This paper is truly a joint effort and it could not have been written without the contribution of both authors. Garson, though, deserves credit (or blame) for first seeing the need for two kinds of quantifier scope, and also for devising essentials of the positive theory.

This paper is truly a joint effort and it could not have been written without the contribution of both authors. Garson, though, deserves credit (or blame) for first seeing the need for two kinds of quantifier scope, and also for devising essentials of the positive theory.

This paper reexamines some examples, discussed by Mates and others, of sentences containing both definite descriptions and quantifiers. It has frequently been claimed that these sentences provide evidence for the view that definite descriptions themselves are quantifiers. The main goal of this paper is to argue this is not so. Though the examples are compatible with quantificational approaches to definite descriptions, they are also compatible with views that treat definite descriptions as basically scopeless. They thus provide no reason to see (...) definite descriptions as quantifiers. Even so, this paper shows that the examples do raise a surprising range of complex issues about how quantifier scope works, and where it occurs. Thus, a clear picture of how these examples work will help us to understand better where definite descriptions fit into the larger picture of quantifiers and related phenomena. (shrink)

One of the fascinations of Sluicing – one that figured in Ross’s (1969) original exploration of the construction – is that it seems to overcome many island effects. Most speakers find contrasts between the pairs of sentences in (1) and (2), for instance.

Previous research has indicated that abstract grammatical rules and forms fall short of predicting quantifier scope and that lexical/pragmatic knowledge plays a significant part in quantifier scope disambiguation (QSD). More recent works have argued that world knowledge in the form of relations among objects may be salient to QSD. This paper contributes to this line of research by providing support to the claim that there is a connection between our lexical knowledge about preposition meanings and (...) class='Hi'>quantifier scope. More specifically, we propose that certain prepositional senses encode dependency relations that have an effect on scope-taking preferences. For example, the preposition of expressing ‘part-whole sense’ contributes to our choice of the inverse scope reading for the construction a day of every month by introducing a dependency between wholes (months) and their respective parts (days). Quantifying over this dependency yields the inverse scope reading: for every month, there is a different day that belongs to it (every month > a day). Furthermore, universal quantification in locative and temporal prepositional phrases tends to support inverse scope. For example, the locative preposition on — as in a store on each side of the street — implies ‘disjointness’ (objects do not occupy more than one place at a time), and hence can be interpreted as a dependency between each side of the street and the respective stores located on them. Quantifying over this dependency yields the inverse scope reading: for each side of the street, there is a different store located on it (each side of the street > a store). For studying the connection between prepositional senses and quantifier scope in the wild, we use a scope-disambiguated corpus created by AnderBois et al. ( 2012), additionally annotated with prepositional senses using the Semantic Network of Adposition and Case Supersenses (SNACS) scheme proposed in Schneider et al. ( 2018, 2020). The results of the corpus study combined with psycholinguistic experiments support the claim made here that certain prepositional senses are strong predictors of quantifier scope. (shrink)

Despite overwhelming evidence suggesting that quantifier scope is a phenomenon that must be treated at the pragmatic level, most computational treatments of scope ambiguities have thus far been a collection of syntactically motivated preference rules. This might be in part due to the prevailing wisdom that a commonsense inferencing strategy would require the storage of and reasoning with a vast amount of background knowledge. In this paper we hope to demonstrate that the challenge in developing a commonsense (...) inferencing strategy is in the discovery of the relevant commonsense data and in a proper formulation of the inferencing strategy itself, and that a massive amount of background knowledge is not always required. In particular, we present a very effective procedure for resolving quantifier scope ambiguities at the pragmatic level using simple quantitative data that is readily available in most database environments. (shrink)

We give a complete characterization of the class of upward monotone generalized quantifiers Q1 and Q2 over countable domains that satisfy the scheme Q1 x Q2 y φ → Q2 y Q1 x φ. This generalizes the characterization of such quantifiers over finite domains, according to which the scheme holds iff Q1 is ∃ or Q2 is ∀ (excluding trivial cases). Our result shows that in infinite domains, there are more general types of quantifiers that support these entailments.

