Fields of Logic and Computation II pp 52-68 | Cite as

# Existential Fixed-Point Logic as a Fragment of Second-Order Logic

## Abstract

The standard translation of existential fixed-point formulas into second-order logic produces strict universal formulas, that is, formulas consisting of universal quantifiers on relations (not functions) followed by an existential first-order formula. This form implies many of the pleasant properties of existential fixed-point logic, but not all. In particular, strict universal sentences can express some co-NP-complete properties of structures, whereas properties expressible by existential fixed-point formulas are always in P. We therefore investigate what additional syntactic properties, beyond strict universality, are enjoyed by the second-order translations of existential fixed-point formulas. In particular, do such syntactic properties account for polynomial-time model-checking?

## Keywords

Atomic Formula Conjunctive Normal Form Parse Tree Predicate Symbol Horn Clause## Notes

### Acknowledgement

Because of the last-minute discovery of the conjunction problem, this paper was submitted after the official deadline, leaving less than the normal time for refereeing. Nevertheless, the referee provided a very useful report. I thank him or her for the report, in particular for informing me about the existence and relevance of [4].

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