Introduction to Knowledge Representation and Navya Nyaya

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Introduction to Knowledge Representation and
Navya Nyaya
Dr. Shrinivasa Varakhedi
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Motivation

• Knowledge Representation is a multi-disciplinary
  subject that applies theories and techniques from
  different fields
• Logic that provides Formal Structures for
  representation and rules of inference
• Ontology defines the kinds of things that exist
  in the application domain
• Epistemology that provides a base for knowledge
  representation and its implementation.
• Where Navya Nyaya system has a lot to contribute
  and participate in Knowledge revolution.

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Knowledge Representation Language

• A KRL is a way of writing down beliefs (or other
  kinds of mental states)
• Not really a language, any more than a
  programming language is.
• Needs to be
• Very expressive In it, we need to be able to
  express anything we want.
• What might some possibilities be?

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KRL Candidates NL ?

• Expressive!
• Suitably declarative
• But
• Ambiguous
• No need do give eg. !
• Context-dependent meanings
• Pronouns, unspecified relations
• In other words, a KR language should represent
  facts in form that expresses what they mean
  afterthey have been understood.

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KRL

• IT should be
• Expressive (Readable by domain expert)
• Unambiguous
• Context-independent
• Compositional
• Computable

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Actual KRLs

• There have been various candidates proposed for
  KRLs over the years. One set of proposals is that
  formal logicbe used as a basic framework for such
  languages.
• Logic consists of
• A language
• which tells us how to build up sentences in
  the language (i.e., syntax)
• and what those sentences mean (i.e,
  semantics)
• An inference procedure
• Which tells us which sentences are valid
  inferences from other sentences

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Alternatives? Conceptual Graphs

• A knowledge representation language is a way to
  encode mental states.
• Conceptual graphs (CGs) are a system of logic
  based on the existential graphs of Charles
  Sanders Peirce and the semantic networks of
  artificial intelligence. They express meaning in
  a form that is logically precise, humanly
  readable, and computationally tractable. With
  their direct mapping to language, conceptual
  graphs serve as an intermediate language for
  translating computer-oriented formalisms to and
  from natural languages. With their graphic
  representation, they serve as a readable, but
  formal design and specification language. CGs
  have been implemented in a variety of projects
  for information retrieval, database design,
  expert systems, and natural language processing.

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Conceptual Graphs

• Conceptual Graph is complete bipartite oriented
  graph, where each node is either a concept or a
  relation between two concepts, there is one or
  two edges each going to concepts, and each
  concept may represent another conceptual graph

brown
has
dog
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John is going to Boston by a bus.
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CGExpr NNExpr

• Go-
• (Agnt)Person John
• (Dest)City Boston
• (Inst)Bus.
• Gamanam
• - kartA John
• - Karma Boston
• - Karanam - Bus

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Tom believes that Mary wants to marry Sailor.
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CGE NNE

• Person Tom(Expr)Believe(Thme)-
  Proposition Person Mary x(Expr)Want(Thm
  e)- Situation ?x(Agnt)Marry(Thme)Sailor
  .
• Sva-kartrka-Sailor-karmaka-vivAhaviSayaka-icChA-p
  rakAraka-Mary-visheSyakajnAnavAn Tom. Svam
  Mary.

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Navya Nyaya Language

• Navya Nyaya system of Logic has developed a
  Language for representing knowledge
• 1. Close to NL
• 2. It is NOT a meta-language or Artificial L,
  but a Restricted Language based on Sanskrit
• 3. Well defined Technical Terms
• 4. Six basic Relations
• 5. Expressive of all types of different
  cognitions

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Six Basic Relations

• AdhAra-Adheya-bhAva
• NirUpya-nirUpaka-bhAva
• Pratiyogi-anuyogi-bhAva (Sambandha)
• Pratiyogi-anuyogi-bhAva (AbhAva)
• ViSayatA
• AvacCedakatA
• PratibandhakatA

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Unique Features of NNL

• Difference in Perception and other cognitions
• Uddeshya-vidheya-bhAva
• Mountain has fire is a perception that grasps
  both the contents simultaneously.
• Mountain has fire is an inference which
  attributes only fire to the mountain already
  known fact.
• This distinction is present even in the Language
  usages.

