An Interval-based Knowledge Model and Query ... - Semantic Scholar

An Interval-based Knowledge Model and Query Language for Temporal Information He Huang1,2 Zhongzhi Shi1 Xiaoxiao He2 Lirong Qiu1,2 Jiewen Luo1,2 1

Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences, P.O. Box 2704-28, Beijing 100080 China 2 Graduate School of the Chinese Academy of Sciences, Beijing, China {huangh,shizz,hexx,qiulr,luojw}@ics.ict.ac.cn

Abstract. Time plays a crucial role in describing dynamic domain and resources on the Web. Most of current ontology languages, without notion of time or change, can only describe domain knowledge in a static sense. In order to bring structure to time-varying information, we propose an interval-based knowledge model (IKM ), which is composed of a temporal knowledge schema, temporal integrity constraints and an interpretation structure. In the IKM , a group of expressive temporal constructs are provided to capture the temporal features of concepts, attributes and relationships; a group of rules are defined to enrich expressivity of the model; formal meaning is given to the model via an interpretation with model-theoretical semantics. A high-level query language is defined on the model, too.

1

Introduction

In a decade, the Web has become a new medium of communication for over ten millions users. Its exponential growing and HTML-based web pages prevent agents from locating and accessing web information automatically and efficiently. The ontology is a key foundation of solving this issue [1]. An ontology is to bring structure to the meaningful content of a domain and define a common vocabulary for people and agents to reuse and share domain knowledge across heterogeneous platforms. In the last decades, many web-based ontology languages have been created for implementing ontologies, including RDFS [2], DAML+OIL [3] and OWL [10], etc. However, these languages describe domain knowledge in a static sense. Having no notion of time or change, they may be adequate for some scientific and technical purposes which are mainly concerned with the latest findings or the current view of the world [4]. But they are unable to describe the temporal and behavioral aspects of dynamic domains where facts are often associated with timestamps. Time plays a crucial role in describing resources on the Web, too. For example, temporal constraints, such as planning and scheduling, may be very important in identifying and composing suitable resources. Modelling time-varying information has been witnessed to be a hotspot in both database-research and logics communities for decades [15][21]. Most re-

searchers in both communities have focused on temporally extending the existing models. These temporal extensions distinguish each other in different ways. Firstly, they differ on the notion of time: interval-based or point-based. Usually intervals are associated with states while time points with events [19]. Dichotomy exists between events and states, in that events delimit states. Duality exists too, in that states are represented by their delimiting events and events are implied by states. Secondly, they differ on the way of adding the temporal dimension: an explicit or implicit notion of time. In an explicit way, facts are timestamped and temporal operators are used; while in an implicit way, temporal information is only implicit in the sequence of activities. In this paper, we propose an interval-based knowledge model (IKM ) by temporally extending our previous work [13] and define a high-level query language on it. This model combines the expressive temporal constructs with a temporal interpretation structure. These temporal constructs can capture time-varying information modelled in both explicit and implicit ways, while the temporal interpretation structure assigns formal semantics to these constructs. And the design of IKM adheres to the following principles: – Both snapshot (nontemporal) and time-varying (temporal) data are supported; – Time interval can be attached to any construct of the model, i.e. concepts, attributes, and relationships; – Some dynamic features and temporal constraints can be captured; and – Consistency rules enforce a correct semantics of temporal information. The rest of this paper is structured as follows. Related work is examined in section 2. In section 3, we give some important definitions for modelling time and temporal information. The interval-based knowledge model is described in detail in section 4, and the query language on the model is defined in section 5. A conclusion and future research are presented in section 6.

2

Related Work

In database-research community, much attention has been cast on developing temporally enhanced ER models, e.g. TERM, TEER, TERC+, etc. These temporal ER models attempt to model the temporal aspects of information, such as valid and transaction time, in a natural and elegant way. Most of temporal ER models support both interval and instant, and extend ER model with temporal constructs. In TERM [5], the notion of history is introduced, and history structures are used to modelling the time-varying aspects of attributes and relationships. TEER [6], instead of adding new temporal constructs, adds new meaning to the existing EER modelling constructs to capture temporal information. TERC+ [17], in addition to the temporal constructs, introduces the dynamic relationship modelling, i.e., transition relationships, generation relationships and timing relationships, which are able to capture the implicit temporal features of some actions.

