We investigate model theoretic properties of XPath with data (in)equality tests over the class of data trees, i.e., the class of trees where each node contains a label from a finite alphabet and a data value from an infinite domain. We provide notions of (bi)simulations for XPath logics containing the child, descendant, parent and ancestor axes to navigate the tree. We show that these notions p...

Early work on quantification in natural languages showed that sentences like Every ape picked different berries, on the reading that the sets of berries picked by any two apes are not the same, can be logically represented with a single polyadic quantifier for the two nominal phrases. However, since that quantifier cannot be decomposed into two quantifiers for the two nominal phrases, a composi...

Satisfiability Modulo Theories (SMT) solvers have proven highly scalable, efficient and suitable for integrating theory reasoning. However, for numerous applications from program analysis and verification, the ground fragment is insufficient, as proof obligations often include quantifiers. A well known approach for quantifier reasoning uses a matching algorithm that works against an E-graph to ...

The Ambient Logic (AL) has been proposed for expressing spatial properties of processes of the Mobile Ambient calculus (MA). Restricting both the calculus and the logic to their static part yields static ambients (SA) and the static ambient logic (SAL), that form a model for queries about semistructured data. SAL also includes the non-standard fresh quantifier (I). This work adresses the questi...

In this paper we naturally define when a theory has bounded quantifier elimination, or is bounded model complete. We give several equivalent conditions for a theory to have each of these properties. These results provide simple proofs for some known results in the model theory of the bounded arithmetic theories like CPV and PV1. We use the mentioned results to obtain some independence results i...

It has been widely assumed that a universal quantifier such as every evokes an asymmetry among entailments in its first argument (i.e., the NP) and its second argument (i.e., the VP). In particular, the first argument of every is downward entailing (henceforth DE), whereas its second argument is non-downward entailing (non-DE). Entailment-sensitive linguistic phenomena, arising as a consequence...

We investigate second-order quantifier elimination for a class of formulas characterized by a restriction on the quantifier prefix: existential predicate quantifiers followed by universal individual quantifiers and a relational matrix. For a given second-order formula of this class a possibly infinite sequence of universal first-order formulas that have increasing strength and are all entailed ...

Sentences with disjunction in the scope of a universal quantifier, Every A is P or Q, tend to give rise to distributive inferences that each of the disjuncts holds of at least one individual in the domain of the quantifier, Some A is P & Some A is Q. These inferences are standardly derived as an entailment of the meaning of the sentence together with the scalar implicature that it is not the ca...

We obtain an almost everywhere quantifier elimination for (the noncritical fragment of) the logic with probability quantifiers, introduced by the first author in [9]. This logic has quantifiers like ∃≥3/4y, which says that “for at least 3/4 of all y”. These results improve upon the 0-1 law for a fragment of this logic obtained by Knyazev [11]. Our improvements are: 1. We deal with the quantifie...

Kratzer’s picture [, , ]: • Modals are quantifiers over possible worlds. • Possibility modals are existential quantifiers, necessity modals are universal quantifiers. They are duals of each other. • Modals quantify over the worlds given by a background such as “in view of what the laws are” (i.e. the worlds compatible with what the laws are in the evaluation world). • The “ambiguity” betwe...