Context in Artificial Intelligent and Information Modeling

Transcription

1 Context in Artifiial Intelligent and Information Modeling Manos Theodorakis ½ and Niolas Spyratos ¾ ¾ ½ FIT-Fraunhofer Institute for Applied Information Tehnology, D-53754, Sankt Augustin, Germany Universite de Paris-Sud, LRI-Bat 490, Orsay Cedex, Frane Abstrat. The modeling, representation and use of ontext is the hallenge for the oming years in Artifiial Intelligene, espeially when we now fae very large knowledge bases, omplex problems and multimedia means. The notion of ontext is important sine it an apture many of the interesting aspets of the way we understand the world, suh as relativity, loality, partiality, and ontextdependene. In Artifiial Intelligene, a number of formal or informal definitions of some notion of ontext have appeared in several areas. However, all these notions of ontext are very diverse and serve different purposes. In this paper, we give an overview of the notion of ontext in Artifiial Intelligene and we fous in information modeling to present our approah of how to model ontext. In partiular, we present a ontext-based model for struturing and aessing information in large information bases. Keywords: Context, ontextualization, knowledge representation, information modeling, ontextual knowledge, ontextualized knowledge, abstration mehanisms. 1 Introdution The notion of ontext plays an important role in a number of domains and it is of fundamental importane in ognitive psyhology, linguistis, and omputer siene. In omputer siene, a number of formal or informal definitions of some notion of ontext have appeared in several areas, suh as artifiial intelligene [17, 20, 15], software development [25, 14], databases [2, 13], mahine learning [23], and knowledge representation [24, 35, 39, 34, 40]. However, all these notions of ontext are very diverse and serve different purposes. In software development the notion of ontext appears in the form of views [2, 13], aspets [25], and roles [14], for dealing with data from different perspetives, or even in the form of workspaes whih are used to support ooperative work [19]. In mahine learning, ontext is treated as environmental information for onept lassifiation [23]. In the so alled multiple databases, ontext appears as a olletion of meta-attributes for apturing lass semantis [18]. In artifiial intelligene, the notion of ontext appears as

2 a means of partitioning knowledge into manageable sets [17], or as a logial onstrut that failitates reasoning ativities [20, 15]. In partiular, in the area of knowledge representation, the notion of ontext appears as an abstration mehanism for partitioning an information base into possibly overlapping parts (e.g. [24, 34, 39, 40, 11, 31, 9, 8]). The modeling, representation and use of ontext is the hallenge for the oming years, espeially when we now fae very large knowledge bases, omplex problems and multimedia means. The notion of ontext is important sine it an apture many of the interesting aspets of the way we understand the world, suh as relativity, loality, partiality, and ontext-dependene. In Artifiial Intelligene, the lak of expliit representation of ontext is one of the reasons of the failure of many Knowledge-Based Systems [5]. In this paper, we examine different representations of the notion of ontext in Artifiial Intelligene and we present our approah of how to model ontext. Finally, we ompare all these approahes based on speifi riteria on modeling ontexts. In this paper, we review the notion of ontext in different areas in Artifiial Intelligene and we present an approah of modeling the notion of ontext. In partiular, we present a ontext-based model for struturing and aessing information in large information bases. A ontext is seen as a set of objets within whih eah objet has a set of names and optionally a referene: the referene of the objet is just another ontext whih hides detailed information about the objet. In Setion 2, we review different formalizations of ontext in Artifiial Intelligene. In Setion 3, we fous on the area of information modeling and we present our approah of modeling the notion of ontext, and in Setion 4, we ompare these approahes aording to speifi riteria for modeling ontext. 2 Context in Artifiial Intelligene 2.1 Situation Theory Contexts has been onsidered in the basis of Situation Theory [3]. Situation Theory is a unified mathematial theory of meaning and information ontent that is applied to speifi areas of language, omputation and ognition. The theory deals with situations and meaning (as a relation between situations). The notion of ontext is represented by situations. Situations are first-lass itizens of the theory and are defined intentionally. A situation is onsidered to be a strutured part of the reality, that an agent (somehow) manages to pik out, and to whih sentenes in a theory are stated. Speifially, the work of Barwise and Perry on situated reasoning and semantis [3] is motivated by interest in dealing with effiieny of language (all qualifiations for John an run are aptured in the ontext of the sentene s utterane), partiality of information (the symbol flower is meaningless in a theory of omputer network), and self-referene (the utterane This is an embarrassing moment would be made in some situation but learly refers to the same situation ). Surav and Akman [30] (mainly inspired by Barwise and Perry s work) approahes ontext as an amalgamation of grounding situation and the rules that govern the relations within the ontext. They present a ontext by a situation type that supports two

