We show that Kubota and Levine’s characterization of the HPSG-based theory of non-constituent coordination proposed in Yatabe Proceedings of the 7th International Conference on Head-Driven Phrase Structure Grammar, CSLI, Stanford, pp 325–344, 2001) and later works is inaccurate, and that the theory in question does not require any ad hoc mechanisms to account for the long-known fact that right-node raising and left-node raising can affect semantic interpretation. In the course of demonstrating this, we fill in some details of this HPSG-based (...) theory that were left unspecified in the previous literature, and we also present novel accounts of split-antecedent relative clauses and of respectively interpretation that are consistent with the theory. Furthermore, we argue that the phenomenon of summative agreement may provide a reason to prefer this theory over CG-based theories like Kubota and Levine’s. (shrink)

As Quine observed, the following sentence has a reading which, if true, would be of special interest to the authorities: Ralph believes that someone is a spy. This is the reading where the quantifier is naturally understood as taking wide scope relative to the attitude verb and as binding a variable within the scope of the attitude verb. This essay is interested in addressing the question what the semantic analysis of this kind of reading should look like from a Fregean (...) perspective—a perspective according to which attitude states are generally relations to structured Fregean thoughts composed of senses. The Fregean view faces a challenge of compositionality here. This essay describes the challenge and offers a response on the Fregean's behalf. (shrink)

Questions with a quantificational subject have readings that seemingly involve quantification into questions (called ‘QiQ’ for short). In particular, in single-wh questions with a universal quantifier, QiQ-readings call for pair-list answers, similar to pair-list readings of multiple-wh questions. This paper unifies the derivation of QiQ-readings and distinguishes QiQ-readings from pair-list readings of multiple-wh questions. I propose that pair-list multiple-wh questions and QiQ-questions both involve a wh-dependency, namely, that the wh-/quantificational subject stands in a functional dependency with the trace of the (...) wh-object. In particular, in a pair-list multiple-wh question, the wh-subject binds into the trace of the wh-object across an identity operator; in a QiQ-question, the quantificational subject binds into the trace of the wh-object across a predication operator. These operations give rise to distinct definedness requirements, which vary with the quantificational force of the wh-/quantificational subject. The proposed analysis explains a contrast in domain exhaustivity between the pair-list readings of multiple-wh questions and questions with a universal quantifier, while also doing justice to the intuitive similarities between these two types of questions. I further propose that the observed QiQ-effect in a QiQ-question is derived by extracting one of the minimal proposition sets that satisfy the aforementioned quantificational predication condition. The values of these sets determine whether the QiQ-reading is available and whether a QiQ-question admits pair-list answers and/or has a choice flavor. (shrink)

In most cases, a wh-question calls for an answer that names an entity in the set denoted by the extension of the wh-complement. However, evidence from questions with necessity modals and questions with collective predicates argues that sometimes a wh-question must be interpreted with a higher-order reading, in which this question calls for an answer that names a generalized quantifier. This paper investigates the distribution and compositional derivation of higher-order readings of wh-questions. First, I argue that the generalized quantifiers that (...) can serve as semantic answers to wh-questions must be homogeneously positive. Next, on the distribution of higher-order readings, I observe that questions in which the wh-complement is singular-marked or numeral-modified can be answered by elided disjunctions but not by conjunctions. I further present two ways to account for this disjunction–conjunction asymmetry. In the uniform account, these questions admit disjunctions because disjunctions may satisfy the atomicity requirement of singular-marking and the cardinality requirement of numeral modification. In the reconstruction account, the wh-complement is syntactically reconstructed, which gives rise to local uniqueness and yields a contradiction for conjunctive answers. (shrink)

Sentences with multiple occurrences of plural definites give rise to certain effects suggesting that distributivity should be modeled by polyadic operations. Yet in this paper it is argued that the simpler treatment of distributivity using unary universal quantification should be retained. Seemingly polyadic effects are claimed to be restricted to definite NPs. This fact is accounted for by the special anaphoric (dependent) use of definites. Further evidence concerning various plurals, island constraints, and cumulative quantification is shown to support this claim. (...) In addition, it is shown that the evidence against a simple atomic version of unary distributivity is not decisive either. In the (uncommon) cases where distributivity with definites is not strictly atomic, they can be analyzed as dependent on implicit quantifiers. (shrink)

