Introduction to Knowledge Representation and Navya Nyaya

Dr. Shrinivasa Varakhedi

Motivation

Knowledge Representation is a multi-disciplinary subject that applies theories and techniques from different fields

1. Logic – that provides Formal Structures for representation and rules of inference

2. Ontology – defines the kinds of things that exist in the application domain

3. 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.

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?

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.

KRL

IT should be

Expressive (Readable by domain expert)

Unambiguous

Context-independent

Compositional

Computable

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

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.

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

dog brownhas

John is going to Boston by a bus.

CGExpr & NNExpr

[Go]- (Agnt)®[Person: John] (Dest)®[City: Boston] (Inst)®[Bus].

Gamanam - kartA – John- Karma – Boston- Karanam - Bus

Tom believes that Mary wants to marry Sailor.

CGE & NNE

[Person: Tom]¬(Expr)¬[Believe]®(Thme)- [Proposition: [Person: Mary *x]¬(Expr)¬[Want]®(Thme)- [Situation: [?x]¬(Agnt)¬[Marry]®(Thme)®[Sailor] ]]. Sva-kartrka-Sailor-karmaka-vivAha—viSayaka-icChA-prakAraka-Mary-visheSyaka—jnAnavAn Tom. Svam = Mary.

Navya Nyaya Language

Navya Nyaya system of Logic has developed a Language for representing knowledge1. Close to NL 2. It is NOT a meta-language or Artificial L, but a Restricted Language based on Sanskrit3. Well defined Technical Terms 4. Six basic Relations 5. Expressive of all types of different cognitions

Six Basic Relations

AdhAra-Adheya-bhAvaNirUpya-nirUpaka-bhAvaPratiyogi-anuyogi-bhAva (Sambandha)Pratiyogi-anuyogi-bhAva (AbhAva)ViSayatAAvacCedakatAPratibandhakatA

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.

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.

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-jnAnam.

At the same time you have devices to show the difference between them.– On a shell – shukti-niStha-visheSyatA-nirUpita-rajatatva-

niStha-prakAratAkam jnAnam.– In a silver shop – rajata-niStha- shukti-niStha-visheSyatA-

nirUpita-rajatatva-niStha-prakAratAkam jnAnam

Distinction among contents of cognitions

NNL makes clear distinction among the contents of a cognition.Every cognition objectifies three type of contents– VisheSya– PrakAra– SamsargaApart 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”

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

Pot has colorPot has waterWater has tasteFloor 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.

NirUpya-nirUpaka-bhAva

Rama is son of DasharathaSita is wife of RamaVishvamitra 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.

Pratiyogi-anuyogi-bhAva

Face has similarity of moon.

In this example, “similarity” has two relatives :Face & Moon.Face is anuyogi of similarityMoon is pratiyogi of similarity

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.

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

Some expressions with modern notations

[samavAya]-(avacCinna)-[[[Gandhtva]-(avacCinna)-[[Gandha]-(niStha)-[AdheytA]]]]-(nirUpita)-[adhikaraNatA]-(vatI)-[PrthivI]

Several such examples are worked out.Let’s see the computability of Cg and similar

expressions…..(Of course NNL gets thru this test)

A monkey scratches its ear with a pawn.

.

monkey scratchagent object ear

instrument

pawpart of

part of

Conceptual Graphs

FOPL transformation to CG– for each node predicate– general concept variable, specific concept atom

type:instance 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)) dog:Emmabrown

has

FOPL transformation to CG– for each node predicate– general concept variable, specific concept atom

type:instance 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))

The CG Inference Task

Given: an initial scenario CGa query (= unknown node in the scenario)

Find: a sequence of joins which instantiate that node (answer the query)

objperson:joe necktieagnt buy:b01

buy:b01

inst

?

Scenario:

Query:

Goal: find ?

(“what is the instrument of the buy?” Ans: $10)

Inference using Joins

objperson:joe necktiebuy:b01agnt

inst

?

Query: inst(b1,X)?Query: “What is the instrument of the buy?” (Ans: $10)

objperson physobjbuy:*xagnt

inst

money:@?

valueposs

schema for buy(x) is

inst

money:@?

valueposs

necktie:*x

value

schema for necktie(x) is

$10

worn-by

person

money:$10

worn-by

person

Ans: $10!

An alternative sequence of joins

objperson:joe necktiebuy:b01agnt

inst

?

Query: inst(b1,X)?

objperson physobjbuy:*xagnt

inst

money:@?

valueposs

schema for buy(x) is

inst

money:@?

valueposs

person:*x

part

head

part

body

schema for person(x) is

part

head

part

body

schema for head(x) is

head has hair

shaperound

has hair

shaperound

money:*x carry-in wallet

schema for money(x) is

carry-in wallet

CG and NNL - complimentary

CG has been found to be similar one to NN.CG can be extended on the basis of NN featuresNNL 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.