1Ò Ò ½ Es ¼ ½ Ò

1Denotaremos

1Efactor Ë Ì Ê Í Ì ´µ Μ El N

1Para Cualquier Vocabulario Ê ½ Ê × ½ Ö

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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 AC 0 and TC 0 over arithmetic models , namely, finite structures with linear order and arithmetic relations, and, on… (More)

We present a second order logic of proportional quantifiers, SOLP, which is essentially a first order language extended with quantifiers that act upon second order variables of a given arity r, and count the fraction of elements in a subset of r–tuples of a model that satisfy a formula. Our logic is capable of expressing proportional versions of different… (More)

We formulate a formal syntax of approximate formulas for the logic with counting quantifiers, SOLP, studied by us in [1], where we showed the following facts: (i) In the presence of a built–in (linear) order, SOLP can describe NP–complete problems and fragments of it capture classes like P and NL; (ii) weakening the ordering relation to an almost order (in… (More)

We present a second order logic of proportional quantifiers, , which is essentially a first order language extended with quantifiers that act upon second order variables of a given arity r, and count the fraction of elements in a subset of r– tuples of a model that satisfy a formula. Our logic is capable of expressing proportional versions of different… (More)

The first order logic Ring(0, +, * , <) for finite residue class rings with order is presented, and extensions of this logic with generalized quantifiers are given. It is shown that this logic and its extensions capture DLOGT IM E-uniform circuit complexity classes ranging from AC 0 to T C 0. Separability results are obtained for the hierarchy of these… (More)

Separations among the first order logic Ring(0, +, *) of finite residue class rings, its extensions with generalized quantifiers, and in the presence of a built-in order are shown, using algebraic methods from class field theory. These methods include classification of spectra of sentences over finite residue classes as systems of congruences, and the study… (More)

This paper presents a syntax of approximate formulae suited for the logic with counting quantifiers SOLP. This logic was formalised by us in [1] where, among other properties, we showed the following facts: (i) In the presence of a built–in (linear) order, SOLP can describe NP–complete problems and some of its fragments capture the classes P and NL; (ii)… (More)

We present a formal syntax of approximate formulas suited for the logic with counting quantifiers SOLP. This logic was studied by us in [1] where, among other properties, we showed: (i) In the presence of a built–in (linear) order, SOLP can describe NP–complete problems and fragments of it capture classes like P and NL; (ii) weakening the ordering relation… (More)

- Argimiro Arratia, Carlos E Ortiz, Para Cualquier Vocabulario Ê ½ Ê × ½ Ö, Ò Ò ½ Es ¼ ½ Ò, Denotaremos, Efactor Ë Ì Ê Í Ì ´µ Μ El N
- 2001

RESUMEN: Se expone un plan para demostrar, utilizando Análisis No-estandar, si la clase de conjuntos cuya cardinalidad se descompone en un n ´ umero par de factores primos distintos, no es definible en la l ´ ogica de primer orden con predicados para el orden lineal, las operaciones de adicí on multiplicací on y exonerací on en base 2, restringiendonos a… (More)

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