## Infinitary Logics and 0-1 Laws (1992)

Venue: | Information and Computation |

Citations: | 43 - 4 self |

### BibTeX

@ARTICLE{Kolaitis92infinitarylogics,

author = {Phokion G. Kolaitis and Moshe Y. Vardi},

title = {Infinitary Logics and 0-1 Laws},

journal = {Information and Computation},

year = {1992},

volume = {98},

pages = {258--294}

}

### OpenURL

### Abstract

We investigate the in nitary logic L 1! , in which sentences may have arbitrary disjunctions and conjunctions, but they involve only a nite number of distinct variables. We show that various xpoint logics can be viewed as fragments of L 1! , and we describe a game-theoretic characterization of the expressive power of the logic. Finally, we study asymptotic probabilities of properties 1! on nite structures. We show that the 0-1 law holds for L 1! , i.e., the asymptotic probability of every sentence in this logic exists and is equal to either 0 or 1. This result subsumes earlier work on asymptotic probabilities for various xpoint logics and reveals the boundary of 0-1 laws for in nitary logics.