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Unique features of NL (contd)

• Verbal cognition that has been generated by
  Sentence is distinct in its form.
• - Pot is red expression means that Pot is
  identical with Red.
• - On the other hand the perception senses the
  Pot as having Red-color as Pot has Redness
• Such subtle distinctions make a lot differences.

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Differences commonality of True and false
Cognitions

• In NNL you can express a cognition with out
  revealing its truth or falsity
• Here is a silver simply rajata-viSayaka-jnAn
  am.
• At the same time you have devices to show the
  difference between them.
• On a shell shukti-niStha-visheSyatA-nirUpita-raj
  atatva-niStha-prakAratAkam jnAnam.
• In a silver shop rajata-niStha-
  shukti-niStha-visheSyatA-nirUpita-rajatatva-niStha
  -prakAratAkam jnAnam

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Distinction among contents of cognitions

• NNL makes clear distinction among the contents of
  a cognition.
• Every cognition objectifies three type of
  contents
• VisheSya
• PrakAra
• Samsarga
• Apart from this you may find even more subtle
  distinction with mode of these types of Contents.
• Floor has chair and table
• Vs Chair-possessing floor has table

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AdhAra-Adheya-bhAva(Relation of locus-located)

• Pot has color
• Pot has water
• Water has taste
• Floor has absence of Pot
• In all these examples the two things are related
  with the relation of AdhAra-adheya-bhAva.
• All the properties will have this link with their
  locus.

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NirUpya-nirUpaka-bhAva

• Rama is son of Dasharatha
• Sita is wife of Rama
• Vishvamitra is guru of Rama and Lakshmana
• Here the relational properties can not be
  understood with out their counter-relatives.
• These counter-relatives are NirUpakas.
• All relational properties will have this link
  with their co-relatives.

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Pratiyogi-anuyogi-bhAva

• Face has similarity of moon.
• In this example, similarity has two relatives
• Face Moon.
• Face is anuyogi of similarity
• Moon is pratiyogi of similarity

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AbhAva-pratiyogi

• To describe absence of something, NN-ontology
  force you to accept a category called absence.
• Pot is absent in the room means absence of
  pot is present in the room.
• Here Pot is pratiyogi absentee and room is
  anuyogi location of absence.

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AvacCedaka Concept of limiter

• To show clear distinction in different cognitions
  and their forms, a new concept called
  avacCedaka is introduced by NN. This relation
  reduces ambiguity.
• Simple example
• Pot has red-color inherence
• Pot has water - contact

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Some expressions with modern notations

• samavAya-(avacCinna)-Gandhtva-(avacCinna)-
  Gandha-(niStha)-AdheytA-(nirUpita)-adhikara
  NatA-(vatI)-PrthivI
• Several such examples are worked out.
• Lets see the computability of Cg and similar
  expressions..(Of course NNL gets thru this test)

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A monkey scratches its ear with a pawn.

• .

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Conceptual Graphs

• FOPL transformation to CG
• for each node ? predicate
• general concept ? variable, specific concept ?
  atom typeinstance ? type(instance)
• relation ? n-ary predicat relation(in1, in2, ,
  inn) with arguments conncecting neighbouring
  concepts
• CG is existencionally quantified conjunction of
  these predicates
• ? X (dog(emma) ? color(emma,X) ? brown(X))

• FOPL transformation to CG
• for each node ? predicate
• general concept ? variable, specific concept ?
  atom typeinstance ? type(instance)
• relation ? n-ary predicat relation(in1, in2, ,
  inn) with arguments conncecting neighbouring
  concepts
• CG is existencionally quantified conjunction of
  these predicates
• ? X (dog(emma) ? color(emma,X) ? brown(X))

brown
has
dogEmma
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The CG Inference Task

• Given an initial scenario CG
• a query ( unknown node in the scenario)
• Find a sequence of joins which instantiate that
  node (answer the query)

Scenario
buyb01
Query
(what is the instrument of the buy? Ans
10)
inst
Goal find
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Inference using Joins
Query What is the instrument of the buy? (Ans
10)
Query inst(b1,X)?
Ans 10!
obj
personjoe
buyb01
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An alternative sequence of joins
Query inst(b1,X)?
obj
personjoe
buyb01
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CG and NNL - complimentary

• CG has been found to be similar one to NN.
• CG can be extended on the basis of NN features
• NNL with modern symbols and notations could be
  tested on Intelligent systems.
• A Student pilot project is already undertaken.
• A serious study in this direction is yet to be
  made.