Generative Ontology of Vaiśesika Rajesh Tavva1 and Navjyoti Singh2 1,2Center for Exact Humanities, International Institute of Information Technology, Hyderabad, Telangana, India [email protected] and [email protected] Abstract classes/universals, but also particulars. But since the In this paper we present a foundational as well as generative punctuator has a recursive form, complex graphs can be ontology which is graph-based. We use a form called generated from simple graphs, and each of these graphs punctuator which is non-propositional and also non-set- depicts some or other portion of reality at some or other theoretic to build our system – Neo-Vaiśesika Formal level of granularity. Hence we also have an interpreter to Ontology. The idea is to present an ontological language interpret the generated graphs as portions of reality. which is formal. This language is a set of potentially infinite We take Vaiśesika - one of the Indian philosophical sentences (graphs) whose structure is captured by a finite set schools which focuses on foundational ontology – as of (graph) grammar rules. We also have an interpreter to interpret the graphs generated by this grammar and show formalized in [4,5,6,7] as our base, and present generative that the interpretation of a node as belonging to a particular as well as interpretative grammars for it in this paper. This ontological category is based purely on its structure/form paper's focus is not on defending Vaiśesika description of and nothing else to provide a robust example of a formal, reality or the rationale behind its categorial system1. This foundational and generative ontology. paper is already taking them as given and trying to make implicit formal notions of Vaiśesika explicit. The idea is to Keywords. Formal Ontology, Graph Grammar, Generative show the possibility of an ontological language which can Ontology, Punctuator, Generative Grammar, Vaiśesika be formalized and also generated, and then interpreted. In section 1 we present Vaiśesika ontology in brief. In Introduction section 2 we present Neo-Vaiśesika Formal Ontology, the system we built by formalizing Vaiśesika ontology. In this Most, if not all, of the (computational) ontologies built till section, we give formal definitions of Vaiśesika categories now [12] are either built manually or through automatic in terms of three basic punctuators. In section 3 we show methods of category-extraction from text. There is no how Vaiśesika can be seen as a generative ontology. In notion of generation there since there are no repeating section 3.1, we give the generative grammar of our system structures (each category is different and hence different where we give the production rules to generate graphs, and structure). All the foundational ontologies are presented as in section 3.2 we give interpretative rules using which we diagrams/graphs with finite number of nodes (which stand can interpret these generated graphs to label each node for categories/sub-categories) and edges (which stand for with some or other Vaiśesika category. The generated class-subclass or some other relations). In this paper we graph is considered to be valid if there is at least one present a novel concept of Generative Ontology which interpretation, in terms of Vaiśesika categories, of the presumes Grammar of Reality which, in turn, is based on generated graph. The grammar is considered to be sound if the idea of a recursive ontological form called the it generates only valid Vaiśesika graphs. Though a formal punctuator. A punctuator is a form which is present proof of the soundness of this grammar is not achieved yet, between any two entities and enables us to distinguish one we present in section 4 some results which show that the from the other. It is because of this form that we are able to system is promising. The main focus of the paper is to differentiate various categories as well as different present the idea of a generative ontology and one example instances of the same category. Since a punctuator is found of such an ontology. not only between two classes, but also between two We tried to provide examples and explanation of particulars, or between a class and a particular, the graphs abstract concepts wherever possible but due to space which are based on punctuators contain not only constraints we are unable to get into detailed explanation sometimes. An extended version of this paper with Copyright © 2015 for this paper by its authors. Copying permitted examples, diagrams and detailed explanation of various for private and academic purposes. 