In description logics community, several approaches have been proposed for representing and reasoning time-dependent concepts. The temporal terminological logic presented in [7] introduces several new temporal operators for concept constructs, including the temporal qualifier at, the existential one sometime, and the universal one alltime, where the first one is used to specify the time while the others are used to constrain temporal variables. In [14], a variable-free extension with both existential and universal temporal quantifications is introduced to constrain temporal expressions on two intervals. Artale and Franconi [11] carefully reduce the expressivity of [7] and present decidable logics and reasoning algorithms. In [12], a new language ALCT is presented to combine the ALC with point-based temporal operators of tense logics, e.g., the Next instant operator, the Until operator, and the Since operator. Although both claiming to address the problem of model time-varying information and adopt the way of temporal extension, distinctions exist between temporal ER models and temporal Description Logics. And these distinctions mainly contribute to the different target communities and different functionalities of ER models and description logics. In database-research community, ER model has long been treated as a conceptual design model [8] rather than an implementation model. Therefore, temporal ER models are very expressive to describe temporal aspects of dynamic domains, usually with network-based structures but without form semantics. In contrast, Description Logics is a logical formalism and implementation model for knowledge representation systems. By carefully adding temporal operators to concept constructor, temporal description logics remain formal semantics and reduce reasoning complexity, but at the cost of expressivity. In order to keep a better balance between formal semantics and more expressivity, we develop an interval-based knowledge model composed of a temporal knowledge schema (in subsection 4.1), temporal integrity constraints (in subsection 4.2) and an interpretation structure(in subsection 4.3). The temporal knowledge schema, benefiting much from temporal ER models, is able to capture temporal information. The temporal integrity constraints can significantly improve the capacity of the schema in resource description. The interpretation model, benefiting from temporal Description Logics, assigns formal semantics to the schema. Before introducing the knowledge model, we first give some definitions of time model (in subsection 3.1) and temporal features (in subsection 3.2 and 3.3) that the knowledge model is to represent.

3

Model of Time and Temporal Features

In this section, we first give the model of time used in this paper, define timestamped concepts, attributes and relationships for explicit notion of time, and then define transition relationships for implicit notion of time.

3.1

Representation of Time

We adopt a linear discrete representation of time [14] in which the time axis is seen as a sequence of time points isomorphic to the set of natural numbers. Formally, a time domain is denoted as T = (Z, ≤), in which Z is a set of time points as primitive temporal entities which are ordered by a total ordering relation ’≤’. A time domain T is bounded if there exist zl , zu ∈ Z, such that zl ≤ z ≤ zu for all z ∈ Z. Time points are called instants. In addition to be identified by an integer, each instant can also be associated with a textual representation called label which is more descriptive than integer index. For example, if the time domain is to represent every day, then 6/1/2005 is a label referring to instant corresponding to that day. In this paper, we assume that the time domain is left bounded. One special instant called now is useful to express the meaning ”valid until further notice” [18]. An interval is a time slice defined by a start point and an end point, denoted as [l, u] or tul = {z ∈ Z|l ≤ z ≤ u}. An instant can be denoted as tzz or [z, z]. Note that intervals may be compared by using Allen’s interval logic [20] to show their relative positioning. A temporal element is defined as a finite set of time intervals. The time interval set T≤∗ is denoted as the set of time interval on T . Note that union, intersection and difference operations are defined on temporal elements. In executing these operations, interval merging or division may be needed. To illustrate this, consider two temporal elements S1 and S2 : S1 = {[10, 15], [20, ∞]}, S2 = {[4, 6], [18, 22]}, then S1 ∪ S2 = {[4, 6], [10, 15], [18, ∞]} S1 ∩ S2 = {[20, 22]} S1 − S2 = {[10, 15], [23, ∞]} S2 − S1 = {[4, 6], [18, 19]} In addition, two relational operators, overlaps and covers, are defined on temporal elements. Given two temporal elements S1 and S2 : if S1 ∩ S2 6= φ, then S1 overlaps S2 ; if S1 ∩ S2 = S1 , then S1 is covered by S2 , or S2 covers S1 . 3.2

Explicit Notions of Temporal Features

In the explicit way of adding temporal dimension, an object may be associated with certain periods during which it belongs to a class. Similarly, an attribute, as well as a relationship, may also be associated with certain periods of validity. Some explicit notions of temporal features are given in following. Definition 1. Given a concept Ci and its each object o, if the fact that o is an instance of Ci (o ∈ Ci ) only exists at certain periods, then Ci is called a temporal concept, o is said to undergo temporal variation with respect to instance-of link, and a temporal element composed of these periods is called the life span of the object, denoted as S(o ∈ Ci ) = {tul ∈ T≤∗ |o ∈ Ci is true during tul }.

