Formal Definitions Of Reason Fallacies To Aid Defect Exploration - - PowerPoint PPT Presentation

Formal Definitions Of Reason Fallacies To Aid Defect Exploration In Argument Gaming

G.S. Mahalakshmi, Lecturer, Anna University, Chennai – 25 mahalakshmi@cs.annauniv.edu, gs_maha@yahoo.co.in

Walton’s definition of Fallacy

A fallacy is

 an argument (or at least something that

purports to be an argument);

 that falls short of some standard of

correctness;

 poses a serious obstacle to the realization of

the goal of a dialogue.  For Walton, a fallacy is fundamentally

negative; it involves a lapse, error, failure, and deception.

Argument Gaming



knowledge sharing - exchange of ideas to promote learning - method

• f interaction – argument gaming



subject of discussion validated – with right justifications and by eliminating false beliefs

 False beliefs – proposed in arguments (which support the argument) - need

to be identified

 Reasons support subject of discussion in argument – false reasons - Reason

fallacies

 To identify reason fallacies or defects or holes is reasoning from argumentation



Indian philosophical perspective – ‘tarka’ methodology

 Motivation – invariable concomitance

 knowledge of co-existence free from fallacious knowledge  Applied when convincing others of a certain issue



When the sun is at the top, vertically over your head, you infer that the time is around 12.00 noon.



When a student answers ‘Penguins fly’, the teacher infers the student’s lack of knowledge about ‘Penguin’

Interpretation of arguments in

 ‘This hill has fire’ (statement)

 Hill – subject; fire – probandum or object to be inferred

 ‘Because it has smoke’ (reason)

 Smoke – probans or Reason

 ‘Since whatever has smoke has fire e.g. an oven’ (example)

 Oven – similar example

 This lake has fire’ (statement)

 Lake – subject; fire – probandum or object to be inferred

 ‘Because it has smoke’ (reason)

 Smoke – probans or Reason

 ‘Since whatever has smoke has fire e.g. an oven’ (example)

 Oven – similar example

 May not be a smoke, it may be ‘fog’, so statement is

disproved

Need for exploration of reason fallacies

 Modern argumentation

 Argument fallacies

 How an argument is put forth, rather than its NL

semantic content

 Argument by expert opinion, straw man fallacy etc.

 No rule framed – surveyed and studied only by examples

 Conceptual Semantic analysis – needed

 Identifying abstract semantics by using relations between

concepts that form the argument

 By exploring relations between parts of argument –

concepts (probans, probandum, subject)

 Invariable concomitance, inherence, causal, contact-contact

etc.

 Possibility of rules – standards inspired by Tarka Sastra

Nyaya - Argument Defects

Defective Reasoning - 5

 tells how (or how not) to interpret a proposition  a subject, which prevents inferential knowledge

Definitions of defects

 Straying

 Reason which is present in a place where there is absence of the

thing to be proved

 Adverse

 Reason is pervaded by negation of the thing to be proved

 Antithetical

 Two valid reasons for presence and absence of the thing to be

proved

 Unestablished

 concept to which the subject is related to is not present or not

related as said, with the subject

 Stultified

 Negation of probandum is established by another proof

 Need for defect categorisation

 Concept and relation centric  would provide more information about reason fallacies present in

the proposed argument

Formal definitions of defects

……

…….

Our idea – categories of Nyaya defects

Defect Table - Possible defects classified per defect category

Defect classification, identification

Argument Analysis Defect Table Defect Categories Nyaya Defect types Defect set

Sample arguments

Arg. Id Argument Subject

• bject of

inference reason 1 sky_lotus has fragrance sky_lotus fragrance Nil 2 artificial-rose has fragrance artificial- rose fragrance Nil 3 lily has fragrance lily fragrance Nil 4 mountain has fire due_to smoke mountain fire smoke 5 penguin fly because it is-a bird penguin fly Bird 6 bats are viviparous because they are mammal bat viviparous mammal 7 Falls does not have fire when there is smoke falls fire smoke 8 Falls does not have fire when there is smoke falls fire smoke

Argument defects

Arg. Id Status in KB Defect Category & Type Status in KB 1 concept doesn't exists HC1 Unestablished to subject concept doesn't exists 2 concept exists, fragrance as a quality(negation) HC7 Unestablished to itself concept exists, fragrance as a quality(negation) 3 concept and quality exists No Defect concept and quality exists 4 Fire, smoke exists as concepts. No invariable relation HC8 Unestablished to invariance Fire, smoke exists as concepts. No invariable relation 5 Penguin and bird exists as concept. Exclusive quality: fly in negation HC4 Straying Uncommon Penguin and bird exists as concept. Exclusive quality: fly in negation 6 Bat, mammal and bird exist as

