Fixed-Point Quantifiers in Higher Order Logics

Authors:
Klaus-Dieter Schewe;José María Turull Torres
Affiliations:
Massey University, Information Science Research Centre & Department of Information Systems, Private Bag 11222, Palmerston North, New Zealand;Massey University, Information Science Research Centre & Department of Information Systems, PO Box 756, Wellington, New Zealand, [k.d.schewe|j.m.turull]@massey.ac.nz
Venue:
Proceedings of the 2006 conference on Information Modelling and Knowledge Bases XVII
Year:
2006

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Abstract

We add inflationary and non-inflationary fixed-points to higher-order logics. We show that, for every order, it is sufficient to increase the order of the given logic by one to capture inflationary fixed-points and by two to capture non-inflationary fixed-points. In the two cases, restricting to the existential fragment of the corresponding logic turns out to be enough. This also holds for non-deterministic fixed-points.