This paper presents and discusses a range of counterexamples to the common view that quantifiers cannot take scope over epistemic modals. Some of the counterexamples raise problems for ‘force modifier’ theories of epistemic modals. Some of the counterexamples raise problems for Robert Stalnaker’s theory of counterfactuals, according to which a special kind of epistemic modal must be able to scope over a whole counterfactual. Finally, some of the counterexamples suggest that David Lewis must countenance ‘would’ counterfactuals in which (...) a covert ‘would’ scopes over the whole consequent of the counterfactual, including an overt ‘might.’. (shrink)

We characterize pairs of monotone generalized quantifiers Q1 and Q2 over finite domains that give rise to an entailment relation between their two relative scope construals. This relation between quantifiers, which is referred to as scope dominance, is used for identifying entailment relations between the two scopal interpretations of simple sentences of the form NP1–V–NP2. Simple numerical or set-theoretical considerations that follow from our main result are used for characterizing such relations. The variety of examples in which they (...) hold are shown to go far beyond the familiar existential-universal type. (shrink)

This paper addresses the question of whether the preverbal even (VP-even) embedded in a nonfinite clause can take wide scope (e.g., Bill refused to even drink WATER). The paper presents novel evidence for wide scope VP-even that is independent of the presuppositions of even. The evidence is based on examples of antecedent-contained deletion (ACD), where embedded VP-even associates with a nominal constituent (or part of it) that raises out of the embedded clause via quantifier raising. Assuming that (...) even must c-command the focus that it associates with, the case at issue forces VP-even to have wide scope, and further shows that VP-even in NPI-licensing contexts is not necessarily an NPI. (shrink)

I document a scope freezing effect found with negated quantifier phrases ). In a sentence with a negated quantifier phrase of the form [NEG DP1], no quantifier phrase DP2 can take scope between NEG and DP1. I show how this scope freezing effect can be explained in terms of the analysis of negated quantifier phrases given in Collins and Postal and Collins.

It is widely believed that existential quantifiers can bring about the semantic effects of a scope which is wider than their actual syntactic scope (See Fodor & Sag (1982), Cresti (1995), Kratzer (1995), Reinhart (1995) and Winter (1995), among many others.) On the other hand, it is assumed that the syntactic scope of universal quantifiers can be determined unequivocally by the semantics. This paper shows that this second assumption is wrong; universal quantifiers can also bring about (...) class='Hi'>scope illusions, though in a very specific environment. In particular, we argue that in the environment of generic tense, universal quantifiers can show the semantic effects of a scope which is wider than the one that is actually realized at LF. Our argument has four steps. First, we show that in generic contexts, universal quantifiers escape standard “scope-islands” (Section 1). Second, we show how the effects of wide scope in generic contexts can be achieved without syntactic wide scope (Section 2.1). Third, we show that this result is actually forced on us, once we take seriously certain independent issues concerning the interpretation of generic tense (Sections 2.2 - 2.4). Finally, the semantics of generic tense and, in particular, its interaction with focus, will yield some intricate new predictions, which, as we show, are borne out (Sections 3 - 5). (shrink)

We introduce generalized quantifiers, as defined in Tarskian semantics by Mostowski and Lindström, in logics whose semantics is based on teams instead of assignments, e.g., IF-logic and Dependence logic. Both the monotone and the non-monotone case is considered. It is argued that to handle quantifier scope dependencies of generalized quantifiers in a satisfying way the dependence atom in Dependence logic is not well suited and that the multivalued dependence atom is a better choice. This atom is in fact (...) definably equivalent to the independence atom recently introduced by Väänänen and Grädel. (shrink)

