Approximating the Expressive Power of Logics in Finite Models

Abstract. We present a probability logic (essentially a first order language extended with quantifiers that count the fraction of elements in a model that satisfy a first order formula) which, on the one hand, captures uniform circuit classes such as AC0 and TC0 over arithmetic models, namely, finite structures with linear order and arithmetic relations, and, on the other hand, their semantics, with respect to our arithmetic models, can be closely approximated by giving interpretations of their formulas on finite structures where all relations (including the order) are restricted to be “modular” (i.e. to act subject to an integer modulo). In order to give a precise measure of the proximity between satisfaction of a formula in an arithmetic model and satisfaction of the same formula in the “approximate” model, we define the approximate formulas and work on a notion of approximate truth. We also indicate how to enhance the expressive power of our probability logic in order ...

• Type: Conference
• Year: 2004
• Where: LATIN
• Authors: Argimiro Arratia, Carlos E. Ortiz
• Keywords: Arithmetic Model, Information Retrieval, LATIN 2004, finite Structures, first Order