Cognitive Processing of Verbal Quantifiers in the Context of Affirmative and Negative Sentences: a Croatian Study

Studies from English and German have found differences in the processing of affirmative and negative sentences. However, little attention has been given to quantifiers that form negations. A picture-sentence verification task was used to investigate the processing of different types of quantifiers in Croatian: universal quantifiers in affirmative sentences (e.g. all), non-universal quantifiers in compositional negations (e.g. not all), null quantifiers in negative concord (e.g. none) and relative disproportionate quantifiers in both affirmative and negative sentences (e.g. some). The results showed that non-universal and null quantifiers, as well as negations were processed significantly slower compared to affirmative sentences, which is in line with previous findings supporting the two-step model. The results also confirmed that more complex tasks require a longer reaction time. A significant difference in the processing of same-polarity sentences with first-order quantifiers was observed: sentences with null quantifiers were processed faster and more accurately than sentences with disproportional and non-universal quantifiers. A difference in reaction time was also found in affirmatives with different quantifiers: sentences with universal quantifiers were processed significantly faster and more accurately compared to sentences with relative disproportionate quantifiers. These findings indicate that the processing of quantifiers follows after the processing of affirmative information. In the context of the two-step model, the processing of quantifiers occurs in the second step, along with negations

Characterizing integers among rational numbers with a universal-existential formula

We prove that Z in definable in Q by a formula with 2 universal quantifiers followed by 7 existential quantifiers. It follows that there is no algorithm for deciding, given an algebraic family of Q-morphisms, whether there exists one that is surjective on rational points. We also give a formula, again with universal quantifiers followed by existential quantifiers, that in any number field defines the ring of integers.Comment: 6 page

On Second-Order Monadic Monoidal and Groupoidal Quantifiers

We study logics defined in terms of second-order monadic monoidal and groupoidal quantifiers. These are generalized quantifiers defined by monoid and groupoid word-problems, equivalently, by regular and context-free languages. We give a computational classification of the expressive power of these logics over strings with varying built-in predicates. In particular, we show that ATIME(n) can be logically characterized in terms of second-order monadic monoidal quantifiers

Complexity of the Two-Variable Fragment with (Binary-Coded) Counting Quantifiers

We show that the satisfiability and finite satisfiability problems for the two-variable fragment of first-order logic with counting quantifiers are both in NEXPTIME, even when counting quantifiers are coded succinctly.Comment: 24 pages, 1 pstex_t figur

Statistical relational learning with soft quantifiers

Quantification in statistical relational learning (SRL) is either existential or universal, however humans might be more inclined to express knowledge using soft quantifiers, such as ``most'' and ``a few''. In this paper, we define the syntax and semantics of PSL^Q, a new SRL framework that supports reasoning with soft quantifiers, and present its most probable explanation (MPE) inference algorithm. To the best of our knowledge, PSL^Q is the first SRL framework that combines soft quantifiers with first-order logic rules for modelling uncertain relational data. Our experimental results for link prediction in social trust networks demonstrate that the use of soft quantifiers not only allows for a natural and intuitive formulation of domain knowledge, but also improves the accuracy of inferred results

The influence of tense in adverbial quantification

We argue that there is a crucial difference between determiner and adverbial quantification. Following Herburger [2000] and von Fintel [1994], we assume that determiner quantifiers quantify over individuals and adverbial quantifiers over eventualities. While it is usually assumed that the semantics of sentences with determiner quantifiers and those with adverbial quantifiers basically come out the same, we will show by way of new data that quantification over events is more restricted than quantification over individuals. This is because eventualities in contrast to individuals have to be located in time which is done using contextual information according to a pragmatic resolution strategy. If the contextual information and the tense information given in the respective sentence contradict each other, the sentence is uninterpretable. We conclude that this is the reason why in these cases adverbial quantification, i.e. quantification over eventualities, is impossible whereas quantification over individuals is fine

Complexity of the Guarded Two-Variable Fragment with Counting Quantifiers

We show that the finite satisfiability problem for the guarded two-variable fragment with counting quantifiers is in EXPTIME. The method employed also yields a simple proof of a result recently obtained by Y. Kazakov, that the satisfiability problem for the guarded two-variable fragment with counting quantifiers is in EXPTIME.Comment: 20 pages, 3 figure