Logic Journal of IGPL Advance Access originally published online on January 6, 2009
Logic Journal of IGPL 2009 17(1):55-76; doi:10.1093/jigpal/jzn026
An Indian logic-based argument representation formalism for knowledge-sharing1
Department of Computer Science & Engineering, Anna University, Chennai-25, Tamilnadu, India
E-mail: mahalakshmi{at}cs.annauniv.edu; tvgeedir{at}cs.annauniv.edu
Knowledge-sharing is the fundamental aspect of learning from ancient days. By exchanging questions and answers in a debate fashion, knowledge is explored. Argumentation can be thought of as a knowledge-sharing mechanism where construction of arguments and counter-arguments towards reaching mutually agreed upon conclusions is modelled after the rational discussion of knowledge-sharing. The procedural approach of generation and exchange of arguments is with the intention of reaching a definite conclusion at the end of discussion irrespective of the winning or losing of the individual arguments. A procedural argumentation system for knowledge-sharing, similar to the one discussed above will be of immense use only when the representational facts of world knowledge are well captured and represented as identical with the representation of natural intelligence. Indian Philosophy suggests various rules for classifying and representing the world knowledge to enhance the procedure of argumentation in reaching new inferences. This paper discusses a new mathematical model that caters to the special requirements of classification and hypothetical argumentative reasoning (tarka) of Indian philosophy. The main focus is the emphasis given to the existence of relations between concepts and foundation of invariable connection between concepts/relations of the arguments that is indicated by the philosophy. The extracted knowledge from the arguments exchanged is captured using ‘Indianised logics’, an Indian Logic based argument representation formalism. The arguments are deeply analysed for the presence of conceptual and relational conflicts. This is achieved by referring to the presence and/or absence of invariable concomitance, so that, the decision of justifying the represented invalid knowledge with or without proof shall be made clear in knowledge-sharing through rational discussion.
Key Words: Mathematical model • Knowledge representation • Procedural argumentation • Logic • Indian philosophy • Knowledge-sharing and Argument
Received for publication 27 April 2006.
1This work is an extended version of the paper titled ‘A Mathematical Model for Argument Procedures based on Indian Philosophy’, Proc. of International Conf. on Artificial Intelligence & Applications (AIA’06) as part of 24thIASTED International Multi-conference on Applied Informatics (AI’06), Innsbruck, Austria, February 13–16, 2006.
References
-
[1] Aghila G, Ranjani Parthasarathi, Geetha TV. Design of conceptual ontology based on Nyaya theory and Tolkaappiyam. In: Proc. 3rd International Conf. on South Asian Languages (2001) January. India.
[2] Aghila G, Ranjani Parthasarathi, Geetha TV. Indian Logic-based conceptual ontology using Description Logic. In: Proc. National Conf. on Data Analysis and Recognition (2001) July. India.
[3] Aghila G, Mahalakshmi GS, Geetha TV. KRIL – A Knowledge Representation System based on Nyaya Shastra using Extended Description Logics. In: VIVEK Journal. (2003).
[4] Bart Verheij. Artificial Argument Assistants for Defeasible Argumentation. (2003) April. Netherlands: Department of Metajuridica, University of Masstricht.
[5] Bench-Capon TJM. Representation of Case Law as an Argumentation Framework in. In: Legal Knowledge and Information Systems—Bench-Capon TJM, Daskalopulu A, Winkels RGF, eds. (2002) Amsterdam: IOS Press. 103–112. Jurix 2002: Proceedings of Fifteenth Annual Conference.
[6] Bharadwaja Vijay. Form and Validity in Indian Logic. (1990) Shimla: Indian Institute of Advanced Study.
[7] Cakra Pani Dasa. Nyaya/Vedanta - The Philosophy of Logic and Reasoning. accessed latest by 14 May 2005. (The South Asian Study House). http://www.geocities.com/Athens/Acropolis/2681/nyaya.html.
[8] Chhanda Chakraborti. Logic: Informal, Symbolic and Inductive, (2006) New Delhi: Prentice Hall of India.
[9] Cornelius Goekoop. The Logic of Invariable Concomitance in the Tattvacintamani: Gangesa's Anumitinirupana and Vyaptivada with Introduction, Translation and Commentary by Cornelius Goekoop. (1967) Holland: D.Reidel Publishing Company.
[10] Daniela V Carbogim, David Robertson, John Lee. Argument based Applications to Knowledge Engineering. (1999) Brazil: Division of Informatics, University of Edinburgh.
[11] Davis R, Shrobe H, Szolovits P. What is a Knowledge Representation?. AI Magazine (1993) 14(1):17–33.
[12] Diego Calvanese, De Giuseppe Giacomo, Maurizio Lenzerini. Description Logics: Foundations for Class-based Knowledge Representation. (2002) Italy: Dipartimento di Informatica e Sistemistica, Universit‘a di Roma ‘‘La Sapienza’’, Via Salaria 113, I-00198 Roma.
[13] SaaminaathaIyer UVe Dr. Pavanandhi munivar iyatriya Nannool moolamum Mayilainaathar uraiyum. (1995) Chennai: Dr.U.Ve.SaaminaathaIyer Noolnilaiyam.
[14] Esther Solomon. Indian Dialectics: Methods of Philosophical Discussion. 2. India: Ahmedabad:Inst. of Learning and Research, Gujarat Vidya Sabha.
