Abstract
Ontology, as a philosophical discipline of the study of reality, has gained traction in recent times and is appropriated into computer science giving rise to a new discipline called ‘Ontology Engineering’. One of the main goals of ontology engineering, is how to specify meaning to a computer. But that question takes us back to the foundational issue of what meaning is, and how does one go about studying it so that one can specify it to a computer as explicitly and as accurately as possible. The answer to this question lies in ‘Formal Ontology’. Formal ontology is the study of forms of entities in reality as opposed to their contents. The term was first coined by Edmund Husserl who envisioned it as the ‘eidetic science of the object as such’ i.e., the study of all those features of an object insofar as they make it what it is i.e., an object. But what the forms of entities in reality are, and how to study them is still anopen issue.
The notion of a formal ontology so far has been mainly understood as the application offormal logic, particularly First-Order Logic (FOL) and its variants, to ontology. But since FOL is based on propositional form which is primarily a syntactic form, and does not have any semantics of its own, it requires something outside itself to give semantics to it. One needs to look at various conceptions of reality to provide such semantics.
We look at three such conceptions of reality: (1) as sets of entities (2) as parts and wholes,
and (3) as states of affairs (SOAs), and claim that the SOA-conception of reality is the most
apt candidate to study reality formally and, in turn, to do formal ontology. But we also show
that the propositional form, and in turn, FOL, is incapable of capturing the structure of SOAs.
Though there had been various attempts to overcome the problems of classical logic like FOL
by construction of new and alternative logics, almost all these logics still swear by the
fundamental notion of the subject-predicate form ( propositional form ) which is
fundamentally a sentential or linguistic or logical form as opposed to an entitative or
extra-linguistic or ontological form. Hence these logics are also incapable of capturing the
structure of SOAs. In fact, there has been so far no proper ontological form which captures
the structure of SOAs, in toto . We propose a non-propositional, non-set-theoretic, onto-logical form , called punctuator to
capture the structure of SOAs in toto , and in turn to do formal ontology.
We then consider Vaiśeṣika, the foundational ontology in Indian analytic tradition, and
present a formalized version of it - Neo-Vaiśeṣika Formal Ontology (NVFO) - using only
punctuators to give an instance of a formal ontology as construed above. NVFO was founded
by Singh (2002, 2003, 2008) and later refined and extended by Navjyoti Singh and Rajesh
Tavva (Tavva & Singh, 2015). Notwithstanding our appeal to take recourse to formal ontology to specify meaning to a
computer explicitly, we also propose a novel idea called generative ontology to make the
specification of this meaning to a computer as accurate as possible. In a generative ontology,
a potentially infinite number of complex ontological structures (SOAs/punctuators) can be
generated from a finite number of atomic (or irreducible) ontological structures
(SOAs/punctuators). This becomes possible because the form of punctuator is recursive in
nature. A punctuator is a boundary (a non-entity) which brings two entities together in some
relational context R which, itself, is further composed of chains of entities (and punctuators
between them), hence making the structure of a punctuator complex as well as recursive.
Because of this complexity of a punctuator as a web of entities and punctuators between
them, the structure of a punctuator can be best understood as a graph (as composed of nodes
and edges). Graph grammars, being a natural extension of string as well as tree grammars, are highly
expressive and powerful enough to capture the generative structure of a wide variety of
scenarios - both simple and complex. Unfortunately, this power is not leveraged by many.
Most of the graph grammars available hitherto are either toy grammars or limited to
addressing highly specialized problems. The current thesis presents a domain-independent
grammar i.e., a grammar for reality, as theorized in Vaiśeṣika. We contend that Vaiśeṣika
ontology, given that it implicitly exhibits the ontological structure of a punctuator, is one such
ontology which can be generated from some basic alphabet of punctuators. Hence it is not only a formal ontology but also a generative ontology. Given the fact that most of the existing
foundational ontologies (those which deal not with a particular domain of reality but with
entire reality as such) are not generated but manually constructed, the idea of a generative
ontology becomes significant because of its capacity to impar