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- W311767895 abstract "Minimal predicates P satisfying a given first-order description (P) occur widely in mathematical logic and computer science. We give an explicit first-order syntax for special first-order 'PIA conditions' (P) which guarantees unique existence of such minimal predicates. Our main technical result is a preservation theorem showing PIA-conditions to be expressively complete for all those first-order formulas that are preserved under a natural model-theoretic operation of 'predicate intersection'. Next, we show how iterated predicate minimization on PIA-conditions yields a language MIN(FO) equal in expressive power to LFP(FO), first-order logic closed under smallest fixed-points for monotone operations. As a concrete illustration of these notions, we show how our sort of predicate minimization extends the usual frame correspondence theory of modal logic, leading to a proper hierarchy of modal axioms: first-order-definable, first-order fixed-point definable, and beyond." @default.
- W311767895 created "2016-06-24" @default.
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- W311767895 date "2004-01-01" @default.
- W311767895 modified "2023-09-23" @default.
- W311767895 title "Minimal Predicates, Fixed Points, and Definability" @default.
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