In this paper we introduce a theoretical framework and a logical application for analysing the semantics and pragmatics of contrastive conjunctions in natural language. It is shown how expressions like although, nevertheless, yet, and but are semantically definable as connectives using an operator for implication in natural language and how similar pragmatic principles affect the behaviour of both contrastive conjunctions and indicative conditionals. Following previous proposals, conditions on contrast in a conjunction are analysed as presuppositions of die conjunction. Further linguistic (...) evidence leads to a distinction between restrictive and non-restrictive connectives of contrast, and consequently between direct and indirect contrast, which are given a precise definition. A general interface for a theory of contrast using possible world semantics for implication is then presented. As a test case, we show how this interface is applicable to the semantics for conditionals that was introduced by Veltman in his article 'Data semantics and the pragmatics of indicative conditionals' (1986). This application yields an extension of Veltman's Data Logic, called Contrastive Data Logic Once appropriate modifications are added to Veltman's pragmatic considerations, we show that contrastive data logic provides an adequate tool for the analysis of substantial linguistic data concerning contrast and implication in natural language. (shrink)

On a widely suggested knowledge-first account of belief, to believe p is to phi as if one knew p. I challenge this view by arguing against various regimentations of it. I conclude by generalizing my argument to alternative knowledge-first views suggested by Williamson and Wimmer.

On reading the last sentence, did you interpret me as saying falsely that everything — everything in the entire universe — was packed into my carry-on baggage? Probably not. In ordinary language, ‘everything’ and other quantifiers (‘something’, ‘nothing’, ‘every dog’, ...) often carry a tacit restriction to a domain of contextually relevant objects, such as the things that I need to take with me on my journey. Thus a sentence of the form ‘Everything Fs’ is true as uttered in a (...) context C if and only if everything that is relevant in C satisfies the predicate ‘F’; ‘everything’ ranges just over the contextually relevant things. Such generality is restricted in a context-relative way. (shrink)

Kripke [1975] gives a formal theory of truth based on Kleene's strong evaluation scheme. It is probably the most important and influential that has yet been given—at least since Tarski. However, it has been argued that this theory has a problem with generalized quantifiers such as All—that is, All ϕs are ψ—or Most. Specifically, it has been argued that such quantifiers preclude the existence of just the sort of language that Kripke aims to deliver—one that contains its own truth predicate. (...) In this paper I solve the problem by showing how Kleene's strong scheme, and Kripke's theory based on it, can in a natural way be extended to accommodate the full range of generalized quantifiers. (shrink)

The notion of a proposition is central to philosophy. But it is subject to paradoxes. A natural response is a hierarchical account and, ever since Russell proposed his theory of types in 1908, this has been the strategy of choice. But in this paper I raise a problem for such accounts. While this does not seem to have been recognized before, it would seem to render existing such accounts inadequate. The main purpose of the paper, however, is to provide a (...) new hierarchical account that solves the problem. (shrink)

This note explains the circumstances under which a type 1 quantifier can be decomposed into a type 1, 1 quantifier and a set, by fixing the first argument of the former to the latter. The motivation comes from the semantics of Noun Phrases (also called Determiner Phrases) in natural languages, but in this article, I focus on the logical facts. However, my examples are taken among quantifiers appearing in natural languages, and at the end, I sketch two more principled linguistic (...) applications. (shrink)

The paper elaborates two points: i) There is no principal opposition between predicate logic and adherence to subject-predicate form, ii) Aristotle's treatment of quantifiers fits well into a modern study of generalized quantifiers.

I examine notions of equivalence between logics (understood as languages interpreted model-theoretically) and develop two new ones that invoke not only the algebraic but also the string-theoretic structure of the underlying language. As an application, I show how to construe modal operator languages as what might be called typographical notational variants of _bona fide_ first-order languages.

‘Only’ associates with focus and licenses NPIs. This paper looks at the distributional pattern of NPIs under ‘only’ and presents evidence for the movement theory of focus association and against an in situ approach. NPIs are licensed in the ‘scope’ (or the second argument) of ‘only’, but not in the complement (or its first argument), which I will call the ‘syntactic restrictor’. While earlier approaches argued that ‘only’ licenses NPIs in the unfocused part of the sentence it occurs in except (...) in its focus, evidence from DP-‘only’ shows that NPIs are also not licensed in the unfocused part of the syntactic restrictor. The distribution of NPIs provides a test for the size of the syntactic restrictor, and this test is applied to the case of VP-‘only’. The evidence shows that (i) the restrictor can be smaller than the entire VP and is not necessarily identical to the surface complement of ‘only’; (ii) in the case of association with a head the restrictor comprises an XP containing the head; and (iii) in cases of association into an island, the restrictor comprises the entire island. Generalizations (i)–(iii) can be captured straightforwardly by a movement approach but are incompatible with an in situ analysis. Contextual domain- restriction of the kind used in in situ approaches accounts for the appropriate semantics in cases where the semantic focus is properly contained in the syntactic restrictor of ‘only’. (shrink)

