We propose an alternative non-monotonic modal formalism called non-monotonic modal logic of belief. It is based on replacing the classical fixpoint equation E = ThS(A ∪ {Mφ : E 6`S ¬φ}) with the belief fixpoint equation E = ThS(A ∪ {Mφ : E 6`S ¬Mφ}). The solutions of the belief fixpoint equation, called belief S-expansions, are tightly related to the logic of belief KD45. We show interpretation...

We study a decidable fixpoint extension of temporal description logics. To this end we employ and extend decidability results obtained for various temporally first-order monodic extensions of (firstorder) description logics. Using these techniques we obtain decidability and tight complexity results for various fixpoint extensions of temporal description logics.

We prove a general finite-time convergence theorem for fixpoint expressions over a well-quasi-ordered set. This has immediate applications for the verification of well-structured systems, where a main issue is the computability of fixpoint expressions, and in particular for game-theoretical properties and probabilistic systems where nesting and alternation of least and greatest fixpoints are co...

Approximation theory is a fixpoint theory of general (monotone and non-monotone) operators which generalizes all main semantics of logic programming, default logic and autoepistemic logic. In this paper, we study inductive constructions using operators and show their confluence to the well-founded fixpoint of the operator. This result is one argument for the thesis that Approximation theory is ...

In this paper we investigate the theoretical foundation of a new bottom-up semantics for linear logic programs, and more precisely for the fragment of LinLog (Andreoli, 1992) that consists of the language LO (Andreoli & Pareschi, 1991) enriched with the constant 1. We use constraints to symbolically and finitely represent possibly infinite collections of provable goals. We define a fixpoint sem...

We prove a general finite convergence theorem for “upward-guarded” fixpoint expressions over a well-quasi-ordered set. This has immediate applications in regular model checking of well-structured systems, where a main issue is the eventual convergence of fixpoint computations. In particular, we are able to directly obtain several new decidability results on lossy channel systems.

We present an enhancement of the generic fixpoint algorithm TD which can deal with widening and narrowing even for non-monotonic systems of equations. In constrast to corresponding enhancements proposed for other standard fixpoint algorithms, no extra priorities on variables are required. Still, a mechanism can be devised so that occurrences of the widening/narrowing operator are inserted as we...

In this paper we introduce a decidable fixpoint extension of temporal Description Logics. We exploit the decidability results obtained for various monodic extensions of Description Logics to obtain decidability and tight complexity results for temporal fixpoint extensions of these Description Logics and more generally for the decidable monodic fragments of first order logic.