3 types of infons: parameter free infons to state the fats and the usual bindings. Parametri infons (whih orresponds to parametri onditionals) aim at apture the if-then relations and axioms within the ontext. 2.2 Situation Calulus The simplest approah to representing that the value of some prediate or funtion symbol is dependent on some situation or ontext is to add a ontext argument to the list of arguments for eah prediate and funtion in the theory [22]. For example, the prediate ÓÒ ÐÓ ½ ÐÓ ¾ µ is written as ÓÒ ÐÓ ½ ÐÓ ¾ ½ µ. This allows one to stay within a lassial first-order framework and apture a simple form of ontext-relativity for formulae. While adequate for many pragmati ases for ontexts, this approah is inadequate for dealing naturally with strutured spaes of ontexts, ontext-speifi voabularies and ontext inheritane. A problem, for example, of this approah is that it does not allow a prediate to have different arguments in different ontexts as it does not provide adequate namespae separation between theories. 2.3 Context in first-order logi Motivated by the observation that one an never represent an objet in omplete generality, MCarthy [20] introdued the notation Ø Ôµ (pronouned as is true ) meaning that a logial sentene Ô holds in the ontext,where is meant to apture all that is not expliit in Ô that is required to make Ô a meaningful statement represented what it is intended to state. Formulas Ø Ôµ are always asserted within a ontext, i.e., something like Ø ¼ Ø Ôµµ. The most important in this theory the writing of axioms desribing and interrelating ontexts. Then, the most ommon operation is to lift a formula from one ontext into another. Doing this requires the differenes between the origin and target ontexts to be taken into aount to obtain a formula with the same truth onditions as the origin formula had in the origin ontext. There are many other relations among ontexts, for example, the relation Ô Ð Þ ½ µ, that indiates ¾ involves no more assumptions than ½ and every proposition meaningful in ½ is translatable into one meaningful in ¾. The onsequenes are: (i) ontexts annot be desribed ompletely, (ii) propositions and ontexts are always relative to another ontext, (iii) ontexts an be nested in any depth, (iv) ontexts are related among others with different relations, (e.g., lifting axioms from one ontext to another, speialization of ontexts). One of the first attempts at formalizing ontext under MCarthys supervision was presented by Guha [15]. Motivated largely by his work in the Cy projet, an attempt to build an extremely large knowledge base to support ommon-sense reasoning, Guha observed that without struturing the voabularies and sentenes of the system, it was nearly impossible to onstrut Cy without running into inonsisteny and a proliferation of qualifiations for non-logial symbols when stating sentenes. Contexts also enabled the Cy designers to state theories at different levels of detail and to have Cy employ the appropriate theory. Thus, Guha treated a ontext as having a voabulary and a set of possible truth assignments assoiated with it so that the formula Ø Ôµ holds