• concept. Mammal-viviparous, bird-

~viviparous HC2, HC5 Antithetical Bat, mammal and bird exist as

• concept. Mammal-viviparous, bird-

~viviparous 7 Falls and smoke exist as concept. Absence of fire as concept. Direct relation between fire and smoke HC1, HC5 Straying Common Falls and smoke exist as concept. Absence of fire as concept. Direct relation between fire and smoke 8 Falls and smoke exist as concept. Absence of fire as concept. Invariable relation between fire and smoke HC1, HC6 Adverse Falls and smoke exist as concept. Absence of fire as concept. Invariable relation between fire and smoke

Future enhancements

 Other provisional definitions of

invariable concomitance

 More Reason fallacies in Buddhist

philosophy

 Coverage of argument fallacies

Key References

1.

Gautama, The Nyaya Sutras, translated by S.C. Vidyabhusana, edited by Nanda Lal Sinha, Sacred Book of the Hindus, Allahabad, (1930). Reprinted in

• 1990. Delhi: Motilal Banarsidass

2.

• C. L. Hamblin. Fallacies. London:Methuen, (1970).

3.

Jaakko Hintikka, Socratic Epistemology: Explorations of Knowledge-Seeking by Questioning, Cambridge University Press, 239pp., (2007)

4.

G.S.Mahalakshmi and T.V.Geetha: Navya-Nyaya Approach to Defect Exploration in Argument Gaming for Knowledge Sharing, In proc. of International Conf. on Logic, Navya-Nyaya & Applications - A Homage To Bimal Krishna Matilal (ICLNNA ‘07), Jadavpur Univ., Calcutta, India, (2007).

5.

Sathis Chandra Vidyabhusana, A History of Indian Logic – Ancient, Medieaeval and Modern Schools, Motilal Banarsidass Publishers Private Ltd., Delhi, India, ISBN:81-208-0565-8. pp. 84, (1988).

6.

Swami Virupakshananda: Tarka Samgraha, Sri Ramakrishna Math, Madras (1994).

7.

Toshihiro Wada, Invariable Concomitance in Navya-Nyaya, Sri Garib Dass Oriental Series No. 101, Indological and Oriental Publishers, New Delhi, India, (1990).

8.

Walton, D. and Woods, J., Argument: The Logic of the fallacies, Toronto:

Thank You…

Gautama – Ontology editor based on Nyaya

G.S. Mahalakshmi, Lecturer, Anna University, Chennai – 25 mahalakshmi@cs.annauniv.edu, gs_maha@yahoo.co.in

Idea

 Indian logic based approach of knowledge representation

 classifies the world knowledge into concepts, and relations, both

enriched with special qualities.

 Nyaya Sastra

 categorization of world knowledge  elaborate in tapping the minute details in the defined knowledge units.

 Nyaya logics

 mechanism which defines the concept and relation elements of ontology  based on the epistemology of Nyaya-Vaisheshika school of Indian logic.

 NORM

 an ontology reference model based on Nyaya logic  syntax and semantics of NORM rdf.  To overcome the difficulty involved

 we propose Gautama,

 Gautama

 a tool for editing the ontology based on Nyaya logics.

Nyaya Logics - Argument

A=< Aid, CS,COI,CR,RS-OI,RS-R,RR-OI,Astate,Astatus,Astr> Aid - Argument index CS,COI,CR - concept categories; RS-OI,RS-R,RR-OI - relation categories; Astate – state of argument; Astate {premise, inference, conclusion} Astatus – defeat status of arguments; Astatus{defeated, undefeated, ambiguous, undetermined}

NORM Model

(a) ontology with concepts as nodes and

external relations as edges

(b) a concept with qualities as nodes, internal

relations as thin edges, tangential relations as dotted edges

(c) a quality with values as nodes, grouping

relations as edges

NORM - Concept

C= <Cname, Ccat, QM,QO,QE,Cpr,Cpar,Ccon> Cname – name of the concept Ccat={CS,COI,CR} QM = Quality Mandatory of type Quality Q QO = Quality optional of type Quality Q QE = Quality Exceptional of type Quality Q Cpr = Concept priority weight factor Cpar= parent concept C, par = 0 to n; n – max. no. of concepts in committed ontology Ccon = constraint set under which concept C is said to exist;

NORM - Quality

Q=<Qname,Vi,Qcon> Qname – name of the quality Vi – Quality value list; i = 0 to v, max. no. of values allowed for Qname Qcon – constraint set of Qname

