Data types may be considered as objects in any suitable category, and need not necessarily be ordered structures or many-sorted algebras. Arrays may be specified having as parameter any object from a category J.f with finite products and eoproducts, if products distribute over coproducts. The Lehmann-Smith least fixpoint approach to recursively-defined data types is extended by introducing the ...

Interpretation is a theory of approximate solving of fixpoint equations applied to program analysis. Most program analysis problems, among others reachability analysis, come down to solving a fixpoint equation

D We present a fixpoint semantics for disjunctive logic programs. We extend the concept of the Herbrand base of a logic program to consist of all positive clauses that may be formed using the atoms in the Herbrand base. A monotonic closure operator is defined, operating on the lattice formed by the power set of the extended Herbrand base. The closure operator is shown to achieve a least fixpoin...

We introduce fixpoint definitions, a rule-based reformulation of fixpoint constructs. The logic FO(FD), an extension of classical logic with fixpoint definitions, is defined. We illustrate the relation between FO(FD) and FO(ID), which is developed as an integration of two knowledge representation paradigms. The satisfiability problem for FO(FD) is investigated by first reducing FO(FD) to differ...

Polyadic Higher-Order Fixpoint Logic (PHFL) is a modal fixpoint logic obtained as the merger of Higher-Order Fixpoint Logic (HFL) and the Polyadic μ-Calculus. Polyadicity enables formulas to make assertions about tuples of states rather than states only. Like HFL, PHFL has the ability to formalise properties using higher-order functions. We consider PHFL in the setting of descriptive complexity...

We present a method to compute uniform interpolants with fixpoints for ontologies specified in the description logic ALC. The aim of uniform interpolation is to reformulate an ontology such that it only uses a specified set of symbols, while preserving consequences that involve these symbols. It is known that in ALC uniform interpolants cannot always be finitely represented. Our method computes...