Nonmonotonic Proof Systems: Algebraic Foundations

Article type: Research Article

Authors: Ghosh, Sujata | Chakraborty, Mihir Kr.

Affiliations: Department of Mathematics Siksha Bhavana, Visva Bharati, Santiniketan, West, Bengal, India | Department of Pure Mathematics, University of Calcutta, 35 Ballygunge Circular Road, Kolkata - 700019, India

Abstract: A general framework for the algebraization of a category of nonmonotonic logics has been suggested. This method has been applied to the systems of Gabbay, and to Cumulative, Preferential and Ranked systems. The minimal logics required to serve as the base logics for the above systems are investigated. MAK triples and KLM triples are formed in ways similar to MAK models and KLM models but now on the algebraic structures for the nonmonotonic systems, thereby a new type of semantics is given to these systems.

Keywords: nonmonotonic logic, algebraic semantics, cumulative system, preferential system, ranked system

Journal: Fundamenta Informaticae, vol. 59, no. 1, pp. 39-65, 2004