Formal Ontologies and Nyaya-Vaiseshika System


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Lecture from Prof. Navjyoti Singh's course on Vaiseshika System of Formal Ontologies.

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Formal Ontologies and Nyaya-Vaiseshika System

  1. 1. Context, History, Concepts and Tools
  2. 2. Basic stance of ontology is – meanings are entities, events and relations Meanings occur in CognitionMeanings are impressed in cognition and meanings are expressed in natural language impress-meanings recur Ontology seeks entitative account of such recurrence Ontological engineering seeks automation of such accountCentral issue of ontological engineering is – how to specify meaning for robots or computational agents
  3. 3. Problem of the Specification of MeaningsFor human agents –dictionaries (terms), glosses (usages of term) and thesauri (relation of terms) do the jobReusable term can often be seen as a class (concept) of objects class and sub-class inheritances become computable Lower terms inherit meanings from higher ones: vegetation:plant:flower:roseAnother dimension to computing meaning is added byseeing object as having properties (roles) multiple inheritances in objects become computable „Red-rose‟ inherits meanings from quality:color:red as well as vegetation genus
  4. 4. Top-down and bottom-up approaches for computing meaning WORDS class|sub-class Foundatio * nal Ontologies object|property * whole|part * Domain action|event Ontologies * etc. ? PARTICULARS Bottom-up approach takes particular entities as primitives and not terms Ontology is a theory of actual particulars and their change and not a theory of their representationBottom-up approach depends on rigorous foundational ontology that is independent of natural language
  5. 5. Comprehensive Foundational Ontologies Aristotelian Ontology Vaiśes Ontology ikarelation among real entities are relation among real entities are logical real entities different categories of reals have hierarchy of universals is valid across different highest universal categories of reals „Existence‟ is a declaration „Existence‟ is a specific entity Declarative Categories Differentiated Categories Descriptive Ontologies
  6. 6. Aristotelian Categories (ta onta) ousia sumbebhkotasubstance accident ousia poion poson pros ti pou pote keisthai echein poiein pascheinsubstance quality quantity relation place time posture possess action passion ionsecondary virtue discrete equal/un attitudes equal genus – equal – degree; degree; species unequal; contrary contrary heirarchy no contraryprôtai ousiai primary disposition continuous superior Logical Relation – capacity 1. inhering ‘in’ (‘accidents inhere in substance’) 2. being ‘said of’ (genus-species) affections similar shape knowledge contrary
  7. 7. Vaiśes Categories (padārtha-s) ikadravya a gun karma sāmānya viśes a samavāya abhāvasubstance quality action universal differentiator inherence absence <9> <24> <5> <2> <infinite> <1> <4> pr thvī gandha utks a epan para prāgābhāva earth smell rising wide prior absence<infinite> <1> ap rasa apaks a epan ^ pradhvam sābhāva water Taste falling hierarchy posterior absence<infinite> structure  tejas rūpa ākuñcana apara anyonyābhāva fire Color contracting narrow reciprocal absence<infinite> <indefinite> vāyu sparśa prasāran a atayantābhāva wind Touch expanding absolute absence<infinite> ākāśa śabda gamana medium Sound locomotion <1> mobile & atomic kāla khyā sam non-mobile time number special qualities <1> general qualities dik parimāna special qualities of self Logical Relation – expanse magnitude quality of self & mobile 1. attribute | attributee <1> 2. locus | located ātman pr thaktva self otherness<infinite> manas samyoga <#/infinite/indefinite> indicates number of sub-categories or number of entities in each substance mind conjunct<infinite> vibhāga disjunct qualities grasped by one sense organ and their corresponding material substrates paratva entities not explicitly listed by Kan but accepted as consistent with system āda remoteness aparatva proximity buddhi Sukha duhkha icchā dvesa prayatnacognition happiness misery desire aversion volition  psychic qualities dharma adharma samskāra gurutva dravatva sneha  dispositional merit demerit tendency weight fluidity viscosity qualities
  8. 8. Foundational Ontology and Automation Expressibility Open vocabulary Open grammar FOUNDATIONAL ONTOLOGY vocabulary FORMAL NATURAL ONTOLOG SEMANTIC Y ARTIFICIAL LANGUAGE DOMAIN ONTOLOGIES Controlled grammar Controlled vocabulary vocabulary Demand of ontological engineering is to rendercomprehensive foundational ontology as formal ontologyinstead of natural semantics,robotic agent requires formal ontology capable of handling impress-meanings
  9. 9. Development of Formal Ontology Formal ontology is not application of formal logic to ontology ratiocination among entities ratiocination among propositions•Brentano (1890s) revived formal study of Aristotle. Concepts of PUNCTIFORM; PLEROSIS; TELEIOSIS•Husserl (1910s) coined a phrase FORMAL ONTOLOGY•Smith (1982) revived FO in anthology Parts and Moments•Mormann (1995) ), “Trope Sheaves: a Topological Ontology of Tropes,” Logic and Logical Philosophy 3: 129-150•Smith & Varzi (2000), “Bona Fide and Fiat Boundaries,” Philosophy andPhenomenological Research 60, 401-420 Use of topological methods and category theory
  10. 10. Formal Ontology becomes study of envelopes, boundaries, terminals, edges, joints, wholes, holes, clusters, mixtures etc.It does not matter what the stuff is – Forms that shape the stuffadequately characterize composition and behavior of stuffThese studies can be described as DEPICTIVE Formal OntologiesThey do not disclose formal necessity that generates categories of reality In Contrast GENERATIVE Formal Ontology is a quest to formally derive Categories of Reality
  11. 11. GENERATIVE Ontology is possible if boundaries, edges, joints, terminals etc. are conceived as instances of a SINGLE, SIMPLE FORM OF CONTIGUITY which is Recursive