4 if Ô is true in all the valid truth assignments for ontext. Contexts are formalized as first lass objets. Sine then, ontexts have found uses in various artifiial intelligene appliations, inluding: translating knowledge [6], modeling knowledge and belief [12], integrating heterogeneous databases [10], planning [7], ommon sense reasoning [21]. Coherently with the notion of ontext desribed above, Attardi [1] uses viewpoints to represent the notion of relativized truth suh as beliefs, situations and knowledge. Viewpoints denote sets of sentenes whih represent the assumptions of a theory. 2.4 Context in ategorization Categorization is one of the basi mental proesses in ognition. We, as human beings, an ategorize various types of objets, events, and states of affairs, and our ategorizations depend on the irumstane and perspetive (i.e., how things are depend on one s point of view on them). Barwise and Sligman [4] use natural regularities to study the role of ontext in ategorization. To be more speifi onsider the following example of regularity as it appears in [27]: swans are white, whih express an intuitive sense that all swans are white. Although this is the general intuition about swans, there might be exeptions and we an find swans whih are blak (this an happen in Australia). Therefore, this sentene an be evaluated only in appropriate ontexts, suh as in Europe, outside zoos, and so forth. The appropriate ontext wouldn t be a problem if we ould ompletely speify all ontextual fators. However, in many ases it is impossible to state all the relevant ontextual fators. In [4], a notion of ontext is aptured through the notion of perspetive. Different perspetives simply give rise to different ways of lassifying things. For example, distanes an be lassified using either inhes from Manos perspetive or entimeters from Niolas perspetive. 2.5 Graphial Representation of Context A preursory idea of ontext an be traed bak to Peire s existential graphs [26]. Existential Graphs use a logial form of ontext alled a ut whih shows in a topologial manner the sope of a negative ontext on a sheet of paper (the sheet of assertion). Sowa [28,29] introdued oneptual graphs (CG) as an extension of the existential graphs and defined ontexts as onepts whose referent ontains one or more CG. The ontexts are treated as first-lass objets and are embeddable in graphs. Hendrix [16, 17] expanded semanti networks (based on existential graphs) through partitioning ontexts. Unlike Peire, Hendrix allowed overlapping ontexts. Some problems with CG ontexts are that inheritane an only follow the tree struture formed by the embedding of the ontexts and runs from the hild to the parents (ollapsing of ontexts). Furthermore, lifting axioms for ontexts an only be written by resorting to the meta-level failities of CGs, writing meta-level rules.

5 3 Context in Information Modeling 3.1 The notion of ontext Suppose we want to talk about Greek islands by simply using their names without further desription. Let us onsider the island of Crete. We an represent this island by an objet identifier, sayó ½ assoiated with the name Ö Ø. We write Ò Ñ Ó ½ µ Ö Ø and we denote this as follows 1 : Ö Ø Ó ½ Next, let us onsider the island of Santorini. Following a similar approah, we represent this island by an objet identifier Ó ¾ assoiated with the name Ë ÒØÓÖ Ò.However, the island of Santorini is also known under the name Thera. So this time, we assoiate Ó ¾ with the set of names Ë ÒØÓÖ Ò Ì Ö,i.e.Ò Ñ Ó ¾ µ Ë ÒØÓÖ Ò Ì Ö, and we denote this as follows: Ë ÒØÓÖ Ò Ì Ö Ó ¾ Finally, let us onsider one of those tiny, uninhabited islands of Greee that happen to be nameless. We represent suh an island by an objet identifier Ó assoiated with no name, i.e. Ò Ñ Ó µ, and we denote this as follows: Ó Continuing in the same way, we an represent every Greek island in a similar manner. The set of all suh representations is a ontext that we represent by a ontext identifier,say ½. Suppose next we want to talk about the Greek mainland by simply using the names of eah region of Greee without further desription. Proeeding in a similar way as in the ase of Greek islands, we an reate a seond ontext, say ¾, as shown in Figure 1. Suppose now that we want to talk about the geography of Greee seen as a division of Greee into islands and mainland. First, let us onsider the islands. We an represent the islands by an objet identifier, say Ó, and assoiated with the name Á Ð Ò. However, the objet Ó is a higher level objet that olletively represents all Greek islands, i.e. the objet Ó olletively represents the ontents of ontext ½. In other words, if we want to see what Ó means at a finer level of detail, then we have to look into the ontents of ½. Thus we all ontext ½ the referene of objet Ó, and we write Ö Óµ ½. Summarizing our disussion on islands, we write Ò Ñ Óµ Á Ð Ò and Ö Óµ ½, and we denote this as follows: Islands : o 1 Following a similar reasoning, we an represent the mainland by an objet identifier, say Ó ¼ assoiated with the name Å ÒÐ Ò and the referene ¾. We an now group together the islands and the mainland to form a ontext, as shown in Figure 1. Then, geography of Greee an be represented by an objet identifier Ó ¼¼ assoiated with ontext, as shown in Figure 1. The previous examples suggest the following definition of a ontext [35, 32]: Definition 31 Context. A ontext is a set of objets suh that eah objet Ó is assoiated with 1. a set of names, alled the names of Ó in, and denoted by Ò Ñ Ó µ; 1 In this paper, the terms objet and objet identifier will be used interhangeably.