* This work has been evolving for a while now. Some parts trace back to the few pages on the context-dependency of quantifiers in my dissertation. Reading Recanati’s paper on domains of discourse made me rethink some of my earlier conclusions without in the end actually changing them much. Other parts formed the material for several discussions in my seminar on context-dependency at MIT in the fall of 1995, which included several sessions exploring the issues raised in an early version (...) of Kratzer. Connecting the choice function approach to indefinites with a general analysis of contextual domain restriction was an idea that I considered then without however working out any details. Conversations with Lisa Matthewson and studying her paper inspired me to tackle the problem again. Connections to questions about the context-dependency of conditional sentences also tickled my fancy, since I have been working on conditionals for a while now. Having the opportunity to present this material at the Vilem Mathesius Series provided the impetus to flesh out some of my vague thoughts. Major influences come from the work done in recent years at MIT by Lisa Matthewson, Philippe Schlenker, Julie Legate, and Uli Sauerland. I thank Irene Heim, Lisa Matthewson, Orin Percus, Philippe Schlenker, and Jason Stanley for illuminating discussions about this material. At this point, I see this talk as a report on the state of the art, exploring an intriguing possible connection, but I do not claim substantial intellectual property rights. Mistakes are certainly mine, achievements are probably not. (shrink)

The paper proposes a novel analysis of quantificational subordination, e.g. Harvey courts a woman at every convention. {She is very pretty. vs. She always comes to the banquet with him.} (Karttunen 1976), in particular of the fact that the indefinite in the initial sentence can have wide or narrow scope, but the first discourse as a whole allows only for the wide scope reading, while the second discourse allows for both readings. The cross-sentential interaction between scope and (...) anaphora is captured in terms of structured anaphora to quantifier domains, formalized in a new dynamic system couched in classical type logic; given the underlying type logic, Montague-style compositionality at sub-clausal level follows automatically. Modal subordination (Roberts 1987) is analyzed in a parallel way, thereby capturing the parallels between the individual and modal domains argued for in Stone (1999). Several other phenomena are analyzed in terms of structured anaphora: exceptional wide scope, weak / strong donkey readings, anaphoric / uniqueness-implying definite descriptions and interactions between same / different and quantifier scope. (shrink)

Section 1 provides a brief summary of the pair-list literature singling out some points that are particularly relevant for the coming discussion. -/- Section 2 shows that the dilemma of quantifi cation versus domain restriction arises only in extensional complement interrogatives. In matrix questions and in intensional complements only universals support pairlist readings, whence the simplest domain restriction treatment suffices. Related data including conjunction, disjunction, and cumulative readings are discussed -/- Section 3 argues that in the case of extensional complements (...) the domain restriction treatment is inadequate for at least two independent reasons. One has to do with the fact that not only upward monotonic quantifi ers support pairlist readings, and the other with the derivation of apparent scope out readings. The reasoning is supplemented with some discussion of the semantic properties of layered quantifi ers.  The above will establish the need for quantifi cation, so the question arises how the objections explicitly enlisted in the literature against quantifi cation can be answered. Section 4 considers the de dicto reading of the quantifi er s restriction, quanti cational variability, and the absence of pairlist readings with whether questions, and argues that they need not militate against the quanti ficational analysis. -/- Section 5 summarizes the emergent proposal -/- Finally, section 6 discusses the signifi cance of the above findings for the behavior of weak islands. (shrink)

Quantified NPs in questions may lead to an interpretation in which the NP quantifies into the question. Which dish did every guest bring? can be understood as: 'For every guest x: which dish did x bring?'. After a review of previous approaches that tried to capture this quantification formally or to explain it away, it is argued that such readings involve quantification into speech acts. As the algebra of speech acts is more limited than a Boolean algebra – it only (...) contains conjunction, not disjunction or negation – it is predicted that only universal quantifiers can scope out of questions or other speech acts. The approach is extended to indirect questions, which either are embedded speech acts or coerced to denote the true answers, depending on the embedding verb; in the latter case a Boolean structure results, and we find wide-scope readings of non-universal quantifiers. (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)

Quantifier Raising usually exhibits finite-clause boundedness due to the syntactic and semantic constraints it is subject to (Fox 1995, 2000, Cecchetto 2004, a.o.). In this paper, I argue that QR out of a Mandarin prenominal pre-determiner RC is not only properly licensed, obeying both syntactic and semantic constraints, but also needed to account for the exceptional-scope effects observed across relative clause boundaries (Huang 1982, Aoun and Li 1993, a.o.). I further consider constructions where the exceptional-scope effects are (...) not present, including relative clauses containing the focus-sensitive operator _dou_ and full-sized subject RCs, and show that the absence of the exceptional-scope effects in these constructions follows directly from the proposed analysis. (shrink)

