New data on the competition between definites and indefinites

In this paper, we report on four experiments investigating obligatory presupposition effects. Specifically, we look at the inferences arising from not using presupposition triggers when their use is supported by the context. We compare these inferences and the contextual factors for their derivation to presuppositions and implicatures. Extending previous work, we explore not only the English definite determiner "the" but also the dual "both" and their respective competition with the universal quantifiers "every" and "all".

Number and Quantity Expressions

This chapter examines the interactions between quantity expressions and number across languages. Quantity expressions may require the presence of specific number markers on the noun or noun phrase they combine with. They may also trigger a singular or plural interpretation for the noun phrase as a whole, as in one N or several N. An important criterion used to distinguish classes of quantity expressions is the way these expressions interact with countability. While some quantity expressions depend on the presence of countable units in order to be interpreted, others do not. Examples of the former type are numerals, vague cardinal quantity expressions (several), and distributive universal quantifiers (each, every), while non-cardinal quantity expressions (a lot) and non-distributive universal quantifiers (all) belong to the second category. The chapter mainly focuses on the nominal domain. The use of quantity expressions in relation to verbal plurality is considered briefly.

Heterogeneous sets: a diachronic typology of associative and similative plurals

This paper provides a diachronic typology of what we call ‘heterogeneous plurals’, an overarching term comprising associative plurals (expressions meaning X[person] & company) and similative plurals (expressions meaning X and similar entities). Based on a 110-language sample, we identify the most recurrent sources of these two types of plurals by means of various types of evidence (homophony/identity, internal reconstruction, comparison with cognate languages). The two types of plurals develop out of different source types: while the sources of associative plurals include elements that work as set constructors (plural anaphoric elements, plural possessives, names meaning ‘group’), those of similative plurals comprise elements with vague reference such as interrogative/indefinite items or uncertainty markers. There are also a few source types that may develop into both associative and similative plurals, such as connectives (‘and/with’) and universal quantifiers (‘every/all’). The differences in the diachronic pathways leading to the two types of plurals are explained in terms of the different referential properties of the nominal bases from which they are formed (proper names/kin terms vs. common nouns), but also taking into account the typical discourse contexts in which the two types of plurals are employed.

Quantum B-algebras with involutions

The aim of this paper is to define and study the involutive and weakly involutive quantum B-algebras. We prove that any weakly involutive quantum B-algebra is a residuated poset. As an application, we introduce and investigate the notions of existential and universal quantifiers on involutive quantum B-algebras. It is proved that there is a one-to-one correspondence between the quantifiers on weakly involutive quantum B-algebras. One of the main results consists of proving that any pair of quantifiers is a monadic operator on weakly involutive quantum B-algebras. We investigate the relationship between quantifiers on bounded sup-commutative pseudo BCK-algebras and quantifiers on other related algebraic structures, such as pseudo MV-algebras and bounded Wajsberg hoops.

Domain restriction in child Mandarin: Implications for quantifier spreading

This study explores Mandarin children’s competence with quantifier domain restriction. We present results from two experiments in which adults and four- to five-year old children evaluated two possible candidates for the domain selection associated with the distributive operator dou ‘all’ in Mandarin Chinese. In the first experiment, we investigated whether children and adults are capable of selecting an appropriate domain when two candidate NPs both appear inside dou’s quantification scope; i.e., both of the NPs c-command dou. In the second experiment, still two candidate NPs were presented, but one within dou’s scope and the other outside its scope. Our results indicate that four- to five-year-old children are capable of basic distributive computation associated with dou, but they may choose an NP that adults do not usually choose as the domain of dou, resulting in non-adult interpretations of distributive computation in certain cases. Based on the results, we propose that four- to five-year-old children are less certain about the domain restriction associated with dou-quantification. This proposal has important implications for the current debate on the acquisition of universal quantifiers, specifically, the problem of quantifier spreading. We explain children’s uncertainty about the domain restriction with a universal grammar-based statistical acquisition model.