For example, specifying Student as a temporal concept means that each person had studied, has studied, or will study in the university during different periods. Definition 2. Given a concept Cj and its each object o, if the fact that o is an instance of Cj (o ∈ Cj ) starts at a start point z and then lasts for ever, then Cj is called a nontemporal concept, o is said to undergo no temporal variation with respect to instance-of link. And its life span is S(o ∈ Cj ) = {tzzu } if the time domain is bounded, or S(o ∈ Cj ) = {t∞ z } if unbounded. Note that in definition 2, ”nontemporal” does not mean the objects are not timestamped. It rather means once an object is substantiated as an instance of a concept, it will be the instance of that concept for ever, esp. from a conceptual view. For example, Person is specified as a nontemporal concept, which means after born, a certain person will always be a person regardless of being dead or alive. If an object o has never been an instance of Cj then denotes S(o ∈ Cj ) = φ. Theorem 1. Given two concepts Ci and Cj , if Ci is a subclass of Cj , then each object o of Ci belongs to Cj , and temporal element S(o ∈ Ci ) is covered by S(o ∈ Cj ). Therefore, a temporal concept cannot have a nontemporal subclass. Definition 3. Given an attribute Ai of an object o of a concept Ci (denoted as o.Ai ), if the value of Ai may change over time, then Ai is called a temporal attribute, and the temporal element associated to each value x is called valid periods for o.Ai = x, denoted as S(o.Ai = x) = {tul ∈ T≤∗ |o.Ai = x is true during tul }; if its value keeps constant, then it is called a nontemporal attribute and its valid period is assumed to be equal to the life span of its host object, S(o.Ai = x) = S(o ∈ Ci ). For example, the rank of an instructor is a temporal attribute, which means its value may change from associated professor to professor. In contrast, the attribute birth is nontemporal. Note that defining a concept as temporal is independent of defining some of its attributes as temporal. But for a temporal attribute, the valid period of each of its values must be covered in the span of its host object. Theorem 2. Given an attribute Ai of an object o of a concept Ci , S(o.Ai = x) is covered by S(o ∈ Ci ). Definition 4. Given a relationship Ri between two concepts C1 and C2 , if the fact that Ri links two objects o1 and o2 , denoted o1 Ri o2 or Ri (o1 , o2 ), only exists in certain periods, then Ri is called a temporal relationship, and the temporal element composed of these periods is called valid periods of o1 Ri o2 , denoted as S(o1 Ri o2 ) = {tul ∈ T≤∗ |o1 Ri o2 is true during tul }; if the fact keeps constant, then it is called a nontemporal relationship and its valid periods are assumed to be the intersection of the spans of the two involving objects, denoted S(o1 Ri o2 ) = S(o1 ∈ C1 ) ∩ S(o2 ∈ C2 ).

For example, the ”directs” relationship between concept Instructor and concept Lab is temporal, which means an instructor can be dean of a lab in some times and not in other times. Usually, ”hasParent” is a nontemporal temporal, which means the child-parent relationship between two persons will never change after a child is born. Similarly, defining a concept as temporal is independent of defining some of its relationships to other concepts as temporal, too. For a temporal relationship, the active periods of each instantiation must be covered by the intersection of life spans of the participating objects; while for a nontemporal relationship, the active period is equal to the intersection. Therefore, a temporal relationship cannot have a nontemporal relationship as its sub-relationship. Theorem 3. Given a relationship Ri between two concepts C1 and C2 , if o1 Ri o2 , then S(o1 Ri o2 ) ∩ (S(o1 ∈ C1 ) ∩ S(o2 ∈ C2 )) = S(o1 Ri o2 ). Note that subclasses can inherit attributes and relationships from their superclasses. 3.3

Implicit Notions of Temporal Features

In the implicit way of adding temporal dimension, the relative positioning of activities models the inter-object dynamic aspects of applications. Some implicit notions of temporal features are given in following, by referring to [17]. Transition relationships express the behavior of an object that change from being an instance of a source concept to that of a target concept. The transition abstraction represents a become-a relationship. There are two types of transition, based on whether or not the object is preserved as an instance of the source class. An evolution occurs when the object ceases to be an instance of the source class. An extension occurs when the object remains an instance of the source class. A transition relationship, either evolution or extension, requires that the source concept and the target concept at least have one common superclass. Obviously, an evolution relationship can not connect two concepts in which the target concept is a subclass of the source concept, while an extension relationship can not connect two concepts that are disjoint to each other.

