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Introduction to Knowledge Representation and Navya Nyaya

Motivation . . . Knowledge Representation is a multi-disciplinary subject that applies theories and techniques from different fieldsLogic that provides Formal Structures for representation and rules of inferenceOntology defines the kinds of things that exist in the application domainEpistemo

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Introduction to Knowledge Representation and Navya Nyaya

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    1. Introduction to Knowledge Representation and Navya Nyaya

    2. Motivation

    3. 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?

    4. 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.

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

    6. 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

    7. 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.

    8. 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

    9. John is going to Boston by a bus.

    10. CGExpr & NNExpr [Go]- (Agnt)®[Person: John] (Dest)®[City: Boston] (Inst)®[Bus]. Gamanam - kartA – John - Karma – Boston - Karanam - Bus

    11. Tom believes that Mary wants to marry Sailor.

    12. 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.

    13. 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

    14. Six Basic Relations AdhAra-Adheya-bhAva NirUpya-nirUpaka-bhAva Pratiyogi-anuyogi-bhAva (Sambandha) Pratiyogi-anuyogi-bhAva (AbhAva) ViSayatA AvacCedakatA PratibandhakatA

    15. 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.

    16. 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.

    17. 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

    18. 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”

    19. 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.

    20. 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.

    21. 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

    22. 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.

    23. 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

    24. 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)

    25. A monkey scratches its ear with a pawn. .

    26. 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))

    27. 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)

    28. Inference using Joins

    29. An alternative sequence of joins

    30. 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.

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