Fixpoint expressions built from functional signatures interpreted over arbitrary complete lattices are considered. A generic notion of automaton is defined and shown, by means of a tableau technique, to capture the expressive power of fixpoint expressions. For interpretation over continuous and complete lattices, when, moreover, the meet symbol ^ commutes in a rough sense with all other functio...

This paper presents a rule-based database language which extends stratified DATALOG by adding a controlled form of inflationary fixpoint, immersed in a context of classical stratified negation with least fixpoint. The proposed language, called Semi-Inflationary DATALOG (DATALOG for short), smoothly combines the declarative purity of stratified negation with the procedural style of the inflation...

The modal μ-calculus extends basic modal logic with secondorder quantification in terms of arbitrarily nested fixpoint operators. Its satisfiability problem is EXPTIME-complete. Decision procedures for the modal μ-calculus are not easy to obtain though since the arbitrary nesting of fixpoint constructs requires some combinatorial arguments for showing the well-foundedness of least fixpoint unfo...

In recent years several extensions of first-order logic have been investigated in the context of finite-model theory. Fixpoint logic and the infinitary logic L∞ω with a finite number of variables have turned out to be of particular importance. The study of fixpoint logic generated interactions with both database theory and complexity theory, while the infinitary logic L∞ω proved to be a useful ...

We investigate the logical difference problem between general EL-TBoxes. The logical difference is the set of concept subsumptions that are logically entailed by a first TBox but not by a second one. We show how the logical difference between two EL-TBoxes can be reduced to fixpoint reasoning w.r.t. EL-TBoxes. Entailments of the first TBox can be represented by subsumptions of least fixpoint co...

We look at characterizing which formulas are expressible in rich decidable logics such as guarded fixpoint logic, unary negation fixpoint logic, and guarded negation fixpoint logic. We consider semantic characterizations of definability, as well as effective characterizations. Our algorithms revolve around a finer analysis of the tree-model property and a refinement of the method of moving back...