Partial Fixed-Point Logic on Infinite Structures
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
Inflationary fixed points in modal logic
ACM Transactions on Computational Logic (TOCL)
Backtracking games and inflationary fixed points
Theoretical Computer Science - Automata, languages and programming: Logic and semantics (ICALP-B 2004)
Recursive Definitions and Fixed-Points
Electronic Notes in Theoretical Computer Science (ENTCS)
FO(ID) as an extension of DL with rules
Annals of Mathematics and Artificial Intelligence
Recursive definitions and fixed-points on well-founded structures
Theoretical Computer Science
Second-order principles in specification languages for object-oriented programs
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Fixed-point definability and polynomial time on graphs with excluded minors
Journal of the ACM (JACM)
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We study the relationship between least and inflationary fixed-point logic. By results of Gurevich and Shelah from 1986, it has been known that on finite structures both logics have the same expressive power. On infinite structures however, the question whether there is a formula in IFP not equivalent to any LFP-formula was still open.In this paper, we settle the question by showing that both logics are equally expressive on arbitrary structures. The proof will also establish the strictness of the nesting-depth hierarchy for IFP on some infinite structures. Finally, we show that the alternation hierarchy for IFP collapses to the first level on all structures, i.e. the complement of an inflationary fixed-point is an inflationary fixed-point itself.