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Hierarchies in Transitive Closure Logic, Stratified Datalog and Infinitary Logic
 ANNALS OF PURE AND APPLIED LOGIC
, 1994
"... We establish a general hierarchy theorem for quantifier classes in the infinitary logic L ! 1! on finite structures. In particular, it is shown that no infinitary formula with bounded number of universal quantifiers can express the negation of a transitive closure. This implies the solution of se ..."
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Cited by 11 (4 self)
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We establish a general hierarchy theorem for quantifier classes in the infinitary logic L ! 1! on finite structures. In particular, it is shown that no infinitary formula with bounded number of universal quantifiers can express the negation of a transitive closure. This implies the solution of several open problems in finite model theory: On finite structures, positive transitive closure logic is not closed under negation. More generally the hierarchy defined by interleaving negation and transitive closure operators is strict. This proves a conjecture of Immerman. We also separate the expressive power of several extensions of Datalog, giving new insight in the fine structure of stratified Datalog.
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 ..."
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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.
Finite Models and Finitely Many Variables
 Banach Center Publications
, 1999
"... We consider L  first order logic restricted to k variables, and interpreted in finite structures. The study of classes of finite structures axiomatisable with finitely many variables has assumed importance through connections with computational complexity. In particular, we investigate the relation ..."
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Cited by 1 (0 self)
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We consider L  first order logic restricted to k variables, and interpreted in finite structures. The study of classes of finite structures axiomatisable with finitely many variables has assumed importance through connections with computational complexity. In particular, we investigate the relationship between the size of a finite structure and the number of distinct types it realizes, with respect to L . Some open questions, formulated as finitary LöwenheimSkolem properties, are presented regarding this relationship. This is also investigated through finitary versions of an EhrenfeuchtMostowski property.