The paper presents a constructive 3-valued semantics for autoepistemic logic (AEL). We introduce a derivation operator and define the semantics as its least fixpoint. The semantics is 3-valued in the sense that, for some formulas, the least fixpoint does not specify whether they are believed or not. We show that complete fixpoints of the derivation operator correspond to Moore’s stable expansio...

We present a differential fixpoint iteration method to be used in static program analyses. The differential method consists of two phases: first we transform the program analysis equations into differential ones, and then we apply a differential fixpoint iteration to the equations computing with the differences from the previous iterations. We implemented the method for the exception analysis o...

Theorem (5) states that if an iterate of a function has a unique fixpoint then it is also the fixpoint of the function. It has been included here in response to P. Andrews claim that such a proof in set theory takes thousands of lines when one starts with the axioms. While probably true, such a claim is misleading about the usefulness of proof-checking systems based on set theory. Next, we prov...

Theorem (5) states that if an iterate of a function has a unique fixpoint then it is also the fixpoint of the function. It has been included here in response to P. Andrews claim that such a proof in set theory takes thousands of lines when one starts with the axioms. While probably true, such a claim is misleading about the usefulness of proof-checking systems based on set theory. Next, we prov...

In this paper, we present an abstract fixpoint checking algorithm with automatic refinement by backward completion in Moore closed abstract domains. We study the properties of our algorithm and prove it to be more precise than the counterexample guided abstract refinement algorithm (CEGAR). Contrary to several works in the literature, our algorithm does not require the abstract domains to be pa...

Context. Modal fixpoint logics constitute a research field of considerable interest, not only because of its many applications in computer science, but also because of its rich mathematical theory, which features deep connections with fields as diverse as lattice theory, automata theory, and universal coalgebra. In the 1970s computer scientists started to use modal logics as specification langu...

In this paper we study the problem of automatically generating switching controllers for the class of Linear Hybrid Automata, with respect to safety objectives. We identify and solve inaccuracies contained in previous characterizations of the problem, providing a sound and complete symbolic fixpoint procedure, based on polyhedral abstractions of the state space. We also prove the termination of...

In this paper we consider combining two techniques that have been effective in analyzing infinite-state systems: predicate abstraction and fixpoint approximations. Using a carefully crafted model of Airport Ground Network Control, we show that when predicate abstraction in a CEGAR loop fails to verify temporal logic properties of an infinite-state transition system, a combination of predicate a...