurisica and J. Eric. Ontologies for knowledge management: an information systems perspective. Knowledge and Information Systems. 2004. 6, 380–401. DOI 10.1007/s10115-003-0135-4
9. D. Abramson. Constructing school timetable using simulated annealing: sequential and parallel algorithm. 1991.
10. E. K. Burke and S. Petrovic. Recent research directions in automated timetabling. European Journal of Operational Research. 2002. 140. 266-280.
11. A. O. Modupe, O. E. Olusayo and O. S. Olatunde. Development of a university lecture timetable using modified genetic algorithm approach. International Journal of Advance Research in Computer Science and Software Engineering. 2014. 4. 163-168.
12. J. R Hobb and F. Pan. An ontology of time for semantic web. 2004. 3, 66-85.
13. M. Hamalatha, V. Uma and G. Aghila. Time ontology with reference event based temporal relation (RETR). International Journal of web and Semantic Technology (IJWSSY). 2012. 3.

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