Nyaya-Vaisheshika Qualities

NORM - Relation

R= <Rname,CAq,CBq,Rcat,Rqual,Rpr,Rcon> Rname – name of the relation CAq, CBq ⊆ Ccat ; q = 1 to n; n – max. no. of qualities defined for CA, CB in OT; CA = CB permissible. Rcat={RS-OI,RS-R,RR-OI} Rqual={Ici,D,X,Xp}, Ic – Invariable concomitance; i = 0-3, over {sym, +Ic, -Ic, Neutral}; D – Direct; X – Exclusive; Xp - Exceptional Rpr = Relation priority weight factor Rcon = constraint set over defined relations, {Rcon[i], R1, R2}; R1, R2 ∈ R. i=0, reflexive, here R1, R2 = NULL ; i=1,

‘Gautama’ tool

Gautama - Description



ILO Visualisation Pane:



contains icons to save and print the ontology visualisation created in the top left pane of the

• editor. In addition, drawing icons have also been provided.



Concepts Visualisation Pane:



• nly the concept hierarchy in the ontology is visualised.



Nodes Entry Pane:



provides controls for entering information about the nodes that are yet to be created



C-C denotes concept-concept; V-V denotes value-value and Q-Q denotes quality-quality.



command buttons provided to add concepts, qualities and values.



‘Generate RDF’ button helps in generation of Resource description format



Relations Entry Pane:



‘roles’ shall be created - at all levels as per NORM



command buttons for ‘deletion’ services.



‘load rdf’ button to load a pre-defined ontology at once.



Concepts list Pane:



lists all the concepts



specialised concepts first , followed by the generalised concepts.



Quality List Pane:

NORM RDF



<rdf:concept>

 used to declare a concept prior and after its definition



<rdf:name>

 used to declare the name of a concept / quality / relation.



<rdf:desc>

 used to create descriptions or definitions for a particular concept



<rdf:axiom>

 used to create concept axioms



<rdf:quality>

 used to create member qualities for a given concept



<rdf:type>

 used to declare the type of a concept / quality / relation



<rdf:role>

 used to declare the role of a concept / quality



<rdf:category>

 used to declare the category of relation like external, internal, tangential or

grouping. 

<rdf:operator>

 used to declare the logical operators like and, or while creating the concept

NDL



Concept-satisfiable

 This takes a concept name as the parameter and checks whether the addition of

the concept will not violate the ontology definitions that exist prior to the execution of this command 

Concept-subsumes

 This takes two concepts as input, and checks whether the first concept subsumes

the second concept. This is one of the famous reasoning service provided by any

• ntology-based reasoner.



Concept ancestors and Concept-descendants

 These commands list the ancestral / descending concepts in the ontology

• hierarchy. Role-ancestors and Role-descendants also have similar purpose.



Sub-concept, Super-concept

 These commands retrieve the child nodes or parent nodes of the parametric

concept from the ontology hierarchy 

Chk-concept-related

 This command has three variations. It either checks whether a concept is related

to another concept, through a particular relation name or through a particular set

• f relation categories.



Chk-quality

 This command checks the entire ontology hierarchy to check if the required quality

is available in the ontology 

Chk-concept-quality

 This command checks the entire ontology hierarchy to check if the particular

concept has the required quality.

Future enhancements

Translation of NORM RDF into visualised

• ntology in Gautama

Improving visualisation Color coding for qualities and relations

across levels

 Merging two IL ontologies  Automated IL ontology creation from

text passages

Key References



• G. Aghila, G.S. Mahalakshmi and Dr. T.V. Geetha, ‘KRIL – A

Knowledge Representation System based on Nyaya Shastra using Extended Description Logics’, VIVEK journal, ISSN 0970-1618, Vol. 15, No.3, pp. 3-18, July (2003).



Gautama, The Nyaya Sutras, translated by S.C. Vidyabhusana, edited by Nanda Lal Sinha, Sacred Book of the Hindus, Allahabad, (1930). Reprinted in 1990. Delhi: Motilal Banarsidass



Jonardon Ganeri, Indian Logic: A Reader, Published by Routledge, (2001)



G.S. Mahalakshmi and T.V. Geetha, Reasoning and Evolution of consistent ontologies using NORM, IJAI, Indian Society for Development and Environment Research (ISDER), ISSN 0974-0635, Volume 2, Number S09, pp. 77-94, Spring (2009).



Swami Virupakshananda, Tarka Samgraha, Sri Ramakrishna Math, Madras, (1994).

Thank You…