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Foundations of Ontology Reconciliation

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Foundations of Ontology Reconciliation Chapter 3 Foundations of Ontology Reconciliation Concepts without percepts are empty, percepts without concepts are blind. Immanuel Kant (A critique of pure reason, 1781) This chapter aims at providing a theoretical basis for ontology reconciliation. This leads to philosophical topics such as what meaning is and how it can be represented in an ontology. As innocent as these issues might appear, they open a Pandora’s Box of problems. Our discussion is limited to those issues that are relevant for the current investigation. Section 3.1 presents a brief analysis of meaning from a semiotic perspective. Section 3.2 discusses how meaning can be satisfactorily represented. In particular, we describe Tarskian semantics, its shortcomings, and a way to overcome these problems. Section 3.3 elaborates on these ideas and argues how automatic ontology mapping can be established. Furthermore, we compare our approach to ontology reconciliation with other approaches. We conclude in Section 3.4. 3.1 Meaning We start our discussion with an analysis of meaning in the context of semiotics, i.e. the study of signs, symbols and meanings. One of the founders of semiotics is Charles Sanders Peirce (1839-1914). His account of meaning is discussed below. 3.1.1 The Peircean Model In the model of Peirce, a sign is assumed to consist of three parts, yielding a triadic model (Chandler, 2002). Whereas many authors have accepted the presence of three 40 Foundations of Ontology Reconciliation thought or reference symbol referent Figure 3.1: The Peircean model of a sign components of a sign, there is no consensus on the names of these components and their exact details. In our discussion, we adopt the names that are used by Ogden and Richards (1923) and try to stay away from as many controversial issues as possible. Peirce’s triadic model is often represented as a triangle with the three compo- nents at its corners, as depicted in Figure 3.1. The first part of the sign is the symbol and regards the form which the sign takes. The second part is the thought or reference, which regards the sense made of a sign. The third part is the referent, i.e. that to which the sign refers. Each of the three components is discussed in more depth below. Symbol A symbol can be many things, such as a word, an image or a sound. When someone interprets a symbol as standing for something else, the symbol can be viewed as one of the three components that make up a sign. Many semioticians, among whom de Saussure and Peirce, have argued that symbols may be completely arbitrary, i.e. no natural connection may exist between a symbol and what it stands for. For this reason, Figure 3.1 shows the link between the symbol and the referent as a dashed line. According to Peirce, signs may be arbitrary in different degrees. An example of a sign that is not completely arbitrary is an icon. An icon is a sign in which the symbol resembles what it stands for in some way. An example of an icon is , commonly used for representing an airport. This sign qualifies as an icon for airports because it resembles, in some sense, the shape of an airplane. Other examples of icons are onomatopoeia, i.e. words that sound similar to what they refer to, such as "cuckoo" and "boom". Nevertheless, most symbols in a language are not iconic, but, as Peirce calls it, symbolic. A word such as "airplane" bears no natural relation to a real airplane, not in shape, neither in sound. Also, the concept-names in an ontology and the bit strings in a computer should be regarded as completely symbolic, i.e. as completely arbitrary signs. 3.1 Meaning 41 Thought or reference If the relation between the symbol and its referent is not established by resemblance, how else is it established? According to Peirce, the symbol and referent are related because they are mediated by the thought or reference (or interpretant in his termi- nology). The thought or reference corresponds to the sense that is made of the sign. Therefore, the theory presumes the presence of a sense-maker, or an interpreter. Thus, the symbol is connected to its referent by the thought of its interpreter. Meaning arises in the Peircean model, when the interpreter makes sense of the symbol. This process is called semiosis. The meaning that arises during semiosis can be viewed as a relation between the symbol and the referent, i.e. corresponding to thought or reference. Therefore, other versions of the semiotic triangle have used the word "meaning" to refer to what we call "thought or reference"(Vogt, 2002). Referent The referent is the object, in some kind of external and objective reality, to which the symbol refers. Objects are not restricted to concrete objects, but may be interpreted rather broadly. Referents may be abstract, fictional or refer to a state of affairs. For example, a traffic light sign for stop consists of: a red light facing traffic at an intersection (the symbol), the idea that a red light indicates that vehicles must stop (the thought or reference) and vehicles halting (the referent) (Chandler, 2002). 