We introduce a fixpoint extension of Hintikka and Sandu’s IF (independence-friendly) logic. We obtain some results on its complexity and expressive power. We relate it to parity games of imperfect information, and show its application to defining independence-friendly modal mu-calculi. Philosophia Scientiæ, 8 (2), 2004, 125–144.

We investigate /xpoint operators for domain equations. It is routine to verify that if every endofunctor on a category has an initial algebra, then one can construct a /xpoint operator from the category of endofunctors to the category. That construction does not lift routinely to enriched categories, using the usual enriched notion of initiality of an endofunctor. We show that by embedding the ...

We present new sound and complete axiomatizations of type equality and subtype inequality for a first-order type language with regular recursive types. The rules are motivated by coinductive characterizations of type containment and type equality via simulation and bisimulation, respectively. The main novelty of the axiomatization is the fixpoint rule (or coinduction principle), which has the f...

In [3] we investigate the problem of defining a well-founded and stable semantics for programs with aggregates. Our work is based on Approximation Theory [1] which is a general algebraic framework for approximating non-monotone operators on a complete lattice L by approximating operators on the bi-lattice L. The theory identifies basic properties of the approximating operators and gives a metho...

In this study we shall obtain some sufficient conditions for the existence of positive solutions variable coefficient nonlinear second-order neutral differential equation with distributed deviating arguments. For different cases range p(t) by using Banach contraction principle will give nonoscillatory equation. With purpose use fixpoint theorem. At end research, there is an example that meets h...

Hierarchical graph definitions allow a modular description of graphs using modules for the specification of repeated substructures. Beside this modularity, hierarchical graph definitions allow to specify graphs of exponential size using polynomial size descriptions. In many cases, this succinctness increases the computational complexity of decision problems. In this paper, the modelchecking pro...

Real-time distributed system speciication and veriication in asynchronous propositional temporal logic. Let A be the integrator system deened in Figure 5. We use the xpoint computation procedure to prove that the formula y 60 ! 20t y is an invariant of A. It follows that the gas burner leaks at most one twentieth of the time in any interval of at least 60 seconds. Let R i = hpc = 1 ^ t = 0 ^ x ...

The conventional formalization of logic programming in classical logic explains very convincingly the basic principles of this programming style. However, it gives no easy or intuitive explanations for the treatment of negation. Logic Programming handles negation through the so-called ^Negation as Failure" inference principle which is rather unconventional from the viewpoint of classical logic....