We present the model theoretic concepts that allow mathematics to be developed with notion of potential infinite instead actual infinite. The is understood as a dynamic notion, being an indefinitely extensible finite. main adoption interpretation universal quantifier, which has implicit reflection principle. Each quantification refers large, but finite set. quantified sets may increase, so afte...

We develop a logic of explicit time resource bounds for a language with function pointers and semantic assertions. We apply our logic to examples containing nontrivial “higher-order” uses of function pointers and we prove soundness with respect to a standard operational semantics. Our core technique is very compact and may be applicable to other resource bounding problems, and is the first appl...

This paper investigates the effect of quantification in sentence processing. The experimental results show that temporarily ambiguous sentences that begin with the universally quantified NPs reduced the garden path effect in contrast to the ones that begin with bare NPs. This fact is accounted for by assuming that discourse representation structures are incrementally constructed, and a triparti...

First order formulas in a relational signature can be considered as operations on the relations of an underlying set, giving rise to multisorted algebras we call first order algebras. We present universal axioms so that an algebra satisfies the axioms iff it embeds into a first order algebra. Importantly, our argument is modular and also works for, e.g., the positive existential algebras (where...

This study reexamines the semantics of the Portuguese Present Perfect and proposes ananalysis of this periphrastic past that does not appeal to type-shifting coercionmechanisms. Aspectual coercion was claimed to explain purported mismatches betweenselection restrictions of the Portuguese Present tense and the aspectual properties of thePerfect (Schmitt 2001). The present stu...

In this study the structure for O-minimal expansions of groups is considered Let be an o-minimal expansion of an ordered group (R,0,1,+,<) with distinguished positive element 1. We first prove that the following are equivalent: (1) is semibounded, (2) has no poles, (3) cannot define a real closed field with domain R and order <, (4) is eventually linear and (5) every –definable set is a finit u...

We develop a logic of explicit time resource bounds for a language with function pointers and semantic assertions. We apply our logic to examples containing nontrivial “higher-order” uses of function pointers and we prove soundness with respect to a standard operational semantics. Our core technique is very compact and may be applicable to other resource bounding problems, and is the first appl...

There is an ongoing debate about the meaning of definiteness and the number and types of definite entities (e.g. Russell, 1905; Strawson, 1950; Hawkins, 1978; Löbner, 1985; and many others). Definite noun phrases (NPs) include definite descriptions, demonstratives, pronouns, possessive constructions, proper names, or NPs with a universal quantifier as determiner, and research has focused on whi...

It is known that there is a sound and faithful translation of the full intuitionistic propositional calculus into the atomic polymorphic system Fat, a predicative calculus with only two connectives: the conditional and the second-order universal quantifier. The faithfulness of the embedding was established quite recently via a model-theoretic argument based in Kripke structures. In this paper w...

Do negative quantifiers like "few" reduce people's ability to rapidly evaluate incoming language with respect to world knowledge? Previous research has addressed this question by examining whether online measures of quantifier comprehension match the "final" interpretation reflected in verification judgments. However, these studies confounded quantifier valence with its impact on the unfolding ...