The Theory of Semilinear Sets and Presburger's Elimination of Quantifiers, C. Choffrut

Contents The theory of semilinear sets and Presburger’s elimination of quantifiers,

Monadic Quantifiers Recognized by Deterministic Pushdown Automata

I characterize the class of type 〈1〉 quantifiers (or, equivalently, type 〈1, 1〉 quantifiers satisfying Conservativity and Extension) that are recognized by deterministic pushdown automata in terms of the associated semilinear sets of vectors in N. These semilinear sets are finite unions of linear sets with at most two generators each, which are taken from a common three-element set of the form ...

Quantifier Elimination for Neocompact Sets

We shall prove quantifier elimination theorems for neocompact formulas, which define neocompact sets and are built from atomic formulas using finite disjunctions, infinite conjunctions, existential quantifiers, and bounded universal quantifiers. The neocompact sets were first introduced to provide an easy alternative to nonstandard methods of proving existence theorems in probability theory, wh...

Quantifier elimination for the theory of algebraically closed valued fields with analytic structure

The theory of algebraically closed non-Archimedean valued fields is proved to eliminate quantifiers in an analytic language similar to the one used by Cluckers, Lipshitz and Robinson. The proof makes use of a uniform parameterized normalization theorem which is also proved in this paper and which has far reaching consequences in the geometry of definable sets. This method of proving quantifier ...

COMBINING FUZZY QUANTIFIERS AND NEAT OPERATORS FOR SOFT COMPUTING

This paper will introduce a new method to obtain the order weightsof the Ordered Weighted Averaging (OWA) operator. We will first show therelation between fuzzy quantifiers and neat OWA operators and then offer anew combination of them. Fuzzy quantifiers are applied for soft computingin modeling the optimism degree of the decision maker. In using neat operators,the ordering of the inputs is not...