Errors involving universal quantification are common in contexts depicting sets of individuals in partial, one-to-one correspondence. In this article, we explore whether quantifier-spreading errors are more common with distributive quantifiers each and every than with all. In Experiments 1 and 2, 96 children (5to 9-year-olds) viewed pairs of pictures and selected one corresponding to a sentence...

propositions can be defined by using the universal and existential quantifiers. Theuniversal quantifier (represented by ∀) specifies the properties of all the objects that abideto certain characteristics. For example, to indicate that all natural numbers smaller than 50are also smaller than 100, one could use the expression “∀x: N | x < 50 • x < 100”, whichcan be read as “for al...

Theories of induction in psychology and artificial intelligence assume that the process leads from observation and knowledge to the formulation of linguistic conjectures. This paper proposes instead that the process yields mental models of phenomena. It uses this hypothesis to distinguish between deduction, induction, and creative forms of thought. It shows how models could underlie inductions ...

The syntax of abstract meaning representations (AMRs) can be defined recursively, and a systematic translation to first-order logic (FOL) can be specified, including a proper treatment of negation. AMRs without recurrent variables are in the decidable two-variable fragment of FOL. The current definition of AMRs has limited expressive power for universal quantification (up to one universal quant...

Floating quantifiers (FQs) in English exhibit both universal and language-specific properties, and this paper shows that such syntactic and semantic characteristics can be explained in terms of a constraint-based, lexical approach to the construction within the framework of Head-Driven Phrase Structure Grammar (HPSG). Based on the assumption that FQs are base-generated VP modifiers, this paper ...

The goal of this article is to explain the distribution and meaning of qualsiasi/qualunque in the examples in (1). Universal FC items will be analysed as indefinites (contra Dayal, 1998). Following Aloni (2002, to appear) and Kratzer and Shimoyama (2002), I will assume that indefinites induce sets of propositional alternatives. The interpretation of FC items like qualsiasi will further cruciall...

We introduce the branching transitive closure operator on weighted monadic second-order logic formulas where the branching corresponds in a natural way to the branching inherent in trees. For arbitrary commutative semirings, we prove that weighted monadic second order logics on trees is equivalent to the definability by formulas which start with one of the following operators: (i) a branching t...

We consider the problem of checking whether a proposed invariant φ expressed in first-order logic with quantifier alternation is inductive, i.e. preserved by a piece of code. While the problem is undecidable, modern SMT solvers can sometimes solve it automatically. However they employ powerful quantifier instantiation methods that may diverge, especially when φ is not preserved. A notable diffi...

In this paper, we explore the computational complexity of the conjunctive fragment of the firstorder theory of linear arithmetic. Quantified propositional formulas of linear inequalities with (k − 1) quantifier alternations are log-space complete in ΣP k or ΠP k depending on the initial quantifier. We show that when we restrict ourselves to quantified conjunctions of linear inequalities, i.e., ...