A set of formal constraints like those above, expressed in a suitable modal language, can therefore be used to (partially) characterize a conceptualization, in the sense of excluding unintended extensions of the relevant relations even for possible “worlds” different from the one considered. Notice that in general we cannot identify a single conceptualization by means of a set of formal constraints, since such a set may have many models. The set of such models is exactly what in [9] we defined as ontological commitment. According to these considerations, we cannot see a particular theory as a specification of a conceptualization, since conceptualizations can be only partially characterized. What we can specify is a set of conceptualizations, i.e. an ontological commitment. [...] Strictly speaking, none of them can be considered as a specification of a conceptualization, and hence Gruber’s definition cannot apply. If we want to mantain its original (good) intuitions, we must weaken Gruber’s definition, claiming that an ontology is only a partial account of a conceptualization.

Aristotle defined Ontology as the science of being as such: unlike the special sciences, each of which investigates a class of beings and their determinations, Ontology regards “all the species of being qua being and the attributes which belong to it qua being” (Aristotle, Metaphysics, IV, 1). In this sense Ontology tries to answer to the question: What is being? or, in a meaningful reformulation: What are the features common to all beings?

This is what nowadays one would call General Ontology, in contrast with the various Special or Regional Ontologies (of the Biological, the Social, etc.). This distinction corresponds to the Husserlian one between Formal Ontology and Material Ontology [1]. But the Husserlian notion of “formal” does not involve only generality. For Husserl, the task of Formal Ontology is to determinate the conditions of the possibility of the object in general and the individuation of the requirements that every object’s constitution has to satisfy.

Recently, Nino Cocchiarella defined Formal Ontology as the systematic, formal, axiomatic development of the logic of all forms and modes of being [2]. [...] Cocchiarella’s definition is in our opinion particularly pregnant, as it takes into account both meanings of the adjective “formal”: on one side, this is synonymous of “rigorous”, while on the other side it means “related to the forms of being”. Therefore, what Formal Ontology is concerned in is not so much the bare existence of certain objects, but rather the rigorous description of their forms of being, i.e. their structural features. In practice, Formal Ontology can be intended as the theory of the distinctions, which can be applied independently of the state of the world, i.e. the distinctions: among the entities of the world (physical objects, events, regions, quantities of matter...); among the meta-level categories used to model the world (concept, property, quality, state, role, part...).

An ontological theory contains formulas which are considered to be always true (and therefore sharable among multiple agents), independently of particular states of affairs. Formally, we can say that such formulas must be true in every possible world. [...] an ontological theory differs from an arbitrary logical theory (or knowledge base) by its semantics, since all its axioms must be true in every possible world of the underlying conceptualization. This means that while an arbitrary logical theory (containing for instance a statement like apple(a)_pear(a), expressing uncertainty about the object a) may represent a particular epistemic state, an ontological theory can be only used to represent common knowledge independent from single epistemic states.

...a possible confusion arises between an ontology intended as a particular conceptual framework at the semantic level (interpretations 2-3) and an ontology intended as a concrete artifact at the syntactic level, to be used for a given purpose (interpretations 4-7). This is an important distinction, and it is evident that we cannot use the same technical term to denote both things.

We shall use the term conceptualization to denote a semantic structure which reflects a particular conceptual system (interpretation 3 in Fig. 1), and ontological theory to denote a logical theory intended to express ontological knowledge (interpretation 5). The underlying intuition is that ontological theories are designed artifacts, knowledge bases of a special kind which can be read, sold or physically shared. Conceptualizations, on the other hand, are the semantical counterpart of ontological theories. The same ontological theory may commit to different conceptualizations, as well as the same conceptualization may underlie different ontological theories. The term “ontology” will be used ambiguously, either as synonym of “ontological theory” or as synonym of “conceptualization”. We need only to be consistent to the choice made within the same statement.

[...] 1. Ontological engineering is a branch of knowledge engineering which uses Ontology to build ontologies. 2. Ontologies are special kinds of knowledge bases. 3. Any ontology has its underlying conceptualization. 4. The same conceptualization may underlie different ontologies. 5. Two different knowledge bases may commit to the same ontology.

..Referring to the example given, consider a different arrangement of blocks, where c is on the top of d, while a and b together form a separate stack standing on the table (Fig. 4). The corresponding structure would be different from the previous one, generating therefore a different conceptualization. Of course there is nothing wrong in such a view, if one is only interested in isolated snapshots of the block world. But the meanings of the terms used to denote the relevant relations are still the same, since they are invariant with respect to the possible configurations of blocks. In fact, in the metalanguage adopted in their book, Genesereth and Nilsson would use the same terms (on, above, clear, table) to denote the new conceptualization. We prefer to say in this case that the states of affairs are different, but the conceptualization is the same. The structure proposed by Genesereth and Nilsson seems to be more apt to represent a state of affairs rather than a conceptualization. [...] In order to capture such intuitions, the linguistic terms we have used to denote the relevant relations cannot be thought of as mere comments, informal extra-information. Rather, the formal structure used for a conceptualization should somehow account for their meaning. As the logico-philosophical literature teaches us, such a meaning cannot coincide with an extensional relation. Sticking to a set-theoretical framework, a standard way to approximate such meaning is to conceive it as an intension (intensional relation), taking inspiration from Montague semantics. This means that a single extensional relation is always relative to a possible world. [...] According to this intensional interpretation, a conceptualization accounts for the intended meanings of the terms used to denote the relevant relations. Such meanings are supposed to remain the same if the actual extensions of the relations change due to different states of affairs.