Computational Semantics for Monadic Quantifiers

Computational semantics for monadic quantifiers

The paper gives a survey of known results related to computational devices (finite and push–down automata) recognizing monadic generalized quantifiers in finite models. Some of these results are simple reinterpretations of descriptive—feasible correspondence theorems from finite–model theory. Additionally a new result characterizing monadic quantifiers recognized by push down automata is proven...

Fuzzy quantifiers in natural language:: semantics and computational models

On Second-Order Monadic Groupoidal Quantifiers

We study logics defined in terms of so-called second-order monadic groupoidal quantifiers. These are generalized quantifiers defined by groupoid word-problems or equivalently by context-free languages. We show that, over strings with built-in arithmetic, the extension of monadic second-order logic by all second-order monadic groupoidal quantifiers collapses to its fragment mon-QGrpFO. We also s...

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 ...

A Double Team Semantics for Generalized Quantifiers

We investigate extensions of dependence logic with generalized quantifiers. We also introduce and investigate the notion of a generalized atom. We define a system of semantics that can accommodate variants of dependence logic, possibly extended with generalized quantifiers and generalized atoms, under the same umbrella framework. The semantics is based on pairs of teams, or double teams. We als...