Modal sentences of the form "every F might be G" and "some F must be G" have a threefold ambiguity. in addition to the familiar readings "de dicto" and "de re", there is a third reading on which they are examples of the "plural de re": they attribute a modal property to the F's plurally in a way that cannot in general be reduced to an attribution of modal properties to the individual F's. The plural "de re" readings of modal (...) sentences cannot be captured within standard quantified modal logic. I consider various strategies for extending standard quantified modal logic so as to provide analyses of the readings in question. I argue that the ambiguity in question is associated with the scope of the general term 'F'; and that plural quantifiers can be introduced for purposes of representing the scope of a general term. Moreover, plural quantifiers provide the only fully adequate solution that keeps within the framework of quantified modal logic. (shrink)

First-order logic is known to have a severely limited expressive power on finite structures. As a result, several different extensions have been investigated, including fragments of second-order logic, fixpoint logic, and the infinitary logic L∞ωω in which every formula has only a finite number of variables. In this paper, we study generalized quantifiers in the realm of finite structures and combine them with the infinitary logic L∞ωω to obtain the logics L∞ωω, where Q = {Qi: iε I} is a family (...) of generalized quantifiers on finite structures. Using the logics L∞ωω, we can express polynomial-time properties that are not definable in L∞ωω, such as “there is an even number of x” and “there exists at least n/2 x” , without going to second-order logic. We show that equivalence of finite structures relative to L∞ωω can be characterized in terms of certain pebble games that are a variant of the Ehrenfeucht—Fraïssé games. We combine this game-theoretic characterization with sophisticated combinatorial tools from Ramsey theory, such as van der Waerden's Theorem and Folkman's Theorem, in order to investigate the scope and limits of generalized quantifiers in finite model theory. We obtain sharp lower bounds for expressibility in the logics L∞ωω and discover an intrinsic difference between adding finitely many simple unary generalized quantifiers to L∞ωω adding infinitely many. In particular, we show that if Qis a finite sequence of simple unary generalized quantifiers, then the equicardinality, or Härtig, quantifier is not definable in L∞ωω. We also show that the query “does the equivalence relation E have an even number of equivalence classes” is not definable in the extension L∞ωω of L∞ωω by the Härtig quantifier I and any finite sequence Q of simple unary generalized quantifiers. (shrink)

In this paper I argue for a restriction on certain types of LF movement, which I call ‘wh-related LF movement’. Evidence comes from a number of wh-in-situ constructions in German, such as the scope-marking construction and multiple questions. For semantic reasons, the in situ element in those constructions has to move at LF to either a position reserved for wh-phrases, or even higher up in the structure. The restriction (the Minimal Quantified Structure Constraint, MQSC) is that an intervening quantified (...) expression blocks this movement. In the case of every, the MQSC leads to an unambiguously distributive interpretation of the question. In the case of all other intervening operators, including negation, it leads to ungrammaticality. (shrink)

A person of average height would assert a truth by the conditional ‘if I were seven feet tall, I would be taller than I am,’ in which an indicative clause ‘I am’ is embedded in a subjunctive conditional. By contrast, no one would assert a truth by ‘if I were seven feet tall, I would be taller than I would be’ or ‘if I am seven feet tall, I am taller than I am’. These examples exemplify the fact that whether (...) a sentence's evaluation remains at the actual world in the scope of a modal or conditional depends on the combination of mood in the embedded and matrix clauses rather than, as is commonly thought, just on the presence of an operator ‘actually’. This essay argues that this phenomenon provides evidence that mood admits of bound and free readings along the lines of tenses and pronouns. It therefore favors the hypothesis that natural language contains variables and quantifiers for possible worlds in the object language. This, in turn, requires that the truth of a semantic value of a sentence (or whatever structure is embedded in a modal) be relativized to a sequence of worlds rather than to an individual world, and thus be distinguished from a proposition in the traditional sense. The essay also compares the framework defended with an alternative account of similar phenomena by Kai Wehmeier. (shrink)

