Formal Semantics

Quantification, Negation, and Focus: Challenges at the Conceptual-Intentional Semantic Interface Tista Bagchi National Institute of Science, Technology, and Development Studies (NISTADS) and the University of Delhi Since the proposal of Logical Form (LF) was put forward by Robert May in his 1977 MIT doctoral dissertation and was subsequently adopted into the overall architecture of language as conceived under Government-Binding Theory (Chomsky 1981), there has been a steady research effort to determine the nature of LF in language in light of structurally (...) diverse languages around the world, which has ultimately contributed to the reinterpretation of LF as a Conceptual-Intentional (C-I) interface level between the computational syntactic component of the faculty of language and one or more interpretive faculties of the human mind. While this has opened up further possibilities of research in phenomena such as quantifier scope and scope interactions between negation, quantification, and focus, it has also given rise to a few real challenges to linguistic theory as well. Some of these are: (i) the split between lexical meaning – a matter supposedly belonging to the phase-wise selection of lexical arrays – and issues of semantic interpretation that arise purely from binding and scope phenomena (Mukherji 2010); (ii) partially relatedly, the level at which theta role assignment can be argued to take place, an issue that is taken up by me in Bagchi (2007); and (iii) how supposedly “pure” scopal phenomena relating to quantifiers, negation, and emphasizing expressions such as only and even (comparable to, e.g., Urdu/Hindi hii and bhii, Bangla –i and –o) also have dimensions of both focus and discourse reference. While recognizing all of these challenges, this talk aims to highlight particularly challenge (iii), both in terms of scholarship in the past and for the rich prospects for research on languages of south Asia with the semantics of quantification, negation, and focus in view. The scholarship of the past that I seek to relate this issue to is where, parallel to (and largely independently of) the research on LF that had been happening, Barwise and Cooper were developing their influential view of noun phrases as generalized quantifiers, culminating in their key 1981 article “Generalized Quantifiers and Natural Language” while, independently, McCawley, in his 1981 book Everything that Linguists have Always Wanted to Know about Logic, established through argumentation that all noun phrases semantically behave like generalized quantified expressions (further elaborated by him in the second – 1994 – revised edition of his book). I seek to demonstrate, based on limited data analysis from selected languages of south Asia, that our current understanding of quantification, negation, and focus under the Minimalist view owes something significant to the two major, but now largely marginalized, works of scholarship, and that for the way forward it is essential to adopt a more formal-semantic approach as adopted by them and also by later works such as Denis Bouchard’s (1995) The Semantics of Syntax, Mats Rooth’s work on focus (e.g., Rooth 1996, “Focus” in Shalom Lappin’s Handbook of Contemporary Semantic Theory), Heim and Kratzer’s Semantics in Generative Grammar (1998), and Yoad Winter’s (2002) Linguistic Inquiry article on semantic number, to cite just a few instances. (shrink)

In this survey article, I discuss the variety of ways in which language allows us to talk about the future. Topics discussed include how the category of predictive expressions broadly understood relates to the syntactic category of tense; what it means to say that a language does not have tense; how predictiveness relates to modality; and finally technical issue concerning the scope of negation in a semantics that is capable of shifting evaluation towards the future.

This note identifies and corrects some problems in developments of the thesis that predictive expressions, such as English "will", are modals. I contribute a new argument supporting Cariani and Santorio's recent claim that predictive expressions are non-quantificational modals. At the same time, I improve on their selectional semantics by fixing an important bug. Finally, I show that there are benefits to be reaped by integrating the selection semantics framework with standard ideas about the future orientation of modals.

This paper extends a trivalent semantics for indicative conditionals to a language including the modal operators "might" and "must". Specifically, we combine Cooper's (1968) truth-functional, trivalent analysis of the conditional connective with Kratzer's (1986, 2012) idea that if-clauses restrict modal operators. By hard-wiring both trivalence and the restriction operation into the truth conditions of conditional-modal expressions, we obtain an attractive theory that yields plausible predictions for the interaction of conditionals and modals, explains the intuitive appeal of the Restrictor View and (...) avoids the typical problems of Kratzer-style accounts, especially regarding the probability of conditional-modal expressions. (shrink)

