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  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

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Our idea – categories of Nyaya defects

Defect Table - Possible defects classified per defect category

Defect classification, identification Nyaya Defect types Argument Analysis Defect Categories Defect Table Defect set

Sample arguments Arg. object of Id Argument Subject inference reason 1 sky_lotus has fragrance sky_lotus fragrance Nil artificial- 2 artificial-rose has fragrance fragrance Nil rose 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 HC1 1 concept doesn't exists Unestablished to subject concept doesn't exists concept exists, fragrance as a HC7 concept exists, fragrance as a 2 quality(negation) Unestablished to itself quality(negation) 3 concept and quality exists No Defect concept and quality exists Fire, smoke exists as concepts. No HC8 Fire, smoke exists as concepts. No 4 invariable relation Unestablished to invariance invariable relation Penguin and bird exists as concept. HC4 Penguin and bird exists as concept. 5 Exclusive quality: fly in negation Straying Uncommon Exclusive quality: fly in negation Bat, mammal and bird exist as Bat, mammal and bird exist as 6 concept. Mammal-viviparous, bird- HC2, HC5 concept. Mammal-viviparous, bird- ~viviparous Antithetical ~viviparous Falls and smoke exist as concept. Falls and smoke exist as concept. 7 Absence of fire as concept. Direct HC1, HC5 Absence of fire as concept. Direct relation between fire and smoke Straying Common relation between fire and smoke Falls and smoke exist as concept. Falls and smoke exist as concept. 8 Absence of fire as concept. Invariable HC1, HC6 Absence of fire as concept. Invariable relation between fire and smoke Adverse 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 Gautama, The Nyaya Sutras, translated by S.C. Vidyabhusana, edited by 1. Nanda Lal Sinha, Sacred Book of the Hindus, Allahabad, (1930). Reprinted in 1990. Delhi: Motilal Banarsidass C. L. Hamblin. Fallacies. London:Methuen, (1970). 2. Jaakko Hintikka, Socratic Epistemology: Explorations of Knowledge-Seeking 3. by Questioning, Cambridge University Press, 239pp., (2007) G.S.Mahalakshmi and T.V.Geetha: Navya-Nyaya Approach to Defect 4. 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). Sathis Chandra Vidyabhusana, A History of Indian Logic – Ancient, 5. Medieaeval and Modern Schools, Motilal Banarsidass Publishers Private Ltd., Delhi, India, ISBN:81-208-0565-8. pp. 84, (1988). Swami Virupakshananda: Tarka Samgraha, Sri Ramakrishna Math, Madras 6. (1994). Toshihiro Wada, Invariable Concomitance in Navya-Nyaya, Sri Garib Dass 7. Oriental Series No. 101, Indological and Oriental Publishers, New Delhi, India, (1990). Walton, D. and Woods, J., Argument: The Logic of the fallacies, Toronto: 8.

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=< A id , C S ,C OI ,C R ,R S-OI ,R S-R ,R R-OI ,A state ,A status ,A str > A id - Argument index C S ,C OI ,C R - concept categories; R S-OI ,R S-R ,R R-OI - relation categories; A state – state of argument; A state {premise, inference, conclusion} A status – defeat status of arguments; A status {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= <C name , C cat , Q M ,Q O ,Q E ,C pr ,C par ,C con > C name – name of the concept C cat ={C S ,C OI ,C R } Q M = Quality Mandatory of type Quality Q Q O = Quality optional of type Quality Q Q E = Quality Exceptional of type Quality Q C pr = Concept priority weight factor C par = parent concept C , par = 0 to n; n – max. no. of concepts in committed ontology C con = constraint set under which concept C is said to exist;

NORM - Quality Q=<Q name ,V i ,Q con > Q name – name of the quality V i – Quality value list; i = 0 to v, max. no. of values allowed for Q name Q con – constraint set of Q name

Nyaya-Vaisheshika Qualities