Program schemes, arrays, Lindström quantifiers and zero-one laws
Theoretical Computer Science
Generalized Quantifiers, an Introduction
ESSLLI '97 Revised Lectures from the 9th European Summer School on Logic, Language, and Information: Generalized Quantifiers and Computation
Program Schemes, Arrays, Lindström Quantifiers and Zero-One Laws
CSL '99 Proceedings of the 13th International Workshop and 8th Annual Conference of the EACSL on Computer Science Logic
Capture Complexity by Partition
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
Partially Ordered Connectives and Monadic Monotone Strict NP
Journal of Logic, Language and Information
A logical characterization of the counting hierarchy
ACM Transactions on Computational Logic (TOCL)
Program Schemes, Queues, the Recursive Spectrum and Zero-one Laws
Fundamenta Informaticae - Machines, Computations and Universality, Part II
Properties of Almost All Graphs and Generalized Quantifiers
Fundamenta Informaticae - Bridging Logic and Computer Science: to Johann A. Makowsky for his 60th birthday
Program Schemes, Queues, the Recursive Spectrum and Zero-one Laws
Fundamenta Informaticae - Machines, Computations and Universality, Part II
Random graphs and the parity quantifier
Journal of the ACM (JACM)
| Hi-index | 0.00 |
We study 0-1 laws for extensions of first-order logic by Lindstrom quantifiers. We state sufficient conditions on a quantifier Q expressing a graph property, for the logic FO[Q] - the extension of first-order logic by means of the quantifier Q - to have a 0-1 law. We use these conditions to show, in particular, that FO[Rig], where Rig is the quantifier expressing rigidity, has a 0-1 law. We also show that FO[Ham], where Ham is the quantifier expressing Hamiltonicity, does not have a 0-1 law. Blass and Harary pose the question whether there is a logic which is powerful enough to express Hamiltonicity or rigidity and which has a 0-1 law. It is a consequence of our results that there is no such regular logic (in the sense of abstract model theory) in the case of Hamiltonicity, but there is one in the case of rigidity. We also consider sequences of vectorized quantifiers, and show that the extensions of first-order logic obtained by adding such sequences generated by quantifiers that are closed under substructures have 0-1 laws.