This paper provides a new framework for formalizing conditional obligations in natural language: it pairs a unary deontic operator with trivalent semantics for the indicative conditional and Kratzer's idea that the antecedents of conditionals restrict the scope of modals in the consequent. Combining these three ideas, we obtain a fully compositional theory of "if" and "ought'" that validates plausible principles for deontic reasoning. Moreover, it resolves classical challenges such as the "if A then ought A" problem, the paradox of the (...) miners and the modeling of contrary-to-duty obligations (e.g., Chisholm's quartet). All in all, our proposal is attractive from a logical point of view and squares well with general theories of natural language reasoning. (shrink)

Dreams are not real, so when we recount them we prefix an intensional operator like “I dreamed that…”. Linguists will analyze this construction in terms of clausal complementation syntax and possible worlds semantics. But talking about a dream is often more like telling a story, with a potentially complex discourse structure (involving propositional discourse units connected by coherence relations like NARRATION, BACKGROUND, and EXPLANATION) that is hard to fit inside a single syntactically embedded that-clause (or a sequence of independently embedded (...) clauses). I show how we can analyze actual, complex dream report stories using a formal discourse semantics framework. I then explore how to extend this discourse framework to visual dream reporting, like in movies and comics, where it’s not immediately clear that we even have any intensional operators or embeddings to begin with. (shrink)

A language is a system of signs used for communication, and linguists are tasked with, among other things, uncovering the syntax and semantics of such systems. In this paper I explore to what extent pictures fit this characterization of a language and hence would fall within the domain of linguistics. I conclude that at the very least there are well-defined systems of depiction for which we can give a precise semantics, in a familiar possible worlds framework, although pictorial propositions are (...) not derived via the linguistically familiar lexicon and recursive composition rules, but via geometric projection. I then show how sequences of pictures, like sequences of utterances, can be used to form coherent discourses. I explore in some detail extensions of the formal discourse semantics of Segmented Discourse Representation Theory to deal with comics, i.e. storytelling through picture sequences. I focus specifically on the representation of events in comics, and the integration of both symbolic and iconic elements. (shrink)

Minimal Type Theory (MTT) shows exactly how all of the constituent parts of an expression relate to each other (in 2D space) when this expression is formalized using a directed acyclic graph (DAG). This provides substantially greater expressiveness than the 1D space of FOPL syntax. -/- The increase in expressiveness over other formal systems of logic shows the Pathological Self-Reference Error of expressions previously considered to be sentences of formal systems. MTT shows that these expressions were never truth bearers, thus (...) never sentences of any formal logic system. (shrink)

The conventional notion of a formal system is adapted to conform to the sound deductive inference model operating on finite strings. Finite strings stipulated to have the semantic value of Boolean true provide the sound deductive premises. Truth preserving finite string transformation rules provide the valid deductive inference. Sound deductive conclusions are the result of these finite string transformation rules.

Without constraints on self-reference, one can prove an absurdity even in a language free of semantic terms. The argument exploits a unary operation which ends up being intensional in virtue of self-reference. However, since intensional operations are already excluded in classical logic, there are no drastic revisionary implications here. Still, the argument reveals a new sort of intensional context, one which does not depend on a propositional attitude verb, a modal operator, an idiom like ’so called’, etc. Moreover, since classical (...) logicians do not seem aware of the potential danger with self-reference, a word of warning is in order. (shrink)

At the turn of the century, electronic mail emerged as a core mode of communication, fundamentally transforming the way individuals and organizations interact. In this digital age, one ubiquitous representational device is the email address. Given the importance of email addresses in our lives, it is natural to ask: what do email addresses represent? And how do they represent it? Given that email addresses have a semantic interpretation, and that they have a formal syntax, it is reasonable to assume that (...) they have a compositional semantics. Do they? If so, what is it? (shrink)

Many recent theories of epistemic discourse exploit an informational notion of consequence, i.e. a notion that defines entailment as preservation of support by an information state. This paper investigates how informational consequence fits with probabilistic reasoning. I raise two problems. First, all informational inferences that are not also classical inferences are, intuitively, probabilistically invalid. Second, all these inferences can be exploited, in a systematic way, to generate triviality results. The informational theorist is left with two options, both of them radical: (...) they can either deny that epistemic modal claims have probability at all, or they can move to a nonstandard probability theory. (shrink)