which he calls general indicatives, are correctly analysed as open indicative conditionals prefixed by universal quantifiers. So they are both analysed as (∀x)(if x gets a chance, x bungee-jumps), where x ranges over girls. This analysis is attributed to Geach.2 Barker then shows that this syntactic analysis, together with other premises, entails that the open conditional occurring under the universal quantifier has to be analysed as having the import of material implication.

For the first time a uniform compositional derivation is given for quantified sentences containing exceptive constructions. The semantics of exceptives is primarily one of subtraction from the domain of a quantifier. The crucial semantic difference between the highly grammaticized but-phrases and free exceptives is that the former have the Uniqueness Condition as part of their lexical meaning whereas the latter are mere set subtractors. Several empirical differences between the two types of exceptives are shown to follow from this basic lexical (...) difference. (shrink)

We study definability in terms of monotone generalized quantifiers satisfying Isomorphism Closure, Conservativity and Extension. Among the quantifiers with the latter three properties - here called CE quantifiers - one finds the interpretations of determiner phrases in natural languages. The property of monotonicity is also linguistically ubiquitous, though some determiners like an even number of are highly non-monotone. They are nevertheless definable in terms of monotone CE quantifiers: we give a necessary and sufficient condition for such definability. We further identify (...) a stronger form of monotonicity, called smoothness, which also has linguistic relevance, and we extend our considerations to smooth quantifiers. The results lead us to propose two tentative universals concerning monotonicity and natural language quantification. The notions involved as well as our proofs are presented using a graphical representation of quantifiers in the so-called number triangle. (shrink)

In order to uphold the claim that referential intuitions are a reliable source of evidence for theories of reference, Machery et al. conducted an empirical research by testing truth-value judgments. First, we discuss a conceptual limitation of Machery et al. ’s experiment on truth-value judgments. Then, we present the data of an empirical survey that shows that people’s truth-value judgments are not congruent with their use of proper names. We explain why the results of our empirical research refute the conclusions (...) of Machery et al. ’s experiment on truth-value judgments. We conclude that referential intuitions are still problematic. (shrink)

Potts et seq. presents an analysis of gap-containing supplements where the gap is modelled as a variable over the semantic type of the constituent that the as-clause adjoins to. This much allows the meaning of the gap to be resolved purely compositionally, by defining as as a function that allows the anchor to bind the gap variable. This article presents a class of as-clauses where Potts’s analysis seems to break down, in that the gap cannot be modelled as a variable (...) over the semantic type of the anchor. I propose that these cases can be unified with those in Potts’s work, as well as a larger class of ellipsis phenomena, by assuming that, under certain conditions, surface gaps are composite entities, containing a bound variable and a free variable that are resolved independently of each other. The bound variable is bound by the anchor, and the free variable is resolved by anaphora to a salient discourse object. (shrink)

The aim of the paper is to formalize I. Bellert's proposal to characterize distinct nonequivalent readings of quantificationally ambiguous sentences with help of two features: absoluteness and distributiveness. The formalisation makes use of set theoretical and model theoretical standard notions. Foundamental rules, proposed by Bellert, govering the interpretation of cooccurring quantifiers are quoted and outlines of proofs of important derived rules are given.

This paper is a critical examination of Vendler's well-known aspectual classes (states, activities, accomplishments, achievements). It is argued that it not classes that play a role in the explanation of aspectual phenomena but rather some specific semantic factors from which aspectual classes can be constructed, in particular factors inherent to the (lexical) verb and to the determiners of noun phrases.

