Enriching Knowledge Bases with Counting Quantifiers

Information extraction traditionally focuses on extracting relations between identifiable entities, such as . Yet, texts often also contain Counting information, stating that a subject is in a specific relation with a number of objects, without mentioning the objects themselves, for example, "California is divided into 58 counties". Such counting quantifiers can help in a variety of tasks such as query answering or knowledge base curation, but are neglected by prior work. This paper develops the first full-fledged system for extracting counting information from text, called CINEX. We employ distant supervision using fact counts from a knowledge base as training seeds, and develop novel techniques for dealing with several challenges: (i) non-maximal training seeds due to the incompleteness of knowledge bases, (ii) sparse and skewed observations in text sources, and (iii) high diversity of linguistic patterns. Experiments with five human-evaluated relations show that CINEX can achieve 60% average precision for extracting counting information. In a large-scale experiment, we demonstrate the potential for knowledge base enrichment by applying CINEX to 2,474 frequent relations in Wikidata. CINEX can assert the existence of 2.5M facts for 110 distinct relations, which is 28% more than the existing Wikidata facts for these relations.Comment: 16 pages, The 17th International Semantic Web Conference (ISWC 2018

Under what Conditions is a Plural Represented as More than One? Two Methods for Testing

This paper reviews the findings from a series of psycholinguistic experiments using two different methods designed to probe the conceptual representation of plural expressions. Experiments using a novel number interference paradigm suggested that singular indefinite NPs within distributed predicates are mentally represented as multiple entities (Patson & Warren 2010), but that distributed predicates are conceptually represented as multiple events only in the presence of strong cues to plurality (Patson & Warren 2015). These findings show that the number interference paradigm can be used to probe when comprehenders mentally represent multiple events and entities. A second set of experiments used a picture-judgment task to begin to understand the nature of the plural representations created by comprehenders. These studies suggest that the conceptual representations of plural definite descriptions are no more similar to pictures of small sets of items than they are to pictures of singletons (Patson et al. 2014). These findings and others contribute to a more nuanced view of how language comprehenders compute and represent number. Importantly, these findings introduce two experimental paradigms useful for probing plural representations

Specificity and definiteness in sentence and discourse structure

In this paper, I argue that this informally given list of characteristics covers only a certain subclass of specific indefinites. […] In particular, I dispute the definition of specific indefinites as "the speaker has the referent in mind" as rather confusing if one is working with a semantic theory. Furthermore, I discuss "relative specificity", it. cases in which the specific indefinite does not exhibit wide, but intermediate or narrow scope behavior. Based on such data, I argue that specificity expresses a referential dependency between introduced discourse items. Informally speaking, the specificity of the indefinite expression something [...] expresses that the reference of the expression depends on the reference of another expression, here, on the expression a monk, not the speaker

Quantifier Elimination over Finite Fields Using Gr\"obner Bases

We give an algebraic quantifier elimination algorithm for the first-order theory over any given finite field using Gr\"obner basis methods. The algorithm relies on the strong Nullstellensatz and properties of elimination ideals over finite fields. We analyze the theoretical complexity of the algorithm and show its application in the formal analysis of a biological controller model.Comment: A shorter version is to appear in International Conference on Algebraic Informatics 201

Variable types for meaning assembly: a logical syntax for generic noun phrases introduced by most

This paper proposes a way to compute the meanings associated with sentences with generic noun phrases corresponding to the generalized quantifier most. We call these generics specimens and they resemble stereotypes or prototypes in lexical semantics. The meanings are viewed as logical formulae that can thereafter be interpreted in your favourite models. To do so, we depart significantly from the dominant Fregean view with a single untyped universe. Indeed, our proposal adopts type theory with some hints from Hilbert \epsilon-calculus (Hilbert, 1922; Avigad and Zach, 2008) and from medieval philosophy, see e.g. de Libera (1993, 1996). Our type theoretic analysis bears some resemblance with ongoing work in lexical semantics (Asher 2011; Bassac et al. 2010; Moot, Pr\'evot and Retor\'e 2011). Our model also applies to classical examples involving a class, or a generic element of this class, which is not uttered but provided by the context. An outcome of this study is that, in the minimalism-contextualism debate, see Conrad (2011), if one adopts a type theoretical view, terms encode the purely semantic meaning component while their typing is pragmatically determined

Number-neutral bare plurals and the multiplicity implicature

Bare plurals (dogs) behave in ways that quantified plurals (some dogs) do not. For instance, while the sentence John owns dogs implies that John owns more than one dog, its negation John does not own dogs does not mean "John does not own more than one dog", but rather "John does not own a dog". A second puzzling behavior is known as the dependent plural reading; when in the scope of another plural, the 'more than one' meaning of the plural is not distributed over, but the existential force of the plural is. For example, My friends attend good schools requires that each of my friends attend one good school, not more, while at the same time being inappropriate if all my friends attend the same school. This paper shows that both these phenomena, and others, arise from the same cause. Namely, the plural noun itself does not assert 'more than one', but rather the plural denotes a predicate that is number neutral (unspecified for cardinality). The 'more than one' meaning arises as an scalar implicature, relying on the scalar relationship between the bare plural and its singular alternative, and calculated in a sub-sentential domain; namely, before existential closure of the event variable. Finally, implications of this analysis will be discussed for the analysis of the quantified noun phrases that interact with bare plurals, such as indefinite numeral DPs (three boys), and singular universals (every boy)