Upward-closed hereditary families in the dominance order

Scope Dominance with Upward Monotone Quantifiers

We give a complete characterization of the class of upward monotone generalized quantifiers Q1 and Q2 over countable domains that satisfy the scheme Q1x Q2y ! Q2y Q1x . This generalizes the characterization of such quantifiers over finite domains, according to which the scheme holds iff either Q1 is 9 or Q2 is 8 (excluding trivial cases). Our result shows that in infinite domains, there are mor...

Computing Scope Dominance with Upward Monotone Quantifiers

This paper describes an algorithm that characterizes logical relations between different interpretations of scopally ambiguous sentences. The proposed method uses general properties of natural language determiners in order to generate a model which is indicative of such entailment relations. The computation of this model involves information about cardinalities of noun denotations and containme...

Nash Equilibrium for Upward-Closed Objectives

We study in nite stochastic games played by n-players on a nite graph with goals speci ed by sets of in nite traces. The games are concurrent (each player simultaneously and independently chooses an action at each round), stochastic (the next state is determined by a probability distribution depending on the current state and the chosen actions), in nite (the game continues for an in nite numbe...

Symboli Representation of Upward-Closed Sets

Upward closed talocrural dislocation without fracture