There is a common assumption in the semantics of modal auxiliaries in natural language; in utterances of MOD φ , where MOD is a modal and φ is the prejacent, context determines the particular flavor of modality expressed by the modal. Such is the standard contextualist semantics of Kratzer and related proposals. This winds up being a problem, because there is a significant class of modals which have constraints on the admissible modal flavor that are not traceable to context. For (...) example, in MUST φ , subsentential properties of φ, like the aspectual class of the predicate in the prejacent, can affect the flavor of MUST. By encoding the above assumption into the semantics, such contextualist accounts fail to be able to explain, much less to predict, this pattern. Worse yet, attempts to exploit the resources of the theory in service of an explanation run afoul of important commitments of the view, like the hypothesis that modals have a uniform semantics. Given these circumstances, these data might seem like a justification for dispensing with the uniformity hypothesis. The present paper lays out the above problem in detail. Against the pessimistic view, I argue that the the contextualist account can in fact explain and predict these patterns while preserving the uniformity hypothesis. This requires adopting an amendment to the semantics of modals based on the work of Valentine Hacquard. Aside from maintaining the contextualist paradigm and preserving uniformity, the proposal also clarifies the role of context in the interpretation of modals. As it will turn out, the role of context ought to be circumscribed in its flavor-determining role for modals. (shrink)

Formal semantics is the study of linguistic meaning using precise mathematical characterizations; this chapter introduces formal semantics to scholars and students of natural-language processing. We give simple logical representations of English sentences, and show how meanings are composed in a grammar. We then consider two more advanced issues that arise in processing texts, anaphora and temporality, using Discourse Representation Theory. Finally we discuss the relationship between deep logic-based methods for semantic analysis and shallower distributional methods that have been used in (...) much recent NLP work, introducing some limitations of distributional methods, and hence motivating deeper or hybrid approaches. (shrink)

A long-standing tension in semantic theory concerns the reconciliation of positive gradable adjective (GA) ascriptions and comparative GA ascriptions. Vagueness-based ap- proaches derive the comparative from the positive, and face non-trivial challenges with incommensurability and non-GA comparatives. Classic degree-based approaches effectively derive the positive from the comparative, out of sync with the direction of evidence from morphology, and create some difficulties in accounting for GA scale-mates with differing thresholds (e.g., cold ∼ warm ∼ hot). We propose a new reconciliation that (...) capitalizes on recent proposals analyzing GAs as predicates of states. On our account, GAs lexically involve both a threshold property and a background state structure. Positive occurrences of GAs make use of the threshold property, while comparative occurrences make use of degrees representing elements of the background structure. Our approach preserves the virtues of classic degree-based approaches while offering a natural account of scale-mates, and without appeal to covert morphemes like POS or related devices. As we show, it is possible to inject our solution back into the classic degree-based approach, but we find reasons to prefer our states-based account. (shrink)

Noun phrases with overt determiners, such as <i>some apples</i> or <i>a quantity of milk</i>, differ from bare noun phrases like <i>apples</i> or <i>milk</i> in their contribution to aspectual composition. While this has been attributed to syntactic or algebraic properties of these noun phrases, such accounts have explanatory shortcomings. We suggest instead that the relevant property that distinguishes between the two classes of noun phrases derives from two modes of existential quantification, one of which holds the values of a variable fixed (...) throughout a quantificational context while the other allows them to vary. Inspired by Dynamic Plural Logic and Dependence Logic, we propose Plural Predicate Logic as an extension of Predicate Logic to formalize this difference. We suggest that temporal <i>for</i>-adverbials are sensitive to aspect because of the way they manipulate quantificational contexts, and that analogous manipulations occur with spatial <i>for</i>-adverbials, habituals, and the quantifier <i>all</i>. (shrink)