Recent AI regulations require deployers of high-risk systems to assess impacts on values like fundamental rights and other legally protected interests. However, existing practice-most notably Fundamental Rights Impact Assessments (FRIAs) under the EU AI Actremains mostly limited to qualitative guidelines. As a result, risk evaluation can be inconsistent and highly variable across assessments. To address this issue, we propose a reference model for value-impact assessment that specifies the core components that any more detailed formalization should incorporate. The model builds on (...) a classical risk paradigm, integrating distinct measures for hazard, exposure, vulnerability, and response or mitigation. We use the EU AI Act's FRIA as a reference case for applying the model to AI risk assessments. The model provides three especially salient recommendations. First, it rejects purely ordinal risk matrices in favor of geometric or ratio-scaled severity ladders, enabling the coherent calculation of expected risk. Second, in analyzing risk mitigation measures, it requires separate estimates of efficacy and reliability, with explicit success criteria and scope conditions that allow for dynamic updating. Third, the model operationalizes regulatory precaution, or risk appetite, through the integration of tail-sensitive risk metrics (e.g., Conditional Value-at-Risk). This lets regulators give appropriate weight to low-probability, high-impact (or catastrophic) harms to fundamental rights without distorting ordinary expected-risk calculations. The result is a structured foundation for more consistent value-impact assessments. (shrink)

The relationship between Lexical-Functional Grammar (LFG) functional structures (f-structures) for sentences and their semanticinterpretations can be formalized in linear logic in a way thatcorrectly explains the observed interactions between quantifier scopeambiguity, bound anaphora and intensionality.Our linear-logic formalization of the compositional properties ofquantifying expressions in natural language obviates the need forspecial mechanisms, such as Cooper storage, in representing thescoping possibilities of quantifying expressions. Instead, thesemantic contribution of a quantifier is recorded as a linear-logicformula whose use in a proof will (...) establish the scope of thequantifier. Different proofs can lead to different scopes. In eachcomplete proof, the properties of linear logic ensure thatquantifiers are properly scoped. (shrink)

One well known problem regarding quantifiers, in particular the 1storder quantifiers, is connected with their syntactic categories and denotations. The unsatisfactory efforts to establish the syntactic and ontological categories of quantifiers in formalized first-order languages can be solved by means of the so called principle of categorial compatibility formulated by Roman Suszko, referring to some innovative ideas of Gottlob Frege and visible in syntactic and semantic compatibility of language expressions. In the paper the principle is introduced for categorial languages generated (...) by the Ajdukiewicz’s classical categorial grammar. The 1st-order quantifiers are typically ambiguous. Every 1st-order quantifier of the type k > 0 is treated as a two-argument functorfunction defined on the variable standing at this quantifier and its scope (the sentential function with exactly k free variables, including the variable bound by this quantifier); a binary function defined on denotations of its two arguments is its denotation. Denotations of sentential functions, and hence also quantifiers, are defined separately in Fregean and in situational semantics. They belong to the ontological categories that correspond to the syntactic categories of these sentential functions and the considered quantifiers. The main result of the paper is a solution of the problem of categories of the 1st-order quantifiers based on the principle of categorial compatibility. (shrink)

This work presents the structure, distribution and semantic interpretation of quantificational expressions in languages from diverse language families and typological profiles. The current volume pays special attention to underrepresented languages of different status and endangerment level. Languages covered include American and Russian Sign Languages, and sixteen spoken languages from Africa, Australia, Papua, the Americas, and different parts of Asia. The articles respond to a questionnaire the editors constructed to enable detailed crosslinguistic comparison of numerous features. They offer comparable information on (...) semantic classes of quantifiers (generalized existential, generalized universal, proportional, partitive), syntactically complex quantifiers (intensive modification, Boolean compounds, exception phrases, et cetera), and several more specific issues such as quantifier scope ambiguities, floating quantifiers, and binary (type 2) quantifiers. The book is intended for semanticists, logicians interested in quantification in natural language, and general linguists as articles are meant to be descriptive and theory independent. The book continues and expands the coverage of the Handbook of Quantifiers in Natural Language (2012) by the same editors, and extends the earlier work in Matthewson (2008), Gil and others (2013) and Bach et al (1995). (shrink)

