Slides - Association for Logic in India
Transcription
Slides - Association for Logic in India
Formal Definitions Of Reason Fallacies To Aid Defect Exploration In Argument Gaming G.S. Mahalakshmi, Lecturer, Anna University, Chennai – 25 [email protected], [email protected] 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) ‘Because it has smoke’ (reason) Lake – subject; fire – probandum or object to be inferred ‘Because it has smoke’ (reason) Oven – similar example This lake has fire’ (statement) Smoke – probans or Reason ‘Since whatever has smoke has fire e.g. an oven’ (example) Hill – subject; fire – probandum or object to be inferred 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 Adverse concept to which the subject is related to is not present or not related as said, with the subject Stultified Two valid reasons for presence and absence of the thing to be proved Unestablished Reason is pervaded by negation of the thing to be proved Antithetical Reason which is present in a place where there is absence of the thing to be proved 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 Nyaya Defect types Argument Analysis Defect Categories Defect Table Defect set Sample arguments Arg. Id Argument Subject object of inference reason 1 sky_lotus has fragrance sky_lotus fragrance Nil 2 artificial-rose has fragrance artificialfragrance rose 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 1 Status in KB Defect Category & Type Status in KB concept doesn't exists HC1 Unestablished to subject concept doesn't exists HC7 Unestablished to itself concept exists, quality(negation) 2 concept exists, 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 HC1, HC6 Falls and smoke exist as concept. Absence of fire as concept. Invariable 8 fragrance as a Falls and smoke exist as concept. Absence of fire as concept. Invariable fragrance as a 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 [email protected], [email protected] Idea Indian logic based approach of knowledge representation classifies the world knowledge into concepts, and relations, both enriched with special qualities. Nyaya Sastra Nyaya logics categorization of world knowledge elaborate in tapping the minute details in the defined knowledge units. 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) (b) (c) ontology with concepts as nodes and external relations as edges a concept with qualities as nodes, internal relations as thin edges, tangential relations as dotted edges 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: 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: 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. lists all the concepts specialised concepts first , followed by the generalised concepts. Quality List Pane: NORM RDF <rdf:concept> <rdf:name> used to declare the role of a concept / quality <rdf:category> used to declare the type of a concept / quality / relation <rdf:role> used to create member qualities for a given concept <rdf:type> used to create concept axioms <rdf:quality> used to create descriptions or definitions for a particular concept <rdf:axiom> used to declare the name of a concept / quality / relation. <rdf:desc> used to declare a concept prior and after its definition 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 Concept-subsumes 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 These commands retrieve the child nodes or parent nodes of the parametric concept from the ontology hierarchy Chk-concept-related These commands list the ancestral / descending concepts in the ontology hierarchy. Role-ancestors and Role-descendants also have similar purpose. Sub-concept, Super-concept 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 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 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 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…