[15] Gautama(Gotama). The Nyaya Sutras.—Nanda Lal Sinha, ed. (1930) Allahabad: Sacred Book of the Hindus. translated by S.C. Vidyabhusana, Reprinted in 1990. Delhi: Motilal Banarsidass.
[16] Gradinarov PI. Phenomenology and Indian Epistemology – Studies in Nyaya-Vaisesika Transcendental Logic and Atomism. (1990) Sophia Indological Series.
[17] Gruber TR. Towards principles for the design of ontologies used for knowledge-sharing, Padova, Italy, 1992, revised and appears in. In: Formal Ontology in Conceptual Analysis and Knowledge Representation.—Guarino, Poli, eds. (1993) August. Kluwer Publishers.
[18] Gruber TR. A Translation Approach to Portable Ontology Specifications. In: Academic Press. (1993).
[19] Hajime Sawamura. Logic of Argumentation based on Tetralemma with an Eastern Mind. USA: New York. AAMAS’04, July 19-23, 2004, ACM 1-58113-864-4/04/0007.
[20] Herbert Granger. Argumentation and Heraclitus book. (2004) 26. Oxford Studies in Ancient Philosophy.
[21] James Robert Ballantyne. Lectures on the Nyaya Philosophy- Embracing the text of Tarka Samgraha, Presbyterian Mission Press. Allahabad, India. 1849 digitized by Google Books on the web at http://books.google.com.
[22] Karl Potter H. Presuppositions of India's Philosophies. (1991) Delhi: Motilal Banarsidass. Englewood Cliffs, N.J.: Prentice Hall Inc. Indian Edition.
[23] Mahalakshmi GS, Aghila G, Geetha TV. Multi-level ontology representation based on Indian Logic System. In: Proc. 4th International Conference on South Asian Languages (2002) October. India.
[24] Mahalakshmi GS, Geetha TV. A Mathematical Model for Argument Procedures based on Indian Philosophy. In: Proc. of International Conf. Artificial Intelligence and Applications (AIA 2006) as part of the 24th IASTED International Multi-conference Applied Informatics (AI 2006), (2006) February. Austria: Innsbruck. 13–16.
[25] Nico Roos. On Resolving conflicts between arguments. In: Computational Intelligence. (2000) Number 3;16.
[26] Oetke C. Indian Logic and Indian Syllogism. In: Indo-Iranian Journal. (2003) 46. Kluwer Academic Publishers. 53–69(17).
[27] Prakken H, Sartor G. Computational Logic: Logic Programming and Beyond. (2002) Berlin: Springer-Verlag. 342–380. Essays In Honour of Robert A. Kowalski, Part II. Volume 2048 of Lecture Notes in Computer Science.
[28] Soma Ilavarasu Prof. Nannool Ezhuthathikaaram. (1999) Chennai: Manivasagar Publishers.
[29] Radhakrishnan S. Indian Philosophy. (1999) 2. Oxford University Press. 386–387.
[30] Ramakrishna Rao KB. accessed latest by April 2006. http://www.celticguitarmusic.com/life_of_shankara.htm.
[31] Ramakrishnan Puligandla. Fundamentals of Indian Philosophy, (1997) New Delhi, India: D.K. Printword(P) Ltd. Originally published in 1975.
[32] Richard King. Indian Philosophy – An Introduction to Hindu and Buddhist Thought. (1999) New Delhi, India: Maya Publishers Pvt. Ltd. EUP, Indian Edition.
[33] Rob Reich. Confusion about the Socratic Method: Socratic Paradoxes and Contemporary Invocations of Socrates (1998) Stanford University, Philosophy of Education Yearbook. At http://www.ed.uiuc.edu/EPS/PES-yearbook/1998/reich.html.
[34] Sarvepalli Radhakrishnan, Moore Charles A, eds. The method of vada debate in. In: A Source Book in Indian Philosophy. (1989) Princeton University Press. 361–365.
[35] Satis Chandra Vidyabhusana. A History of Indian Logic – Ancient, Medieaeval and Modern Schools. (1921) Delhi, India: Motilal Banarsidass Publishers Private Ltd. ISBN:81-208-0565-8.
[36] Swami Virupakshananda. Tarka Samgraha. (1994) Madras: Sri Ramakrishna Math.
[37] Toshihiro Wada. Invariable Concomitance in Navya-Nyaya. (1990) New Delhi, India: Indological and Oriental Publishers. Sri Garib Dass Oriental Series No. 101, ISBN: 81-7030-227-7.
[38] Udayana. Nyayakusumanjali. (1950) Benares: Kashi Sanskrit Series. Edited with various commentaries by Padmaprasadopadhyaya.
[39] Vellai vaaraNanaar K. Tolkaapiyam – Nannool Ezhuthathikaaram. (1974) 3rd Edition. Tamilnadu, India: Annamalai University.
[40] Volker Peckhaus. Dignaga's Logic of Invention. (2001) December 22. New Delhi, India: University of Delhi. First International Conference of the New Millenium on History of Mathematical Sciences, Indian National Science Academy.
[41] Wolfgang Spohn. A Brief Comparison of Pollock's Defeasible Reasoning and Ranking Functions. (2002) Germany: Konstanz University.
CiteULike 
Connotea 
Del.icio.us What's this?
| ||||||||||||||||||||||||||||||||||||||||||||||||||