Guarded fixed point logic

Abstract

Guarded fixed point logics are obtained by adding least and greatest fixed points to the guarded fragments of firstorder logic that were recently introduced by Andréka, van Benthem and Németi. Guarded fixed point logics can also be viewed as the natural common extensions of the modal -calculus and the guarded fragments. We prove that the satisfiability problems for guarded fixed point logics are decidable and complete for deterministic double exponential time. For guarded fixed point sentences of bounded width, the most important case for applications, the satisfiability problem is EXPTIME-complete.

Johan van Benthem on Logic and Information Dynamics

“…The ''modal'' nature of the guarded fragments is confirmed by the fact that they are decidable and have the finite model property. Moreover, their decidability is ''robust'', in the sense that it is inherited by their fixed-point extensions, as shown by Graedel and Walukiewicz [142]. As such, this line of research provided a clear conceptual answer to Vardi's question: it is exactly the locality or ''dynamicity'' of modal logic (shared with the above-mentioned fragments, in the form of guardedness) that is responsible for its robustly good behavior!…”

Bisimulation and Coverings for Graphs and Hypergraphs

“…We here concentrate on special model properties and issues of expressive completeness. For background on the logics involved, modal logics (including many variants and extensions of basic modal logic ML, e.g., in the spirit of epistemic or temporal logics) and guarded logics like the guarded fragment of first-order logic GF, we refer the reader to textbook sources and surveys [8,10] and the original papers [2,11,14,12]. Theorem 2.1.…”

Guarded Open Answer Set Programming with Generalized Literals

“…Take the program P , the open answer set variant of the classical infinity axiom in guarded fixed point logic from [11]:…”

“…In [14], these external manipulations, i.e. not expressible in the language of programs itself, were compiled into fixed point logic (FPL) [11], i.e. into an extension of first-order logic with fixed point formulas.…”

“…Guarded fixed point logic (µGF) [11] is such a decidable fragment of FPL that is able to express fixed point formulas. It restricts the use of quantified variables by demanding that they are guarded by an atom.…”