4

Interval-based Knowledge Model

Based on the definitions in section 3, an interval-based knowledge model is formally defined. This knowledge model is composed of temporal knowledge schema, temporal integrity constrains, and interpretation structure. The temporal knowledge schema (in subsection 4.1) is used to capture the agreed domain knowledge in a generic abstraction way. The integrity constraint (in subsection 4.2) is to significantly enrich the resource description and capture some concerned domain background knowledge. And the interpretation structure (in subsection 4.3) specifies the formal semantics of the temporal knowledge schema.

4.1

Temporal Knowledge schema

Definition 5. A temporal knowledge schema is denoted by T KS = (C, L, A, R, HC , HR , T R, IR) where – C is a set of abstract concepts or classes, e.g. publication, person, C = CN ∪ CT , where CN is the subset of nontemporal concepts, CT the subset of temporal concepts, and CN ∩ CT = φ; – L is a set of built-in data types, e.g., integer, string, time, C ∩ L = φ; – A is a set of attributes, A ⊆ C × L, A = AN ∪ AT , where AN is the subset of nontemporal attributes, AT the subset of temporal attributes, and AN ∩ AT = φ; – R is a set of relationships, R ⊆ C ×C, R = RN ∪RT , where RN is the subset of nontemporal relationships, RT the subset of temporal relationships, and RN ∩ RT = φ; REV ⊆ R denotes the subset of evolution relationships, while REX ⊆ R denotes the subset of extension relationships, and REV ∩REX = φ; – HC is concept hierarchy or taxonomy which denotes subclass-of links between two concepts, HC ⊆ {CN × CN } ∪ {CT × CT } ∪ {CT × CN }; – HR is relationship hierarchy or taxonomy which denotes subrelationship-of links between two relationships, HR ⊆ {RN × RN } ∪ {RT × RT } ∪ {RT × RN }; If R1 , R2 ∈ R, (R1 , R2 ) ∈ HR , then (dom(R1 ), dom(R2 )) ∈ HC , (ran(R1 ), ran(R2 )) ∈ HC ; – TR ⊆ R denotes a set of transitive relationships; – IR ⊆ {RN × RN } ∪ {RT × RT }, denotes pairs of inverse relationships; If R1 , R2 ∈ R, (R1 , R2 ) ∈ IR, then dom(R1 ) = ran(R2 ) and ran(R1 ) = dom(R2 ). 4.2

Temporal Integrity Constraints

The temporal integrity constraints can significantly improve the capacity of T KS and enrich the resource description. Usually they state rules applied in the real world of interest to normalize the resource modelling and to capture some concerned domain background knowledge. These rules use the vocabulary defined in the T KS to add additional axioms, which typically influence the reasoning with instances and can be used as a basis for error detection in constructing the instance base. There are several kinds of integrity constraints, referring to [16]. Description of general attributes General attributes with a range of values are simplest kinds of constraints on concepts. For example, the rank of an instructor in an institute must be associate professor or professor; the status of an instructor can be valued as full-time or part-time. Temporal Cardinality Constraints Temporal cardinality constraints are to fix both the minimum and maximum number of instantiations of a relationship in which an object can get involved during a certain period. The

statement of temporal cardinality constraints is in the form: [min, max]tul Ri , where min and max (min ≤ max) are positive integers called the minimum and the maximum cardinalities of the relationship Ri (∈ R) during tul . For example, any instructor can only manage at almost three projects at the same time, denoted as [0, 3]tul manages, where tul is the valid period of an project. Existence Dependencies A relationship or attribute value in certain periods can imply or exclude certain other relationships or attribute values in those periods. For example, any instructor who is associate professor currently can not advise a doctor student currently. 4.3

