Ontological Commitment and Ontology

This section provides an intensional account of ontological commitment and ontology. Since an ontology specifies a conceptualization, it commits to that conceptualization through an ontological commitment. As defined in (Rayo 2007) an ontological commitment for a sentence is what a sentence requires in order to be true. In the context of the reference theory; an ontological commitment is defined as a relation that holds between a sentence and an object (Parsons 1967) . In that sense, this object needs to exist in order for the sentence to be true. And so, it can be said that, this sentence is committed to that object.

Ontological commitment is also defined in (Parsons 1967) as a relation that holds between a sentence and a class of objects. These two definitions are based on two different accounts of ontological commitment. The first account is the extensional account (Jubien 1974). According to this account of ontological commitment, a language commits to extensions or objects in the domain of interest. The second account of ontological commitment is the intensional account (Jubien 1975). According to the intensional account, a language commits to kinds instead of particulars. In general, it can be said that an ontological commitment is a relation that holds between a language and intension. This intension can be a concept, a property, or an intensional relation. It is also shown in (Jubien 1972) , that ontological commitment is either intensional or inadequate.

Before the intensional account of ontological commitment is presented, let us first examine an example to the extensional account. In (Guarino, Oberle, and Staab 2009) , ontological commitment is defined as a structure K = (C, I). In that structure, the interpretation function I is a total function I : V → D∪R. this interpretation function maps each vocabulary symbol to either an element of D or a relation belonging to the set R. As discussed in sections 3.6.2 and 3.6.4, the elements of D are extensions and not concepts. And so, this structure commits to extensions. And as such, it is considered an extensional ontological commitment. An intensional ontological commitment, however, commits to intensional entities.

Definition; Ontological Commitment: According to the intensional account of ontological

commitment, an intensional ontological commitment of a first order intensional logical language Lw with vocabularies Vw is an intensional structure ( , I) in which I is an

intentional interpretation function and is a conceptualization. The intensional interpretation function I maps each vocabulary symbol of Vw to an element of D. Where

M = (D, I) is the standard model (intended intensional interpretation) of Lw according to

the ontological commitment .

In order to avoid the confusion about what an ontology is, it should be made clear that the ontology has several accounts as well (Smith 2008). Unlike the case with ontological commitment, neither of the different accounts for ontology is inadequate. However, each account is appropriate in the appropriate context. In philosophy, the term Ontology refers to a systematic account of existence. The connection between this definition and the usage of Ontology in artificial intelligence (AI) is that, for AI systems, what “exists” is what can represented (Gruber 1992). In science, ontology of a certain domain includes the terms used in this domain, and the relation between them. This ontology is developed in such a way as to be analogous to scientific theories. Such ontologies are developed and validated by domain experts to be common resources. Also, these ontologies are recognized as being always subject to further development, and are independent of format and implementation. In engineering, Ontology is a specification of a conceptualization. And thus ontologies are considered to be engineering artifacts (Gruber 1992). In this work, the ontology we are interested in is the ontology from the

engineering perspective. This ontology is developed and maintained by engineers and computer scientists. This ontology will be formally defined as follows:

Definition; Ontology: Let be a conceptualization, and Lw an intensional logical

language with vocabulary Vw and ontological commitment . An ontology O, for

with vocabulary Vw and intensional ontological commitment , is a logical theory

consisting of a set of formulas of Lw, designed so that the set of its models approximates

as well as possible the standard model (intended intensional interpretation) of Lw

according to .

Note that, this definition is different from the definition that is based on the “possible world” (Guarino, Oberle, and Staab 2009). The definition that is based on the approach the “possible world” approach assumes several intended models for each language and ontological commitment. Each model is concerning one possible world. In this work, the definition of ontology follows the intensional model for conceptualization in sections 3.6.2 and 3.6.4. And as such, for a language and ontological commitment, there is only one intended interpretation. This intended interpretation (standard model) is what the ontology is required to approximate. It is also worth mentioning that, in the possible world approach, the interpretation is based on a set of possible world that may not even exist.

Chapter 4

4

Intensional Modeling of Data Integration Systems

This chapter proposes an intensional-based model for ontology-driven data integration in open environment. As described in Chapter 3, Intensional modeling is found to be more natural choice for modeling in open environment. This is due to the dynamic and loosely- coupled nature of open environment. In open environment, agents need to enter or leave the system without affecting the overall functionality. It has also been illustrated in Chapter 3 that the belief of an agent and the knowledge of an information system are intensional in nature. Formal intensional semantics for queries and query answering are then presented. The semantics presented in this chapter are based on the intensional epistemic logic (IEL) (Jiang 1993).