Approximations, stable operators, well-founded fixpoints and applications in nonmonotonic reasoning (Q2734934)

The authors develop an algebraic framework for a semantics of nonmonotonic logic in terms of lattices, bilattices, operators and fixpoints. An algebraic theory of fixpoints of non-monotone operators on lattices is presented. A pair of elements of a lattice approximates a third element if it lies between the former ones. An approximating operator is an monotone operator on the bilattice of approximations whose fixpoints approximate the fixpoints of the operator. The authors give an algebraic construction which assigns a certain operator, called the stable operator, to every such approximating operator. This construction leads to an abstract version of the well founded semantics. Many major semantics for logic programming (LP), autoepistemic logic (AL), and default logic (DF) are described in a uniform way by applying algebraic fixpoint theory to particular operators for LP, AL, DL.NEWLINENEWLINEFor the entire collection see [Zbl 0960.00037].