1. One can refer to [4] and [14] for that. definitions, axioms etc. presented in this paper is available explicate the system below. at [9]. According to F reality is constituted of only entities and punctuators. Here entities refer to all kinds of beings like objects, events, relations and so on. And any two 1. Vaiśesika Ontology beings/entities are considered two, not one, because there is a separator/boundary/vacuum/non-being between them Vaiśesika, as mentioned in introduction, is one of the many 4 Indian philosophical schools, which focuses on which we call punctuator/point . But a punctuator is not foundational ontology. It classifies all entities of reality only a separator but also a connector/link which links two 2 entities. So here non-being is not an all-encompassing into 6 categories : (1) Substance (e.g: material entities like 5 tables, chairs as well as non-material entities like soul, vacuum whose existence Parmenides was denying but space and time) (2) Quality (e.g: color, weight) (3) Action every non-being is a particular in the sense that it rides on a particular pair of entities/beings which it separates as (e.g: rising up, falling down, motion) (4) Universal (e.g: 6 tableness, chairness, redness) (5) Ultimate Differentiator well as brings together into contiguity in some relational (located in each ultimate substance (explained below) and context. Our idea of punctuator/point is quite similar to, at differentiates one from the other) and (6) Inherence the same time slightly different from, Leibniz’s idea of (explained below). Notice that there is no category like punctum/point and Brentano’s idea of punctiform/point. Relation in this system because any chain constituting a Leibniz [10] tries to explicate this notion by taking a relational context (section 2) can be abstracted into geometrical example like a line segment. He makes a something called a relation. Out of all the categories listed distinction between potential point (euclidean point) and above inherence (Fig. 2.2) is the most significant one for actual point (non-euclidean point). The line segment, us. It gives stability to reality and is the entity constituting according to Leibniz, is not really made up of euclidean the second most pervasive relation found in reality, the first points, they are not parts of the segments the way smaller being self-linking relation (more about it later). We call the segments are. The euclidean points (lengthless, breadthless relational chain constituted of inherence entity as inherence and heightless points) are only potentially there on the relation, and this inherence relation can be found in all the segment but not actually constituting it. The actual points following cases: (1) Universals inhere in substances, are the boundaries or the endpoints of the segment. These, qualities and actions (2) Qualities and actions inhere in Leibniz also calls as punctums because they punctuate the substances (3) Substances (wholes) inhere in other line segment from its neighbourhood (in one-dimensional substances (their parts) and (4) Ultimate Differentiators space). A potential (euclidean) point can become an actual inhere in ultimate substances. Ultimate substances (US) are (non-euclidean) point if one cuts the line segment, say, into those substances which have no parts and hence cannot be two halves. The midpoint which was there before cutting differentiated from each other3. Examples of USs are time, was only potential, but after cutting it becomes actual. So space, souls and atoms (these are different from those of according to Leibniz a punctum is like a boundary that physics, they are the smallest indivisible units according to separates two entities. Brentano [11] also comes up with a Vaiśesika). Since USs have no parts, each of them has an similar idea and he calls it punctiform or point. He says no ultimate differentiator (UD) inhering in it which continuum can be built up by adding one individual point differentiates it from the rest of the entities. The remaining to another. The point exists as a boundary, as a limit. substances which are not USs are automatically Similarly for us, a point is a boundary between two differentiated from others since they are entities, but not constituting those entities. wholes/mixtures/compounds made up of various USs These both – entity and punctuator – are defined in F in which are already differentiated by UDs. We will try to terms of each other. But the mutual dependency of define all these categories formally using only the idea of definitions ends here. All the other definitions are based on inherence. these primitives only. Definition 2.1: An entity is that which is never punctuated from itself. 2. Neo-Vaiśesika Formal Ontology Definition 2.2: A punctuator pr(x|y) has the form <x|y, R> where x and y are entities punctuated from each other Vaiśesika ontology, due to Kanada [1], Prasastapada [2] in some relational context R. This R refers to all the chains and Udayana [3] has been formalized by Navjyoti [4,5,6,7] of entities (along with punctuators between them) which resulted in Neo-Vaiśesika Formal Ontology. From connecting x and y where each chain looks like C = p(x|e1) now we will refer to this formal system as F for short.