The sentence Irving was closer to me than he was to most of the others contains a quantifier, most of the other, in the scope a comparative. The first part of this paper explains the challenges presented by such cases to existing approaches to the semantics of the comparative. The second part presents a new analysis of comparatives based on intervals rather than points on a scale. This innovation is analogized to the move from moments to intervals in (...) tense semantics. The remainder of the paper is concerned with an interval-based semantics of degree in relation to issues other than the comparative proper. The paper begins with a discussion of the role negative polarity has played in studies on the semantics of comparatives. (shrink)

Abstract: This paper, building upon the "Dual-Mechanism Model" proposed in Content-Consistent Logic: The Irreplaceability of Traditional Logic in Natural Language Inference (Sun, 2026), further addresses relational reasoning and generalized quantifier reasoning in natural language. It argues that traditional logic is not inherently incapable of handling relations, but rather has not yet established a mechanism for relational deduction and inheritance suited to natural language. Although modern first-order logic can formalize relational structures through variables and quantifiers, its core objective is truth-preservation (...) rather than content-coherent deduction in natural language. Consequently, it cannot replace the innate reasoning mechanisms of natural language itself. This paper proposes that relational reasoning in natural language fundamentally still depends on predicate inheritance within conceptual subordination structures. Through principles such as concept extension, quantifier internalization, relation binarization, the single-step subordination rule, logical descent, and logical ascent, many relational inferences can be reduced back to conceptual reasoning forms in traditional logic. On this basis, the paper further examines how generalized quantifiers (e.g., "most," "almost all," "many," "few") are constrained and mapped in natural language, arguing that their essence is not truth-functional computation in the modern logical sense, but rather content-consistent mapping within a determined domain. The paper systematically analyzes the seven types of generalized quantifier inference examples presented by Zhou (2019), demonstrating that natural language can accomplish complex relational reasoning through conceptual hierarchies, quantifier specification, scope restriction, and descent/ascent logical mechanisms, without relying on higher-order formalization systems in modern logic. The paper further points out that several valid syllogistic forms requiring reduction in traditional syllogistic can be directly supported by descent and ascent inheritance principles at the conceptual level, thus laying the groundwork for a future comprehensive replacement of reduction techniques. This paper maintains that the core objective of natural language logic is not abstract truth-value computation, but the consistency-preservation of conceptual content. Logic is primarily a system of content deduction, rather than a binary truth-functional calculus. The foundational status of traditional logic in natural language inference has not been genuinely superseded by modern logic. (shrink)

It is reasonably well-understood that natural language displays polymorphic behaviour in both its syntax and semantics, where various constructions can operate on a range of syntactic categories, or semantic types. In mathematics, logic and computer science it is appreciated that there are various ways in which such type-general behaviours can be formulated. It is also known that natural languages are highly ambiguous with respect to scoping artifacts, as evident with quantifiers, negation and certain modifier expressions. To deal with such issues, (...) formal frameworks have been explored in which the polymorphic nature of natural language can be expressed, and theories of underspecified semantics have been proposed which seek to separate the process of pure compositional interpretation from the assignment of scope. To date, however, there has been no work on bringing these two aspects together; there is no semantic treatments of scope ambiguity and underspecification which explicitly takes into account the polymorphic nature of natural language quantifiers. In this paper, we extend an existing treatment of underspecification and scope ambiguity in Property Theory with Curry Typing (PTCT) to deal with arbitrary types of quantification by adopting a form of polymorphism. In this theory of underspecification, all of the expressions in the theory are terms of the logic; there is no “meta-semantic” machinery. For this reason all aspects of the theory must be able to deal with polymorphism appropriately. (shrink)

Hintikka’s semantic approach to meaning, a development of Wittgenstein’s view of meaning as use, is the general theme of this chapter. We will focus on the analysis of quantified sentences and on the scope of the principle of compositionality and compare Hintikka’s take on these issues with that of Frege. The aim of this paper is to show that Hintikka’s analysis of quantified expressions as choice functions, in spite of its obvious dissimilarities with respect to the higher-order approach, is (...) actually very close to the Fregean stance on compositionality and context dependence. In particular, we will defend that the Fregean approach to quantifiers is unavoidably linked to the idea that quantified expressions are context-dependent, and therefore should not be conceived under the traditional inside-out model for analysis. (shrink)

