Abstract Knaster-Tarski’s theorem, characterising the greatest fix- point of a monotone function over complete lattice as largest post-fixpoint, naturally leads to so-called coinduction proof principle for showing that some element is below fixpoint (e.g., providing bisimilarity witnesses). The dual principle, used an above least fixpoint, related inductive invariants. In this paper we provide ...

The paper proposes two fixpoint path query languages Path-Fixpoint and Path-While for unstructured data whose expressive power is that of Fixpoint and While queries respectively. These languages are multi-sorted like logic languages integrating fixpoint path expressions.

This paper studies parallel recursion. The trace specification language used in this paper incorporates sequentiality, nondeterminism, reactiveness (including infinite traces), three forms of parallelism (including conjunctive, fair-interleaving and synchronous parallelism) and general recursion. In order to use Tarski’s theorem to determine the fixpoints of recursions, we need to identify a we...

Optimal fixpoints of recursive operators extract maximum consistent information from recursive definitions. Although the optimal fixpoint always exists for a recursive operator, it can be uncomputable. The paper considers the restriction of the recursive operator to computable inputs and the set of consistent fixpoints induced by this restriction. The properties of the greatest element of this ...

Topological fixpoint logics are a family of logics that admits topological models and where the fixpoint operators are defined with respect to the topological interpretations. Here we consider a topological fixpoint logic for relational structures based on Stone spaces, where the fixpoint operators are interpreted via clopen sets. We develop a game-theoretic semantics for this logic. First we i...

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...