3.1.2 Sinn und Bedeutung Gottlob Frege (1848-1925) was a German philosopher who has been very influential in the philosophy of language. In his seminal paper "Über Sinn und Bedeutung" (Frege, 1892), Frege argued that the referent of a term alone is insufficient to provide a complete account of meaning. His argument is as follows. Consider the terms morning star and evening star which both have the same referent (or bedeutung in his terminology), namely Venus. If the meaning of a term were fully determined by its referent, then the morning star would mean exactly the same as the evening star.A consequence of this would be that the sentence "the morning star is the evening star" would mean exactly the same as the sentence "the morning star is the morning star". However, the first sentence describes a major astronomical discovery, whereas the last sentence is trivial, i.e. it is true on the basis of its constituents. Frege proposed to solve this problem by adding an extra component to the analysis of meaning, namely sinn. Whereas, the morning star and the evening star have the same referent (bedeutung), they differ in sinn. Consequently, the sentence "the morning star is the evening star" can be explained to differ in meaning from the sentence "the morning star is the morning star". Frege’s distinction between sinn and bedeutung matches well with the Peircean triad (Sowa, 2000, p.192). Frege’s sinn corresponds to Peirce’s thought or reference and Frege’s bedeutung corresponds to Peirce’s referent. In Peirce’s model, the terms morning star and evening star have the same referent. The thought or reference differs 42 Foundations of Ontology Reconciliation as the first term evokes a thought of being visible in the morning and the latter term evokes a thought of being visible in the evening. 3.1.3 Conventionality The semiotic analysis described in this section has stressed once more the need for conventions in symbolic systems. The more arbitrary a sign is, the more important the role of conventions. Whereas iconic signs involve some degree of conven- tionality, communication using symbolic signs is based on convention. This social dimension has been recognized by most semioticians. Whereas humans usually interpret signs by unconsciously relating them to a familiar system of conventions (Chandler, 2002), computer systems must be pro- vided with an explicit account of conventions. Ontologies have been proposed to make such conventions explicit. Thus, the purpose of ontologies in IS can be given a justification from semiotics. The next section discusses how ontologies can be realized in a way that is semiotically justified. In particular, we will discuss how meaning can be represented in a computer. 3.2 Meaning Representation The following quotation characterizes the problem that is currently encountered by AI researchers doing knowledge representation. The notation we use must be understandable to those using it and read- ing it; so it must have a semantics; so it must have a Tarskian semantics, because there is no other candidate. (McDermott, 1987) As the above quotation indicates, Tarskian semantics is the most common way to provide a formal account of meaning. This also appears from formalisms that have been proposed to develop ontologies, which mostly follow a Tarskian approach. Tarskian semantics is discussed in Section 3.2.1 and 3.2.2. Despite its popularity in the KR community, Tarskian semantics is not ideal for all purposes. In fact, it is difficult to justify from a semiotic perspective. We will discuss two problems of Tarskian semantics, namely the problem of indistinguish- able models in Section 3.2.3 and the symbol grounding problem in Section 3.2.4. A way to overcome these problems is discussed in Section 3.2.5. 3.2.1 World As described in a well-known textbook on AI (Genesereth and Nilsson, 1987), the formalization of knowledge begins with determining which objects are assumed to exist and their interrelationships. The set of objects in the world that is inhabited by the agent is called the domain of discourse, denoted by ∆I. There is usually not 3.2 Meaning Representation 43 one unique way to determine which objects exist in the world. Basically, an object may be anything about which we want to say something. For an agent to be able to store knowledge about ∆I, it needs a conceptualiza- tion, denoted by ρ.
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