Interpretation Model

Definition 6. An interpretation structure of T KS with the interval set T≤∗ is denoted as I = (T≤∗ , ∆I , DI , ·I ), where – ∆I is an individual domain; – DI is a value domain with data types, e.g., integer, string, and ∆I ∩ DI = φ; – ·I is an interpretation function which fixes the extension of concepts, attributes and relationships - denoted with the letters Ci , Ai and Pi respectively - in such a way that: I • CiI → (T≤∗ → 2∆ ), each concept Ci is mapped to a function that assigns I(tu )

a set of individuals to each time interval; the notation Ci l stands for all the objects that belong to Ci during time interval tul , denoted as 0 0 I(tu ) Ci l = {o ∈ ∆I |∃tul0 ∈ S(o ∈ Ci ), tul ⊆ tul0 }; I I • AIi → (T≤∗ → 2∆ ×D ), each attribute Ai is mapped to a function that assigns a set of pairs of individual-value to each time interval; the no0 0 I(tu ) tation Ai l (o) = {d ∈ DI |∃tul0 ∈ S(o.Ai = d), tul ⊆ tul0 }, stands for all the values of Ai of o during ttl ; I I • RiI → (T≤∗ → 2∆ ×∆ ), each relationship Ri is mapped to a function that assigns a set of pairs of individuals to each time interval; the notation 0 0 I(tu ) Ri l (o) = {o0 ∈ ∆I |∃tul0 ∈ S(oRi o0 ), tul ⊆ tul0 } stands for all the objects that o is related to by the relationship Ri during tul . Definition 7. An interpretation I is a model of T KS if it satisfies following formulations: 0

0

0

I(tu ) l0

0

0

I(tu ) l0

u0 l0

u0 l0

1. ∀C1 , ∀tul , tul0 , tul ⊆ tul0 , ∀o ∈ C1 2. ∀Ai , ∀tul , tul0 , tul ⊆ tul0 , ∀d ∈ Ai 3. 4. 5. 6. 7.

0

0

I(tu l )

⇒ o ∈ Ci

I(tu l )

(o) ⇒ d ∈ Ai

I(tu ) Ri l0 (o)

(o)

I(tu ) Ri l (o)

∀Ri , ∀tul , t , tul ⊆ t , ∀o0 ∈ ⇒ o0 ∈ ∀Ci ∈ CN , ∀o, S(o ∈ Ci ) 6= φ ⇒ |S(o ∈ Ci )| = 1 ∀Ai ∈ AN , ∀o, S(o.Ai = x) 6= φ ⇒ |S(o.Ai = x)| = 1 ∀Ri ∈ RN , S(oRi o0 ) 6= φ ⇒ |S(o.Ri o0 )| = 1 I(tu ) I(tu ) ∀C1 , C2 , (C1 , C2 ) ∈ HC , ∀tul ⇒ C1 l ⊆ C2 l

8. ∀C1 , C2 , (C1 , C2 ) ∈ HC , ∀o ⇒ S(o ∈ C1 ) ∩ S(o ∈ C2 ) = S(o ∈ C1 ) 9. ∀o, ∀Ci , ∀Ai , o ∈ Ci , Ci .Ai ⇒ S(o.Ai = x) ∩ S(o ∈ Ci ) = S(o.Ai = x) 10. ∀Ci , Cj , (Ci , Cj ) ∈ Ri , ∀o, o0 , oRi o0 ⇒ S(oRi o0 ) ∩ (S(o ∈ Ci ) ∩ S(o0 ∈ Cj )) = S(oRi o0 ) I(tu )

I(tu )

11. ∀R1 , R2 , (R1 , R2 ) ∈ HR , ∀tul , ∀o ⇒ R1 l (o) ⊆ R2 l (o) 12. ∀R1 , R2 , (R1 , R2 ) ∈ HR , ∀o, o0 , oR1 o0 ⇒ S(oR1 o0 ) ∩ S(oR2 o0 ) = S(oR1 o0 ) 13. ∀Ri ∈ REV ∪ REX , ∀Ci , Cj , (Ci , Cj ) ∈ Ri ⇒ ∃Ck , (Ci , Ck ) ∈ HC , (Cj , Ck ) ∈ HC 14. ∀Ri ∈ REV , ∀Ci , Cj , (Ci , Cj ) ∈ Ri , ∀o, o0 , o ∈ Ci , o0 ∈ Cj , oRi o0 , ∀tul ∈ S(oRi o0 ) ⇒ 0 00 0 00 ∃tul0 ∈ S(o ∈ Ci ), ∃tul00 ∈ S(o ∈ Cj ), tul0 meets tul , tul meets tul00 15. ∀Ri ∈ REX , ∀Ci , Cj , (Ci , Cj ) ∈ Ri , ∀o, o0 , o ∈ Ci , o0 ∈ Cj , oRi o0 , ∀tul ∈ 0 00 0 0 00 S(oRi o0 ) ⇒ ∃tul0 ∈ S(o ∈ Ci ), ∃tul00 ∈ S(o ∈ Cj ), tul ⊆ tul0 , tul00 ⊆ tul0 , tul 00 meets tul00 I(tu )

