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Guarded Quantification in Least Fixed Point Logic
, 2002
"... We develop a variant of Least Fixed Point logic based on First Order logic with a relaxed version of guarded quantification. We develop a Game Theoretic Semantics of this logic, and find that under reasonable conditions, guarding quantification does not reduce the expressibility of Least Fixed Point ..."
Abstract

Cited by 2 (1 self)
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We develop a variant of Least Fixed Point logic based on First Order logic with a relaxed version of guarded quantification. We develop a Game Theoretic Semantics of this logic, and find that under reasonable conditions, guarding quantification does not reduce the expressibility of Least Fixed Point logic. But guarding quantification increases worstcase time complexity.
Game Representations of Complexity Classes
 Proc. Eur. Summer School on Logic, Language and Information (European Assoc. Logic, Language and Information
, 2001
"... Many descriptive and computational complexity classes have gametheoretic representations. These can be used to study the relation between different logics and complexity classes in finite model theory. ..."
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Cited by 1 (1 self)
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Many descriptive and computational complexity classes have gametheoretic representations. These can be used to study the relation between different logics and complexity classes in finite model theory.
Negation and Inductive Norms
, 2003
"... In 1982, N. Immerman proved that (positive) least fixed point logic was closed under negation. He used a construction similar to that of Moschovakis [34]: if a logic admits an "inductive norm" that partitions a relation into blocks labelled by integers, then an appropriate "stage c ..."
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In 1982, N. Immerman proved that (positive) least fixed point logic was closed under negation. He used a construction similar to that of Moschovakis [34]: if a logic admits an "inductive norm" that partitions a relation into blocks labelled by integers, then an appropriate "stage comparison relation" might be used to construct a negation of that relation within that logic. In this paper, we generalize this construction to many fragments of positive least fixed point logic, and in particular we will find that if such a fragment is closed under (on a class of finite structures), and admits "stage comparison relations" (on M), then it is closed under negation (on M).