It is known that the branching time language ACTL and the linear time language ∀LTL of universally quantified formulae of LTL have incomparable expressive powers, i.e., Sem(ACTL) and Sem(∀LTL) are incomparable sets. Within a standard abstract interpretation framework, ACTL can be viewed as an abstract interpretation LTL∀ of LTL where the universal path quantifier ∀ abstracts each linear tempora...

Strategy Logic (SL) is a logical formalism for strategic reasoning in multi-agent systems. Its main feature is that it has variables for strategies that are associated to specific agents with a binding operator. We introduce Graded Strategy Logic (GRADEDSL), an extension of SL by graded quantifiers over tuples of strategy variables, i.e., “there exist at least g different tuples (x1, ...,xn) of...

In this paper we present an algorithm to anchor floating quantifiers in Japanese, a language in which quantificational nouns and numeralclassifier combinations can appear separated from the noun phrase they quantify. The algorithm differentiates degree and event modifiers from nouns that quantify noun phrases. It then finds a suitable anchor for such floating quantifiers. To do this, the algori...

The first-order theory of addition over the natural numbers, known as Presburger arithmetic, is decidable in double exponential time. Adding an uninterpreted unary predicate to the language leads to an undecidable theory. We sharpen the known boundary between decidable and undecidable in that we show that the purely universal fragment of the extended theory is already undecidable. Our proof is ...

We present a general simplification of quantified SMT formulas using variable elimination. The simplification is based on an analysis of the ground terms occurring as arguments in function applications. We use this information to generate a system of set constraints, which is then solved to compute a set of sufficient ground terms for each variable. Universally quantified variables with a finit...

Henkin [7] introduced quantifiers which arise when usual (universal and existential) quantifiers are arranged in non-linear order. These quantifiers bre known as partially ordered quantifiers or Henkin quantifiers. Is. was observed already in [7] that languages with these quantifiers are stronger than first-order logic. A result of [ll] shows that even the weakest enkin quantifier has essential...

Many verification techniques nowadays successfully rely on SMT solvers as back-ends to automatically discharge proof obligations. These solvers generally rely on various instantiation techniques to handle quantifiers. We here show that the major instantiation techniques in SMT solving can be cast in a unifying framework for handling quantified formulas with equality and uninterpreted functions....

We say that a first order sentence A defines a digraph G if A is true on G but false on any digraph non-isomorphic to G. Let Da(G) (resp. La(G)) denote the minimum quantifier rank (resp. length) of a such sentence in which negations occur only in front of atomic subformulas and any sequence of nested quantifiers has at most a quantifier alternations. We define the succinctness function qa(n) to...

Linguistic quantifiers are quantifiers defined by linguistic expressions like “around 5” or “most of,” and many types of linguistic quantifiers can be found in the literature (Diaz-Hermida, Bugarin, & Barro, 2003; Glockner, 1997, 2004a, 2004b; Losada, Díaz-Hermida, & Bugarín, 2006) (as semifuzzy quantifiers which allow modeling expressions like “there are twice as many men as women”). We limit ...

The computation of literal projection generalizes predicate quantifier elimination by permitting, so to speak, quantifying upon an arbitrary sets of ground literals, instead of just (all ground literals with) a given predicate symbol. Literal projection allows, for example, to express predicate quantification upon a predicate just in positive or negative polarity. Occurrences of the predicate i...