I(tu )

16. ∀Ri , ∃tul , [min, max]tul Ri , ∀o, Ri l (o) 6= φ ⇒ min ≤ |Ri l (o)| ≤ max 17. ∀Ri ∈ T R, ∀o1 , o2 , o3 , o1 Ri o2 , o2 Ri o3 ⇒ o1 Ri o3 , S(o1 Ri o3 ) = S(o1 Ri o2 ) ∩ S(o2 Ri o3 ) 18. ∀Ri , Rj , (Ri , Rj ) ∈ IR, ∀o1 , o2 , o1 Ri o2 ⇒ o2 Rj o1 , S(o1 Ri o2 ) = S(o2 Rj o1 ) 19. Other domain specific integrity constraints. Among above formulations: 1-3 state if a fact is true in tul , it will be also true in an interval covered by tul ; 4-6 state that each temporal element associated to nontemporal concepts, nontemporal attributes, or nontemporal relationships contains only one interval; 7 and 8 are about theorem 1 (see subsection 3.2); 9 and 10 state theorem 2 and theorem 3 respectively (see subsection 3.2); 11 and 12 state properties satisfied by a couple of superclass and subclass; 13, 14 and 15 state properties associated with transition relationships, evolution relationships and extension relationships respectively (see subsection 3.3); 16 states temporal cardinality constraints on relationships (see subsection 4.2); 17 states the transitive relationship; and 18 states two inverse relationships.

4.4

A Case for Study

A simplified interval-based knowledge model for research lab is presented as a running example throughout this paper, shown in figure 1.

5

Temporal Query Language

In this section, we will present a temporal query language for the interval-based knowledge model. We first discuss the types of temporal constructs incorporated in the query language (in subsection 5.1), and then define the specification of temporal queries and given some examples (in subsection 5.2).

Fig. 1. A simplified interval-based knowledge model for research lab

5.1

Temporal Boolean Expression, Selection and Projection

A query will typically select certain objects based on conditions that involve attributes and relationships of objects. In addition, once an object is selected, the user may be interested in displaying the complete history (temporal assignment) of some of its attributes or relationships, or limit the displayed values to a certain time intervals. To allow for temporal constructs in queries, we will define the concepts of temporal Boolean expression, temporal selection conditions, and temporal projection, by referring to [16]. Temporal Boolean Expression A temporal Boolean expression is a conditional expression on the attributes and relationships of an object associated with a temporal interval or a temporal element. There are two kinds of temporal Boolean expression. The first kind, based on temporal intervals, is to express conditional expression on the attributes and relationships of an object under some temporal constraints. It is in the form: expr rel interval, where expr is a conditional expression, rel is an interval relation (Allen’s 13 interval relation, e.g., before, equals), interval is a time interval. For example, a temporal Boolean expression can be: ((x.rank = ”Prof.”) ∧ (x.status = ”full-time”)) before tul This expression evaluates to true, when applied to an instructor who has or had already been a full-time professor before tul , or else to false. The second, based on temporal elements, is to compare two temporal elements in the form: te op te, where te is a temporal element, op is a set comparison operation, such as =,6=,⊆,⊇, covers, overlaps, on temporal elements. Here, an operator [expr] is introduced to get the temporal element during which expr is true. An example of [expr] is shown below: [(x.rank = ”Prof.”) ∧ (x.status = ”full-time”)] = [(x.rank = ”Prof.”)] ∩ [(x.status = ”full-time”)] An example of a temporal Boolean expression based on temporal elements can be: [directs(x, lab1)] covers {[1/1/2002, 12/31/2002], [1/1/2004, now]} This expression evaluates to true, when applied to an instructor who had been dean of lab1 during the year 2002 and has been dean since 1/1/2004, or else to false. Temporal Selection Temporal selections are used to select particular objects based on temporal Boolean expressions. A temporal selection condition, when applied to a concept, evaluates to those objects that satisfy the condition. For example, consider the following temporal selection condition applied to the Student concept: [joins(x, team1) AND advised-by(x, instructor1)] covers {[now, now]}

which is to select all students who are members of team1 and are advised by instructor1 now. The condition is evaluated for each student individually, and returns those that have a Yes answer. Temporal Projection Temporal projections are used to limit data displayed for the selected objects. A temporal projection is applied to an object and restricts all temporal assignments to a specific time interval for some attributes and relationships of that object. For example, a temporal projection hx.rank, x.statusi : [now, now] is to display the current rank and status of the selected instructors. 5.2