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)

The governance of artificial intelligence faces a fundamental challenge: determining which decisions must retain human involvement. Existing risk-based frameworks primarily classify decisions according to application domain and potential harm severity, yet neglect a foundational question—the ontological characteristics inherent to the decisions themselves. Beyond their external consequences, decisions vary structurally in the existential costs they carry: the irreversible burdens that only beings with embodied mortality can bear. This paper advances the "existential cost" concept from an abstract philosophical thesis to an operational (...) governance framework. We propose the Composite Cost Index (CCI), which operationalizes existential cost through five evaluable dimensions: irreversibility of consequences, temporal constraints, scope of affected parties, intensity of value conflicts, and estimated cognitive load. Based on weighted scoring across these dimensions, the CCI framework delineates three governance tiers—mandatory human retention, conditional delegation, and safe delegation—providing differentiated governance guidance for AI decisions at varying risk levels. Through four representative cases—autonomous vehicle emergency avoidance, AI-assisted medical diagnosis, content recommendation systems, and algorithmic sentencing assistance—we demonstrate the framework's analytical applications and address four potential theoretical objections. The framework's core contribution lies in transforming the normative question of "which decisions must be made by humans" from implicit intuitive judgment to explicit structured assessment, thereby establishing a new analytical tool and discussion platform for AI governance. (shrink)

Precision livestock farming (PLF) is the management of livestock using the principles and technology of process engineering. Key to PLF is the dense monitoring of variegated parameters, including animal growth, output of produce (e.g. milk, eggs), diseases, animal behaviour, and the physical environment (e.g. thermal micro-environment, ammonia emissions). While its proponents consider PLF a win-win strategy that combines production efficiency with sustainability goals and animal welfare, critics emphasise, inter alia, the potential interruption of human-animal relationships. This paper discusses the notion (...) that the objectification of animals by PLF influences the developmental pathways of conventional industrial farming. We conduct a conceptual analysis of objectification by comparing discussions in feminist ethics and animal ethics. We find that in animal ethics, objectification includes deontological arguments regarding instrumentalisation, de-animalisation, alienation, commodification and quantification of animals. The focus on socio-political context and relationality connects these debates to central ideas in care ethics. We adopt a care ethics perspective to assess the implications of the objectification of animals in livestock farming. The basic claim is that sensory knowledge symbolised by the farmers’ unity of hand, head and heart would make it harder to objectify animals than abstract and instrumental reasoning where the pursuit of knowledge is intertwined with the pursuit of control, as in mainstream PLF. Despite of what can be considered as a good caring relationship between farmers and animals that is mediated by PLF, people involved in conventional industrial farming still seem to become further detached from farmers and animals, because the PLF system itself is objectifying. PLF redefines the notion of care, in terms of data transparency, standardisation of methods for analysis, real-time collection and processing of data, remote control, and the use of digital platforms. This creates new expectations and requires a redistribution of responsibilities within a wider scope of relations in the value chain. (shrink)

There are some sentences that include expressions that refer to entities that do not exist. One example is this: Mary is in terror of werewolves. Some argue that this sentence cannot be translated into predicate logic. This may be seen as flaw in predicate logic. Against this, I argue in this paper that the problem is not predicate logic, but rather our commitments with the existence and nature of certain things. By revising some of these commitments, we can see that (...) predicate logic is perfectly capable to deal with the problematic sentences. (shrink)

A semantics for quantified modal logic is presented that is based on Kleene's notion of realizability. This semantics generalizes Flagg's 1985 construction of a model of a modal version of Church's Thesis and first-order arithmetic. While the bulk of the paper is devoted to developing the details of the semantics, to illustrate the scope of this approach, we show that the construction produces (i) a model of a modal version of Church's Thesis and a variant of a modal set (...) theory due to Goodman and Scedrov, (ii) a model of a modal version of Troelstra's generalized continuity principle together with a fragment of second-order arithmetic, and (iii) a model based on Scott's graph model (for the untyped lambda calculus) which witnesses the failure of the stability of non-identity. (shrink)

