Formal Definitions Of Reason Fallacies To

Aid Defect Exploration In

Argument Gaming

G.S. Mahalakshmi, Lecturer, Anna University, Chennai – 25mahalakshmi@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

of 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 Subjectobject 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 defectsA r g . Id Status in KB Defect Category & Type Status in KB

1 concept doesn't existsHC1Unestablished to subject concept doesn't exists

2concept exists, fragrance as a quality(negation)

HC7Unestablished 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

HC8Unestablished to invariance

Fire, smoke exists as concepts. No invariable relation

5 Penguin and bird exists as concept. Exclusive quality: fly in negation

HC4Straying Uncommon

Penguin and bird exists as concept. Exclusive quality: fly in negation

6Bat, mammal and bird exist as concept. Mammal-viviparous, bird-~viviparous

HC2, HC5Antithetical

Bat, mammal and bird exist as concept. Mammal-viviparous, bird-~viviparous

7Falls and smoke exist as concept. Absence of fire as concept. Direct relation between fire and smoke

HC1, HC5Straying Common

Falls and smoke exist as concept. Absence of fire as concept. Direct relation between fire and smoke

8Falls and smoke exist as concept. Absence of fire as concept. Invariable relation between fire and smoke

HC1, HC6Adverse

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 References1. 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 – 25mahalakshmi@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 - RelationR= <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: only 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 ontology-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 of 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 ontology in Gautama

Improving visualisationColor coding for qualities and relations

across levelsMerging two IL ontologiesAutomated 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…