Monadic pseudo BE-algebras

In this paper we define the monadic pseudo BE-algebras and investigate their properties. We prove that the existential and universal quantifiers of a monadic pseudo BE-algebra form a residuated pair. Special properties are studied for the particular case of monadic bounded commutative pseudo BE-algebras. Monadic classes of pseudo BE-algebras are investigated and it is proved that the quantifiers on bounded commutative pseudo BE-algebras are also quantifiers on the corresponding pseudo MV-algebras. The monadic deductive systems and monadic congruences of monadic pseudo BE-algebras are defined and their properties are studied. It is proved that, in the case of a monadic distributive commutative pseudo BE-algebra there is a one-to-one correspondence between monadic congruences and monadic deductive systems, and the monadic quotient pseudo BE-algebra algebra is also defined.

Enhanced Unsatisfiable Cores for QBF: Weakening Universal to Existential Quantifiers

We introduce an enhanced notion of unsatisfiable cores for QBF in prenex CNF that allows to weaken universal quantifiers to existential quantifiers in addition to the traditional removal of clauses. The resulting unsatisfiable cores can be different from those of the traditional notion in terms of syntax, standard semantics, and proof-based semantics. This not only gives rise to explanations of unsatisfiability but, via duality, also leads to diagnoses and repairs of unsatisfiability that are not obtained with traditional unsatisfiable cores. We use a source-to-source transformation on QBF in PCNF such that the weakening of universal quantifiers to existential quantifiers in the original formula corresponds to the removal of clauses in the transformed formula. This makes any tool or method for the computation of unsatisfiable cores of the traditional notion available for the computation of unsatisfiable cores of our enhanced notion. We implement our approach as an extension to the QBF solver DepQBF, and we perform an extensive experimental evaluation on a subset of QBFLIB. We illustrate with several case studies that helpful information can be provided by unsatisfiable cores of our enhanced notion.

'Religion' in Late Antique Zoroastrianism and Manichaeism: Developing a Term in Counterpoint

This article evaluates the development of a generic term for ‘religion’ in late antique Manichaeism and Zoroastrianism. It examines linguistic indications of the use of dēn/δēn as a generic term in the Manichaean Middle Iranian corpora, i.e. Middle Persian, Parthian, and Sogdian, as well as in the corpus of Zoroastrian Middle Persian. The paper considers declination in the plural, the attribution of universal quantifiers or demonstrative adjectives, comparison, and selection, as they occur in the above corpora, to be indicators of generic concepts. Acknowledging that third-century Manichaeism shaped the term for ‘religion’ in the Persian Empire, the paper scrutinizes the reflections of this formative process in Sasanian and also early Islamic Zoroastrianism. The resulting analysis of the linguistic evidence indicates that the newly coined Manichaean concept of ‘religion’ did not find considerable echoes in late antique Zoroastrianism. Furthermore, an investigation of the term daēnā- in the Avestan sources provides earlier evidence for the formation of the term ‘religion’ in pre-Sasanian Zoroastrianism. Finally, the paper highlights the significance of religious contact for the formation of a generic concept of religion.

Negative Quantifiers

This chapter discusses two puzzling phenomena in the domain of negative quantifiers: the so-called nall-problem and the existence of split-scope readings triggered by negative indefinites. The nall-problem concerns the fact that no language in the world lexicalizes negated universal quantifiers (with the meaning ‘not every’) and other negated high-scale elements. Negative Indefinites in languages such as Dutch and German may give rise to so-called split scope readings. Sentences like German Du must keine Krawatte anziehen (‘you must wear no tie’) have a reading where the modal takes scope in between the negation and the indefinite. That suggests that prima facie negative indefinites are not negative quantifiers in a straightforward sense. This chapter briefly discusses and evaluates the main analyses that have been put forward to account for these puzzles.