Some theories assume that sentences like (i) with a presupposition trigger in the scope of a quantifier carry an existential presupposition, as in (ii); others assume that they carry a universal presupposition, as in (iii). No student knows that he is lucky. Existential presupposition: At least one student is lucky.Universal presupposition: Every student is lucky. This work is an experimental investigation of this issue in French. Native speakers were recruited to evaluate the robustness of the inference from (i) (...) to (iii). The main result is that presuppositions triggered from the scope of the quantifier aucun‘no’ are in fact universal. But the present results also suggest that the presuppositions triggered from the scope of other quantifiers depend on the quantifier. This calls for important changes in the main theories of presupposition projection. (shrink)

Ontological pluralists maintain that things may have being in different ways. They also hold that their view is consistent with an orthodox, broadly Quinean, quantifier-first approach to ontology. In this paper, I put pressure on this package of views. I show that ontological pluralists should allow that there is a generic way of being, which is less fundamental than the other, more specific, ways of having being. Given the quantifier-first approach to ontology, to have being in this generic (...) way just is to fall within the domain of a general quantifier. I then suggest that the generic notion of being must be more than a mere disjunction of various specific ways to have being and argue that it follows that it is conceivable that something could have being generically without having being in any specific way. If so, then there is conceivably an important ontological distinction among the things falling within the scope of the general quantifier between those that have being fundamentally and those whose being is merely generic and non-fundamental. Finally, I claim that the conceivability of this ontological distinction requires pluralists to acknowledge a conceptual gap between our quantificational and ontological commitments that is in tension with certain interpretations of the quantifier-first approach to ontology. This conclusion, I suggest, should in turn count against at least one kind of deflationary approach to ontological questions. (shrink)

Most studies of the so-called proportion problem seek to understand how lexical and structural properties of sentences containing adverbial quantifiers give rise to various proportional readings. This paper explores a related but distinct problem: given a use of a particular sentence in context, why do only some of the expected proportional readings seem to be available? That is, why do some sentences allow an asymmetric reading when other, structurally similar sentences seem to require a symmetric reading? Potential factors suggested in (...) the literature include the distribution of donkey pronouns, certain uniqueness implications, and focus structures. I argue here that the use of an adverbial quantifier presupposes HOMOGENEITY: all individual situations that get lumped into a single case for the purposes of evaluating the quantification must agree on whether they satisfy the nuclear scope. For instance, in order for a token of Usually, if a farmer owns a donkey, he beats it to be felicitous when construed under a farmer-dominant asymmetric reading, the context must be consistent with the proposition that each farmer either beats all or none of his donkeys. Thus proportional sentences are indeed systematically ambiguous, but only some readings will be felicitous in a given context. (shrink)

In this paper I propose a set-theoretical interpretation of the logical square of opposition, in the perspective opened by generalized quantifier theory. Generalized quantifiers allow us to account for the semantics of quantificational Noun Phrases, and of other natural language expressions, in a coherent and uniform way. I suggest that in the analysis of the meaning of Noun Phrases and Determiners the square of opposition may help representing some semantic features responsible to different logical properties of these expressions. I (...) will conclude with some consideration on scope interactions between quantifiers. (shrink)

We obtain an almost everywhere quantifier elimination for (the noncritical fragment of) the logic with probability quantifiers, introduced by the first author in [10]. This logic has quantifiers like $\exists ^{ \ge 3/4} y$ which says that "for at least 3/4 of all y". These results improve upon the 0-1 law for a fragment of this logic obtained by Knyazev [11]. Our improvements are: 1. We deal with the quantifier $\exists ^{ \ge r} y$ , where y is (...) a tuple of variables. 2. We remove the closedness restriction, which requires that the variables in y occur in all atomic subformulas of the quantifier scope. 3. Instead of the unbiased measure where each model with universe n has the same probability, we work with any measure generated by independent atomic probabilities pR for each predicate symbol R. 4. We extend the results to parametric classes of finite models (for example, the classes of bipartite graphs, undirected graphs, and oriented graphs). 5. We extend the results to a natural (noncritical) fragment of the infinitary logic with probability quantifiers. 6. We allow each pR , as well as each r in the probability quantifier $(\exists ^{ \ge r} y)$ , to depend on the size of the universe. (shrink)