6 Geography_of_Greee: o Tourist_Guide: o 4 Islands: o Mainland: o 3 Crete: o1 MapOfGreee: o Athens: o Crete: o1 Santorini, Thera: o : o 2 Peloponnese: o6 Maedonia: o Thrae: o LoalInfo, Hotels: o LoalInfo, Dining: o MapOfCrete: o Transportation: o Fig. 1. An example of ontext struture. 2. zero or one ontext, alled the referene of Ó in, and denoted by Ö Ó µ. The reason why we use the symbols Ò Ñ Ó µ and Ö Ó µ in the above definition, instead of the symbols Ò Ñ Óµ and Ö Óµ used in the previous examples, is that an objet an belong to different ontexts and may have different names and/or referene in eah ontext. That is, names and referenes of an objet are ontext-dependent. In our previous examples, while explaining the onstrution of a ontext, we followed a bottom-up approah. That is, we started from simple objets and built up ontexts whih were later on referened by higher level objets ( moving from right to left in Figure 1). Clearly, we ould have followed the opposite onstrution, i.e. a top-down approah ( moving from left to right in Figure 1). In fat, we an even follow a mixed approah, i.e., reating eah ontext independently, then onneting them through referenes. This flexibility is important in oneptual modeling and implies (among other things) the possibility of modular design, i.e. retaining at eah level of abstration the essential information and hiding inessential details (by putting them in a referened ontext). It is important to note that an objet an have two or more names within a ontext and that two different objets an have one or more names in ommon. Moreover, an objet an have no name within a ontext. In other words, our ontextualization mehanism supports synonyms, homonyms,andanonyms. It is also important to note that our ontextualization mehanism does not depend in any partiular data model, but it an be easily embedded in any one [35, 32]. For example, the objets of a ontext an be objets from an objet-oriented database, or tuples from a relational database, or the results of queries in an objet-oriented or a relational database, and so on. This is why we do not speify the nature of the objets in a ontext. Let us now onsider another example, shown in Figure 2, whih represents the views of two persons regarding an institute. Context Á ontains two objets, Ó ½¼ and Ó ½½, namely Å ÒÓ Î Û and Ò Ø Î Û, respetively. These objets represent the views of Manos and Anastasia regarding the same institute. These views are presented in detail within ontexts ½ and (the referenes of objets Ó ½¼ and Ó ½½, respetively).

7 IB ManosView: o AnastasiaView: o Dr_Smith: o1 : o 4 professor: o5 InfSys: o DSS: o Smith: o1 professor: o5 ISgroup: o DSS: o Yannis: o1 head: o 2 Manos: o3 Niolas, Nik: o 5 Yannis: o6 head: o John: o John, Yannis: o Anastasia: o 1 7 Fig. 2. An example of ontext struture: Two views of the same institute. Note that objet Ó ½ (whih represents a person) is shared by several ontexts ( ½, ¾,,,and ) and is assigned different names within eah of these ontexts. Note also that objet Ó (whih represents the Information Systems Lab of the institute) refers to the same ontext ¾ either within ontext ½ or. Intuitively, this expresses that Manos and Anastasia have the same view for the Information Systems Lab. Whereas objet Ó (whih represents the Deision Support Systems Lab) refers to ontext within ontext ½ andtoontext within ontext. Intuitively, this expresses that Manos and Anastasia have different views for the Deision Support Systems Lab. Let us summarize the features of ontext supported by ontext definition: 1. Objet sharing or overlapping ontexts: An objet an belong to one or more different ontexts. When ontexts share objets we say that ontexts overlap. This feature is useful when we want to view an objet under different perspetives. 2. Context-dependent objet names: The same objet an have different names in different ontexts (in whih it belongs). This is very onvenient, beause a name whih has a learly understood meaning in one ontext may not do so in another. 3. Synonyms: The same objet an have different names in the same ontext. That is, alternative ways for naming the same objet are supported. This is the ase of synonymous objets. 4. Homonyms: Two different objets an have the same name within a ontext. This is the ase of homonymous objets. 5. Anonyms: An objet may have no name within a ontext. This is the ase of anonymous objets. 6. Context-dependent referenes: The same objet an have different referenes within different ontexts. In other words, referenes are ontext-dependent. 7. Two different objets, whether or not they belong to the same or different ontexts, an have the same referene. This is onvenient, as a given ontext an be reahable through different objet paths.

