If T is a (first order) universal theory then we can consider the category of existentially closed models of T with embeddings as morphisms. This class of structures is in general not the class of models of a first order theory T ′. (It will be, just if T has a model companion T ′.) The “model theory” of such a “non-elementary class” was a substantial line of research in the 1970’s, mainly amon...

Presupposition projection in quantified sentences is at the center of debates in the presupposition literature. This paper reports on a survey revealing inter-speaker variation regarding which quantifier yields universal inferences—which Q in QpBqpλx.Cpxqppxqq supports the inference @x P B: ppxq. We observe an implication that if some yields a universal inference for a speaker, no, and any in a...

Human conditional reasoning is defeasible: people withdraw logically valid conclusions if they are aware of situations (i.e., exceptions) that prevent the consequent of the rule to happen although the antecedent is given. In this paper we investigate defeasible reasoning with quantified rules. In two experiments we rephrased conditionals from the literature (Experiment 1) and rules from penal c...

Building on a simple construction of the complex numbers and a proof of the Fundamental Theorem of Algebra, we implement, as a HOL derived inference rule, a decision method for the first order algebraic theory of C based on quantifier elimination. Although capable of solving some mildly interesting problems, we also implement a more efficient semidecision procedure for the universal fragment ba...

This paper concentrates on understanding the first order theory of universal specializations of Zariski structures. Models of the theory are pairs, a Zariski structure and an elementary extension with a map (specialization) from the extension to the structure that preserves positive quantifier free formulas. The reader will find that this context generalizes both the study of algebraically clos...

The goal of this study is to introduce a new type of evidence to the debate on the nature of what is known in the literature as quantifier spreading (q-spreading), also referred to as the “symmetry error”. Since the work of Inhelder and Piaget (1964), it has been known that until the age of 7–8, children’s responses are frequently different from those of adults when judging the truth-value of s...

I argue that the interpretation of expressions consisting of disjunction marker and wh-element (wh-DISJ expressions), which varies across languages, constitutes a case of semantic variation. In Hausa, these expressions denote universal generalized quantifiers, which give rise to free choice effects in intensional contexts (Giannakidou 2001). The universal meaning is derived in compositional fas...

Formal semantics has so far mostly focused on three categories of quantifiers (Q)—to wit, Qdeterminers (e.g. every), Q-adverbs (e.g. always), and Q-auxiliaries (e.g. would). All three form constructions that can be analyzed in terms of tripartite logical forms (LFs), consisting of a quantifier, the restriction, and the nuclear scope. This view has been implemented, with varying details, by most...