Donkey sentences have existential and universal readings, but they are not often perceived as ambiguous. We extend the pragmatic theory of nonmaximality in plural definites by Križ (2016) to explain how context disambiguates donkey sentences. We propose that the denotations of such sentences produce truth-value gaps — in certain scenarios the sentences are neither true nor false — and demonstrate that Križ’s pragmatic theory fills these gaps to generate the standard judgments of the literature. Building on Muskens’s (1996) Compositional Discourse (...) Representation Theory and on ideas from supervaluation semantics, the semantic analysis defines a general schema for quantification that delivers the required truth-value gaps. Given the independently motivated pragmatic theory of Križ 2016, we argue that mixed readings of donkey sentences require neither plural information states, contra Brasoveanu 2008, 2010, nor error states, contra Champollion 2016, nor singular donkey pronouns with plural referents, contra Krifka 1996, Yoon 1996. We also show that the pragmatic account improves over alternatives like Kanazawa 1994 that attribute the readings of donkey sentences to the monotonicity properties of the embedding quantifier. (shrink)

Tarski’s Convention T—presenting his notion of adequate definition of truth (sic)—contains two conditions: alpha and beta. Alpha requires that all instances of a certain T Schema be provable. Beta requires in effect the provability of ‘every truth is a sentence’. Beta formally recognizes the fact, repeatedly emphasized by Tarski, that sentences (devoid of free variable occurrences)—as opposed to pre-sentences (having free occurrences of variables)—exhaust the range of significance of is true. In Tarski’s preferred usage, it is part of the meaning (...) of true that attribution of being true to a given thing presupposes the thing is a sentence. Beta’s importance is further highlighted by the fact that alpha can be satisfied using the recursively definable concept of being satisfied by every infinite sequence, which Tarski explicitly rejects. Moreover, in Definition 23, the famous truth-definition, Tarski supplements “being satisfied by every infinite sequence” by adding the condition “being a sentence”. Even where truth is undefinable and treated by Tarski axiomatically, he adds as an explicit axiom a sentence to the effect that every truth is a sentence. Surprisingly, the sentence just before the presentation of Convention T seems to imply that alpha alone might be sufficient. Even more surprising is the sentence just after Convention T saying beta “is not essential”. Why include a condition if it is not essential? Tarski says nothing about this dissonance. Considering the broader context, the Polish original, the German translation from which the English was derived, and other sources, we attempt to determine what Tarski might have intended by the two troubling sentences which, as they stand, are contrary to the spirit, if not the letter, of several other passages in Tarski’s corpus. (shrink)

In this paper, I shall provide a novel response to the argument from context-sensitivity against truth-conditional semantics. It is often argued that the contextual influences on truth-conditions outstrip the resources of standard truth-conditional accounts, and so truth-conditional semantics rests on a mistake. The argument assumes that truth-conditional semantics is legitimate if and only if natural language sentences have truth-conditions. I shall argue that this assumption is mistaken. Truth-conditional analyses should be viewed as idealised approximations of the complexities of natural language (...) meaning. From this perspective, disparity between the scientific model and its real-world target is to be expected. I elaborate on what such an approach to semantics would look like. (shrink)

I summarize several of the main claims, arguments, and innovations in Stojnić's 2021 book. I then take issue with her foundational view, on which both the context of a conversation and the contents of context-sensitive expressions are wholly fixed by the history of a conversation together with grammatical rules.

The main goal of this paper is to show that there are many phenomena that pertain to the construction of truth-conditional compounds that follow characteristic patterns, and whose explanation requires appealing to knowledge structures organized in specific ways. We review a number of phenomena, ranging from non-homogenous modification and privative modification to polysemy and co-predication that indicate that knowledge structures do play a role in obtaining truth-conditions. After that, we show that several extant accounts that invoke rich lexical meanings to (...) explain such phenomena face problems related to inflexibility and lack of predictive power. We review different ways in which one might react to such problems as regards lexical meanings: go richer, go moderately richer, go thinner, and go moderately thinner. On the face of it, it looks like moderate positions are unstable, given the apparent lack of a clear cutoff point between the semantic and the conceptual, but also that a very thin view and a very rich view may turn out to be indistinguishable in the long run. As far as we can see, the most pressing open questions concern this last issue: can there be a principled semantic/world knowledge distinction? Where could it be drawn: at some upper level (e.g. enriched qualia structures) or at some basic level (e.g. constraints)? How do parsimony considerations affect these two different approaches? A thin meanings approach postulates intermediate representations whose role is not clear in the interpretive process, while a rich meanings approach to lexical meaning seems to duplicate representations: the same representations that are stored in the lexicon would form part of conceptual representations. Both types of parsimony problems would be solved by assuming a direct relation between word forms and (parts of) conceptual or world knowledge, leading to a view that has been attributed to Chomsky (e.g. by Katz 1980) in which there is just syntax and encyclopedic knowledge. (shrink)

We give a theory of epistemic modals in the framework of possibility semantics and axiomatize the corresponding logic, arguing that it aptly characterizes the ways in which reasoning with epistemic modals does, and does not, diverge from classical modal logic.