8 8. From within a given ontext, we an reah any objet that belongs to the referene of an objet within that ontext (and, reursively, any objet that lies on a path). A prominent feature of our ontextualization mehanism is that it allows users to fous on a speifi ontextat a time (all it urrent ontext), thus delimiting a portion of interest in the information base. As a onsequene, the sope of user queries is loalized to that portion, i.e., to the set of objets and ontexts that are aessible from the urrent ontext. In turn, query evaluation is performed with respet to that portion of interest and not with respet to the whole information base. As a result, users an find speedily the needed information. An other important feature is that users are able to make ross referenes of an objet from one ontext to another in order to obtain alternative representations of that objet. Note that, in first-order logi, to make ross referenes it is needed to defined in an outer ontext lifting axioms. In this theory, this is done through the objet identity. 3.2 Operations on ontext Moreover, we define a set of operations for manipulating ontexts [38, 34, 33]. These operations support ontext reation, update, opy, union, intersetion, and differene. In partiular, our operations of ontext union, intersetion, and differene are different from these of set theory as they keep trak of the ontext involved. However, they also satisfy the important properties of ommutativity, assoiativity, and distributivity. Our model ontributes to the effiient handling of information, espeially in large information systems, and in distributed, ooperative environments, as it enables (i) representing (possibly overlapping) partitions of an information base; (ii) partial representations of objets, (iii) flexible naming (e.g. relative names, synonyms and homonyms), (iv) fousing attention, (v) handling inonsistent information, and (vi) ombining and omparing different partial representations. 3.3 Struturing the ontents of a ontext Then, we show how a partiular semanti data model (the Telos data model) an be inorporated into the proposed ontextualized framework [35, 36]. Thus, we enhane our notion of ontext by struturing its ontents through the traditional abstration mehanisms, i.e., lassifiation, generalization, and attribution. We show that, depending on the appliation, our notion of ontext an be used either as an alternative way of modeling or as a omplement of the traditional abstration mehanisms. It is important that we study the interations between ontextualization and the traditional abstration mehanisms as well as the onstraints that govern suh interations. In that study, we define also the relation refinement between ontext to support a kind of inheritane of their ontents. 3.4 Querying ontextualized information Contextualized information bases need a speial treatment in order to answer queries. Thus, we propose a general framework for querying information bases whih supports

9 ontextualization [37]. In partiular, we fous on the following issues: (i) aessing information in a ontext struture using paths of names or paths of referenes, (ii) retrieval of ontextualized information by defining useful fundamental query operations on ontexts suh as selet, projet, generate (whih allows the reorganization of ontexts struture), and path selet. In addition to the fundamental operations there are several other derived operations, suh as ontext union, ontext intersetion,andontext differene. We extend the funtionality of querying by allowing traversal of the ontext hierarhy using omplex path expressions. Finally, we illustrate the usefulness of our ontextualization mehanism by presenting higher level query operations that enable users to explore a ontextualized information base. These higher level operations inlude fousing on a ontext of interest, searhing the ontext struture for speifi information, and making ross referenes of a onept from one ontext to another in order to obtain alternative representations of that objet. 4 Comparison It is unlikely that there will be a single ontext formalism that will suffie for all forms of ontext, just as there is no universal knowledge representation language. The following riteria have been identified for omparing the different approahes for formalizing ontext: CFCO: ontexts as first lass objets CSV: ontext speifi voabulary CSS: ontext speifi semantis Nest: nesting of ontexts (subontexts) Inh: inheritane through ontexts SR: self-referene Table 1 shows a omparison of the main approahes for formalizing the notion of ontext examined in this paper (ST: Situation Theory, SC: Situation Calulus, FOL: first-order logi, CG: Coneptual Graphs, IM: Information Modeling). ST SC FOL CG IM CFCO CSV CSS Nest Inh SR Table 1. Comparison of properties of ontext

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