The syntax of intuitionistic propositional second-order logic PSOLi consists of a set of propositional constants P , Q, R, etc, a denumerable set of propositional variables F , G, H, etc, together with the primitive logical signs of the conditional and the universal propositional quantifier, and ponctuation signs (parenthesis). The formulas of PSOLi are the smallest class of expressions of the ...

In this note, we show that the theory of tracial von Neumann algebras does not have a model companion. This will follow from the fact that the theory of any locally universal, McDuff II1 factor does not have quantifier elimination. We also show how a positive solution to the Connes Embedding Problem implies that there can be no modelcomplete theory of II1 factors.

The goal of this paper is to push forward the development of the apparatus of the Fuzzy Class theory. We concentrate on three areas: strengthening the universal quantifier, formalizing the idea that ‘similar’ fuzzy sets fulfill their properties to ‘similar’ degrees, and embedding of classical crisp theories into Fuzzy Class theory.

We present the first work on applying statistical techniques to unrestricted Quantifier Scope Disambiguation (QSD), where there is no restriction on the type or the number of quantifiers in the sentence. We formulate unrestricted QSD as learning to build a Directed Acyclic Graph (DAG) and define evaluation metrics based on the properties of DAGs. Previous work on statistical scope disambiguatio...

We investigate the expressive power of first-order quantifications in the context of monadic second-order logic over pictures. We show that k+1 set quantifier alternations allow to define a picture language that cannot be defined using k set quantifier alternations preceded by arbitrarily many first-order quantifier alternations. The approach uses, for a given picture language L and an integer ...

We present a variant of the Davis–Fechter’s technique for eliminating quantifiers in first-order logic, aimed at reducing the incidence of irrelevant dependencies in the construction of Skolem terms. The basic idea behind this contribution is to treat as a single syntactic unit every maximal ‘quantifier batch’, i.e., group of contiguous alike quantifiers, whose internal order (which has no sign...

We study 0-1 laws for extensions of first-order logic by Lindström quantifiers. We state sufficient conditions on a quantifier Q expressing a graph property, for the logic FO[Q] – the extension of first-order logic by means of the quantifier Q – to have a 0-1 law. We use these conditions to show, in particular, that FO[Rig], where Rig is the quantifier expressing rigidity, has a 0-1 law. We als...

This paper provides experimental evidence suggesting that there are considerable differences in native language attainment, and that these are at least partially attributable to individual speakers’ experience. Experiment 1 tested high academic attainment (hereafter, HAA) and low academic attainment (LAA) participants' comprehension using a sentence-picture matching task. Test sentences compris...

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...

Lindström [11] introduced a very powerful notion of quantifiers, which permits multi-place quantification and the simultaneous binding of several variables. A special case, 'branching' quantifiers, was found to be useful in linguistics, specifically for modelling reciprocal constructions like " Most men and most women admire each other ". Westerståhl [13] showed how to compute the three-place L...