Clause-embedding predicates come in three major varieties: responsive predicates are compatible with both declarative and interrogative complements; rogative predicates are only compatible with interrogative complements; and anti-rogative predicates are only compatible with declarative complements. It has been suggested that these selectional properties are at least partly semantic in nature. In particular, it has been proposed that the anti-rogativity of neg-raising predicates like believe comes from the triviality in meaning that would arise with interrogative complements. This paper puts forward a similar (...) semantic explanation for non-veridical preferential predicates such as hope, which are anti-rogative, unlike their veridical counterparts such as be happy, which are responsive. (shrink)

This paper discusses a set of observations, many of which are novel, concerning differences between the adjectival modals _certain_ and _possible_ and their adverbial counterparts _certainly_ and _possibly_. It argues that the observations can be derived from a standard interpretation of _certain_/_certainly_ as universal and _possible_/_possibly_ as existential quantifiers over possible worlds, in conjunction with the hypothesis that the adjectives quantify over knowledge and the adverbs quantify over belief. The claims on which the argument relies include the following: (i) knowledge (...) implies belief, (ii) agents have epistemic access to their belief, (iii) relevance is closed under speakers’ belief, and (iv) commitment is pragmatically inconsistent with explicit denial of belief. (shrink)

In this paper we study the semantic data complexity of several controlled fragments of English designed for natural language front-ends to OWL (Web Ontology Language) and description logic ontology-based systems. Controlled languages are fragments of natural languages, obtained by restricting natural language syntax, vocabulary and semantics with the goal of eliminating ambiguity. Semantic complexity arises from the formal logic modelling of meaning in natural language and fragments thereof. It can be characterized as the computational complexity of the reasoning problems associated (...) to their semantic representations. Data complexity (the complexity of answering a question over an ontology, stated in terms of the data items stored therein), in particular, provides a measure of the scalability of controlled languages to ontologies, since tractable data complexity implies scalability of data access. We present maximal tractable controlled languages and minimal intractable controlled languages. (shrink)

1. Generic statements are some of the most intriguing statements we make. They are so central to our commonsense reasoning that every attested human language can express them (Dahl 1995; Cohen 2013...

Comparative quantifiers, such as more than three books, cannot take scope over any quantifier in subject position if they occupy object position. This is clearly different from the behavior of other quantifiers (e.g., universal quantifiers). This paper argues that this scope puzzle is due to a more complex internal structure of comparative quantifiers than other quantifiers. In the decompositional approach that I pursue, comparative quantifiers are decomposed into two generalized quantifiers (i.e., in the case above, the comparative operator er than (...) three and the DP many books). In this approach, obligatory narrow scope of comparative quantifiers in object position is a consequence of the interplay of the independently motivated principles of grammar that also constrain other quantifiers. On the basis of the scope puzzle, I specifically argue for two constraints on Scope Shifting Operations (SSOs) a locality condition on SSOs and Scope Economy, proposed by Fox (2000), which prohibits SSOs that have no effect on semantic interpretation. Thus, I argue that the apparently peculiar facts of comparative quantifiers are, in fact, additional evidence for the core properties of SSOs. (shrink)

One approach to understanding how the human cognitive system stores and operates with quantifiers such as “some,” “many,” and “all” is to investigate their interaction with the cognitive mechanisms for estimating and comparing quantities from perceptual input (i.e., nonsymbolic quantities). While a potential link between quantifier processing and nonsymbolic quantity processing has been considered in the past, it has never been discussed extensively. Simultaneously, there is a long line of research within the field of numerical cognition on the relationship between (...) processing exact number symbols (such as “3” or “three”) and nonsymbolic quantity. This accumulated knowledge can potentially be harvested for research on quantifiers since quantifiers and number symbols are two different ways of referring to quantity information symbolically. The goal of the present review is to survey the research on the relationship between quantifiers and nonsymbolic quantity processing mechanisms and provide a set of research directions and specific questions for the investigation of quantifier processing. (shrink)

We study the computational complexity of polyadic quantifiers in natural language. This type of quantification is widely used in formal semantics to model the meaning of multi-quantifier sentences. First, we show that the standard constructions that turn simple determiners into complex quantifiers, namely Boolean operations, iteration, cumulation, and resumption, are tractable. Then, we provide an insight into branching operation yielding intractable natural language multi-quantifier expressions. Next, we focus on a linguistic case study. We use computational complexity results to investigate semantic (...) distinctions between quantified reciprocal sentences. We show a computational dichotomy<br>between different readings of reciprocity. Finally, we go more into philosophical speculation on meaning, ambiguity and computational complexity. In particular, we investigate a possibility to<br>revise the Strong Meaning Hypothesis with complexity aspects to better account for meaning shifts in the domain of multi-quantifier sentences. The paper not only contributes to the field of the formal<br>semantics but also illustrates how the tools of computational complexity theory might be successfully used in linguistics and philosophy with an eye towards cognitive science. (shrink)

I argue that standard definitions of quantifiers are inadequate and offer a new one. The new definition categorizes expressions as quantifiers in accordance with our pre-theoretical judgments, it is broadly applicable to both formal and natural languages, and it eschews unnecessary theoretical commitments about the details of the syntax and semantics of these expressions.

