A Logic of Non-Monotone Inductive Definitions and its Modularity Properties (2004)
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BibTeX
@MISC{Denecker04alogic,
author = {Marc Denecker and Eugenia Ternovska},
title = {A Logic of Non-Monotone Inductive Definitions and its Modularity Properties},
year = {2004}
}
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Abstract
Well-known principles of induction include monotone induction and dierent sorts of non-monotone induction such as inationary induction, induction over well-ordered sets and iterated induction. In this work, we de ne a logic formalizing induction over well-ordered sets and monotone and iterated induction. Just as the principle of positive induction has been formalized in FO(LFP), and the principle of inationary induction has been formalized in FO(IFP), this paper formalizes the principle of iterated induction in a new logic for Non-Monotone Inductive De nitions (NMID-logic). The semantics of the logic is strongly inuenced by the well-founded semantics of logic programming.