Specification of Temporal Queries

In this subsection, we develop a high-level declarative query language on the interval-based knowledge model. The basic syntax of the language is in the form: Query::=SelectClause FromClause (WhereClause)? SelectClause::=SELECT *|(TemporalProjection)+ FromClause::=FROM Source Source::=hURIi WhereClause::=WHERE (TemporalSelection)( AND TemporalSelection)∗ TemporalProjection::=Fields|hFieldsi:TemporalInterval Fields::= (Attribute)(, Attribute)∗ TemporalSelection::=TBooleanExpr1|TBooleanExpr2 TBooleanExpr1::=(BExpr) IntervalRelation TemopralInterval TBooleanExpr2::=(TemporalElement|TExpr) EleComp (TemporalElement|TExpr) BExpr::=Expr(∧ Expr)∗ TExpr::=[BExpr] Expr::= CExpr|AExpr|RExpr CExpr::=(Oject∈Concept) AExpr::= (Oject.Attribute Comp Value) RExpr::= Relationship(Object,Object) TemporalElement::={TemporalInterval(,TemporalInterval)∗ } TemporalInterval::=[TimePoint,TimePoint] IntervalRelation::=equal|meets|met-by|after|before|overlaps|overlapped-by |starts|started-by|finishes|finished-by|during|contains EleComp=⊂ | ⊆ | = |covers|overlaps Comp::=< | ≤ | > | ≥ | = Concept::=symbol Object::=symbol|Var Attribute::=symbol Var::=?symbol Relationship::=symbol TimePoint::=number|symbol|now URI::=symbol In following, some examples are given to illustrate the specification.

Example 1. Find all the instructors who are professor currently, and display their rank and status during the year 2002. SELECT h?x.rank, ?x.statusi : [1/1/2002, 12/31/2002] FROM hhttp://www.somewhere.edu.cn/km/i WHERE((?x ∈Instructor)∧(?x.rank=”Prof.”)) meets [now,now ] Example 2. Display the ID and budget of each project that managed by an instructor, and during the management, the instructor had or has been dean of the AI lab. SELECT ?x.PID, ?x.budget FROM hhttp://www.somewhere.edu.cn/km/i WHERE [(?y ∈ Dean)∧(?z ∈ Lab)∧(?z.name = ”AI”)∧directs(?y, ?z)]covers[(?x ∈ Project) ∧ manages(?y, ?x)] Example 3. Display the name of each graduated student that had been worked for the project with ID prj123. SELECT ?x.name FROM hhttp://www.somewhere.edu.cn/kmi WHERE ((?x ∈ Student)before[now, now])and([(?y ∈ Team)∧joins(?x, ?y)] overlaps[(?z ∈ Project) ∧ (?z.PID = ”prj123”) ∧ takes(?y, ?z)])

6

Conclusion and Future Works

Although temporal ER models and temporal Description Logics share similarity in adding temporal dimension into existing models, distinctions mainly caused by different targets and functionalities of ER model and description logics exist. Temporal ER models, mainly for human users, are very expressive in conceptual design. In contrast, temporal description logics, only providing temporal concept constructors, mainly focus on automatic reasoning on temporal concepts. In this paper, we propose an interval-based knowledge model to combine advantages of the two areas. In the model, a temporal knowledge schema is defined to provide a group of temporal constructs which are expressive enough to capture not only the temporal features of concepts, attributes and relationships, but also some dynamic features. An interpretation structure is carefully defined to give formal semantics to the schema. A high-level temporal query language is also defined based on the knowledge model. Temporal Boolean expressions, temporal selections and temporal projections greatly enrich the functionalities of the query language and facilitate manipulation over time varying information. But our work has some drawbacks. Firstly, the interval-based knowledge model cannot support time granularity yet. Secondly, some features supported by the model, such as transitive relationships and transition relationships, are not reflected in the query language. In the future, we are planning to improve the model in these aspects.

7

Acknowledgements

This work has been funded by the National Basic Research and Development Plan of China (Grant No. 2003CB317004) and the National High-Tech Program of China (Grant No. 2003AA115220).

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