Non-deterministic approximation operators: ultimate operators, semi-equilibrium semantics and aggregates (full version)
This work is incremental, advancing the theoretical framework for non-monotonic logics used in AI and knowledge representation.
The paper extends non-deterministic approximation fixpoint theory by introducing ultimate approximations, providing an algebraic formulation of semi-equilibrium semantics, and generalizing characterizations to disjunctive logic programs with aggregates.
Approximation fixpoint theory (AFT) is an abstract and general algebraic framework for studying the semantics of non-monotonic logics. In recent work, AFT was generalized to non-deterministic operators, i.e.\ operators whose range are sets of elements rather than single elements. In this paper, we make three further contributions to non-deterministic AFT: (1) we define and study ultimate approximations of non-deterministic operators, (2) we give an algebraic formulation of the semi-equilibrium semantics by Amendola, et al., and (3) we generalize the characterisations of disjunctive logic programs to disjunctive logic programs with aggregates.