Homomorphism closed vs. existential positive

Preservations theorems, which establish connection between syntactic and semantic properties of formulas, are a major topic of investigation in model theory. In the context of finite-model theory, most, but not all, preservation theorems are known to fail. It is not known, however, whether the Los-T...

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Bibliographic Details
Published in18th Annual IEEE Symposium of Logic in Computer Science, 2003. Proceedings pp. 311 - 320
Main Authors Feder, T., Vardi, M.Y.
Format Conference Proceeding
LanguageEnglish
Published IEEE 2003
Subjects
Computer science
Context modeling
Logic functions
Terminology
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Summary:Preservations theorems, which establish connection between syntactic and semantic properties of formulas, are a major topic of investigation in model theory. In the context of finite-model theory, most, but not all, preservation theorems are known to fail. It is not known, however, whether the Los-Tarski-Lyndon theorem, which asserts that a first-order sentence is preserved under homomorphisms if it is equivalent to an existential positive sentence, holds with respect to finite structures. Resolving this is an important open question in finite-model theory. In this paper we study the relationship between closure under homomorphism and positive syntax for several nonfirst-order existential logics that are of interest in computer science. We prove that the Los-Tarski-Lyndon theorem holds for these logics. The logics we consider are variable-confined existential infinitary logic, Datalog, and various fragments of second-order logic.
ISBN:0769518842
9780769518848
ISSN:1043-6871
2575-5528
DOI:10.1109/LICS.2003.1210071