Partial Grounded Fixpoints
نویسندگان
چکیده
Approximation fixpoint theory (AFT) is an algebraical study of fixpoints of lattice operators. Recently, AFT was extended with the notion of a grounded fixpoint. This type of fixpoint formalises common intuitions from various application domains of AFT, including logic programming, default logic, autoepistemic logic and abstract argumentation frameworks. The study of groundedness was limited to exact lattice points; in this paper, we extend it to the bilattice: for an approximator A of O, we define A-groundedness. We show that all partial Astable fixpoints are A-grounded and that the Awell-founded fixpoint is uniquely characterised as the least precise A-grounded fixpoint. We apply our theory to logic programming and study complexity.
منابع مشابه
Grounded Fixpoints
Algebraical fixpoint theory is an invaluable instrument for studying semantics of logics. For example, all major semantics of logic programming, autoepistemic logic, default logic and more recently, abstract argumentation have been shown to be induced by the different types of fixpoints defined in approximation fixpoint theory (AFT). In this paper, we add a new type of fixpoint to AFT: a ground...
متن کاملGrounded Fixpoints and Active Integrity Constraints
The formalism of active integrity constraints was introduced as a way to specify particular classes of integrity constraints over relational databases together with preferences on how to repair existing inconsistencies. The rule-based syntax of such integrity constraints also provides algorithms for finding such repairs that achieve the best asymptotic complexity. However, the different semanti...
متن کاملFixpoints and Bounded Fixpoints for Complex Objects
We investigate a query language for complex-object databases, which is designed to (1) express only tractable queries, and (2) be as expressive over flat relations as first order logic with fixpoints. The language is obtained by extending the nested relational algebra NRA with a "bounded fixpoint" operator. As in the flat case, all PTime computable queries over ordered databases are expressible...
متن کاملCompleteness and Definability of a Modal Logic Interpreted over Iterated Strict Partial Orders
Any strict partial order R on a nonempty set X defines a function θR which associates to each strict partial order S ⊆ R on X the strict partial order θR(S) = R ◦ S on X. Owing to the strong relationships between Alexandroff TD derivative operators and strict partial orders, this paper firstly calls forth the links between the CantorBendixson ranks of Alexandroff TD topological spaces and the g...
متن کاملWorkshop on Nonmonotonic Reasoning, Answer Set Programming and Constraints
Logic Programming with Set Constraints V.W. Marek and J.B. Remmel We generalize the set constraints of the form kXl present in the current implementation of smodels ASP solver to the situation where the constraints are arbitrary families of subsets of a given finite set. It turns out that the Niemela-Simons-Soinanen construction of stable models smoothly generalizes to that context. The model t...
متن کامل