We design new languages, by and large, in order to bypass complexities and limitations within the languages we already have. But when we are concerned with language itself we should guard against projecting the simple and powerful syntax and semantics we have concocted back into the sentences we encounter. For some of the features of English, French, or Ancient Greek we routinely abstract away from in the process of formalization might be linguistic universals – the very features that set human (...) languages apart from all the other conceivable ones. How similar natural languages really are to formal ones is an empirical question for linguistics. (shrink)

This paper explores the idea that scalar implicatures are computed with respect todiscourse referents. Given the general consensus that a proper account of pronominal anaphora in natural language requires discourse referents separately from the truth-conditional meaning, it is naturally expected that the anaphoric information that discourse referents carry play a role in the computation of scalar implicatures, but the literature has so far mostly exclusively focused on the truth-conditional dimension of meaning. This paper offers a formal theory of scalar implicatures (...) with discourse referents couched in dynamic semantics, and demonstrates its usefulness through a case study on the plurality inferences of plural nouns in English. (shrink)

The paper suggests a modal predicate logic that deals with classical quantification and modalities as well as intermediate operators, like “most” and “mostly”. Following up the theory of generalized quantifiers, we will understand them as two-placed operators and call them determiners. Quantifiers as well as modal operators will be constructed from them. Besides the classical deduction, we discuss a weaker probabilistic inference “therefore, probably” defined by symmetrical probability measures in Carnap’s style. The given probabilistic inference relates intermediate quantification to singular (...) statements: “Most S are P” does not logically entail that a particular individual S is also P, but it follows that this is probably the case, where the probability is not ascribed to the propositions but to the inference. We show how this system deals with single case expectations while predictions of statistical statements remain generally problematic. (shrink)

The paper uses the theory of generalized quantifiers to discuss existential import and its implications for Aristotelian logic, namely the square of opposition, conversions and the assertoric syllogistic, as well as for more recent generalizations to intermediate quantifiers like “most”. While this is a systematic discussion of the semantic background one should assume in order to obtain the inferences and oppositions Aristotle proposed, it also sheds some light on the interpretation of his writings. Moreover by applying tools from modern formal (...) semantics to the investigation of classical Aristotelian logic and its extensions, we combine different approaches to the logic of quantification. We will present variants of quantifiers that are associated to the four corners of the square of opposition with and without existential import and discuss their role for the logical square, conversions and the syllogistic. It will turn out that there is no way to ascribe existential import that validates all inferences and relations which one is willing to hold in Aristotelian logic. Two options, however, provide reasonable results. Existential import should either be ascribed only to affirmative statements or only be ascribed to universal quantification. The former option is preferable for a mere reconstruction of the classical Aristotelian logic while the latter option is more attractive if Aristotelian logic is generalized to intermediate quantifiers. (shrink)

This paper argues that verb phrase ellipsis requires contrast. The central observation is that ellipsis is ungrammatical in tautologous conditionals; e.g., *_If John wins, then he does_. Ellipsis is correctly ruled out by a focus-based theory of ellipsis (Rooth 1992a, b ), but one that crucially imports focus’s requirement for contrast: an elliptical constituent must have an antecedent that is not merely an alternative to it, but a ‘proper’ alternative. An explanation in terms of contrast failure proves superior to alternative (...) explanations in terms of triviality and matching form. Showing as much catalogues what counts for contrast in ellipsis, encompassing negation, questions, and intensionality. Subjecting ellipsis to a contrast requirement is in direct conflict with the traditional analysis of MaxElide effects (Takahashi and Fox 2005 ), favouring alternative explanations (e.g., Jacobson 2019a, b ), perhaps in terms of contrast itself (Griffiths 2019 ). Overall, this paper establishes that contrast has explanatory power in ellipsis licensing. (shrink)

A special kind of substitution on languages called iteration is presented and studied. These languages arise in the application of semantic automata to iterations of generalized quantifiers. We show that each of the star-free, regular, and deterministic context-free languages are closed under iteration and that it is decidable whether a given regular or determinstic context-free language is an iteration of two such languages. This result can be read as saying that the van Benthem/Keenan ‘Frege Boundary’ is decidable for large subclasses (...) of natural language quantifiers. We also determine the state complexity of iteration of regular languages. (shrink)