Negation has been one of the fascinating things and a significant concern of pragmatic frameworks. In fact, if we divide cognition in terms of deduction based binaries, half of the cognitions falls in the regime of negation. Based on the cultural differences, eastern and western epistemological schools have dealt with negation in different ways.
Under eastern epistemological schools, Nyāya is a school of philosophy which considers the natural language as an imperfect vehicle for scientific and philosophical discourse due to its ambiguities. The philosophers of this tradition have developed a technical language, which can be used for unambiguous linguistic analysis. Nyayikas have presented a detailed account of cognition through negation by giving four types namely, 1. Prāgabhāva, 2. Pradhvaṃsābhāva, 3. Atyantābhāva and 4. Anyōnyābhāva, along with their further sub-divisions.
Another epistemological school, Apohavāda, which is related to Buddhism, presents a scheme in which cognition of something happens in opposition to other things. The idea is further subcategorized as (1) paryudāsa rūpa, and (2) prasajya pratiṣedha; where paryudāsa rūpa refers to intention and prasajya pratiṣedha, which is extension, holds the property of negation.
Western epistemological school Structuralism, in a slightly different fashion, considers the meaning to be constructed of two parts, which are signifier and signified. Structuralists pose that anything in some given set is cognized in opposition to other things in the same set, however, contrary to Apohavāda, there is no such dedicated part of meaning which deals with negation in a similar fashion, like paryudāsa rūpa.
Expanding the idea of Ferdinand de Saussure further, Jacques Derrida in his critique Deconstruction presents a similar approach that there is a self-sufficient, non-deferred meaning as a metaphysics of presence and a concept must be understood in the concept of its opposite.
All of these devices deal with cognition through deduction, however, are very different based on the core ideology. Along with the comparative study of all approaches, this paper tries to find out the best model, which can further be scaled for machine learning and other applications.
Bibliography:
Arjuna, S. R., and Amba Kulkarni. "Segmentation of Navya-Nyaya Expressions." In 11th International Conference on Natural Language Processing, p. 287. 2014.
Derrida, Jacques. Deconstruction in a nutshell: A conversation with Jacques Derrida. No. 1. Fordham Univ Press, 1997.
De Saussure, Ferdinand. Course in general linguistics. Columbia University Press, 2011.
Ganeri, Jonardon. "Towards a formal regimentation of the Navya-Nyaya technical language I." Logic, Navya-Nyaya & Applications. Homage to Bimal Krishna Matilal (2008): 105-121.
Katsura, Shoryu. "The apoha theory of Dignaga." Journal of Indian and Buddhist studies (Indogaku bukkyogaku kenkyu) 28, no. 1 (1979): 493-489.
Kelly III, John, and Steve Hamm. Smart Machines: IBMÕs Watson and the Era of Cognitive Computing. Columbia University Press, 2013.
Kulkarni, Amba, and S. R. Arjuna. "Type-identifier for Navya-Nyaya Expressions."
Matilal, Bimal Krishna, Jonardon Ganeri, and Heeraman Tiwari, eds. The character of logic in India. SUNY Press, 1998.
Modha, Dharmendra S., Rajagopal Ananthanarayanan, Steven K. Esser, Anthony Ndirango, Anthony J. Sherbondy, and Raghavendra Singh. "Cognitive computing." Communications of the ACM 54, no. 8 (2011): 62-71.
Shukla, Raja Ram. Nyaya siddhanta muktavali of vishvanatha panchanana with dinkari. Indian Institute of Advanced Study, Shimla, 2015.