Nonmonotonic proof systems: Algebraic foundations
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.
nonmonotonic logic ranked system algebraic semantics cumulative system preferential system