Lots of things are usefully modelled in science as dynamical systems: growing populations, flocking birds, engineering apparatus, cognitive agents, distant galaxies, Turing machines, neural networks. We argue that relevant logic is ideal for reasoning about dynamical systems, including interactions with the system through perturbations. Thus, dynamical systems provide a new applied interpretation of the abstract Routley-Meyer semantics for relevant logic: the worlds in the model are the states of the system, while the (in)famous ternary relation is a combination of perturbation (...) and evolution in the system. Conversely, the logic of the relevant conditional provides sound and complete laws of dynamical systems. (shrink)

Truthmaker semantics is a recent development in formal and philosophical semantics, with similar motivation and scope to possible worlds semantics. The technical background is rather different, however, and results in a more fine-grained hyperintensional notion of content, allowing us to distinguish between classically equivalent propositions. After briefly introducing the main ideas, this entry will describe the technical apparatus of state spaces and the central notions of content and partial content. It will then outline applications of truthmaker semantics in language, logic, (...) and other areas of philosophy. (shrink)

Sentences with impersonal pronouns, like 'You do it like this', seem to make both statistical and prescriptive claims, that a certain way of behaving is common and that it is prescriptively good. We argue that these kinds of sentences are closely related to another kind of sentence, namely, indefinite singular generics, like 'A person does it like this'. We propose that there is a single underlying mechanism that allows both kinds of sentences to express mixed statistical/prescriptive readings. We then provide (...) a compositional semantic analysis of these sentences and explain how, together with this single underlying mechanism, it accounts for this phenomenon. (shrink)

It is shown that one common formulation of Stalnaker's semantics for conditionals is incomplete: it has no sound and (strongly) complete proof system. At first, this seems to conflict with well-known completeness results for this semantics (e.g., Stalnaker and Thomason 1967; Stalnaker 1970 and Lewis 1973, ch. 6). As it turns out, it does not: these completeness results rely on another closely-related formulation of the semantics that is provably complete. Specifically, the difference comes down to how the Limit Assumption is (...) stated. I close with some remarks about what this means for the logic of conditionals. (shrink)

In the standard theory of deontic modals, ‘ought’ is understood as expressing a propositional operator. However, this view has been called into question by Almotahari and Rabern’s puzzle about deontic ‘ought’, according to which the ethical principle that one ought to be wronged by another person rather than wrong them is intuitively coherent but the standard theory makes it incoherent. In this paper, I take up Almotahari and Rabern’s challenge and offer a refinement of the standard theory to handle the (...) puzzle. I propose that ‘ought’ is evaluated relative to contextual parameters (e.g., Kratzer’s conversational backgrounds, Finlay and Snedegar’s alternative sets) and those contextual parameters are sensitive to agents as well as possible worlds. (shrink)

Any adequate semantics of generic sentences (e.g., “Philosophers evaluate arguments”) must accommodate both what we call the positive data and the negative data. The positive data consists of observations about what felicitous interpretations of generic sentences are available. Conversely, the negative data consists of observations about which interpretations of generic sentences are unavailable. Nguyen argues that only his pragmatic neo-Gricean account and Sterken’s indexical account can accommodate the positive data. Lee and Nguyen have advanced the debate by arguing that the (...) negative data is a problem for both Nguyen’s and Sterken’s accounts; these two accounts seem to incorrectly predict that generics have felicitous interpretations that they, in fact, fail to have. In this paper, we advance this debate—and, more generally, the task of developing an adequate formal semantics of generics—by arguing that a neglected class of theories are compatible with both the positive data and the negative data. Specifically, we argue that treating the generic operator GEN as a relative gradable expression with a positive, upper- and lower- bounded scale helps accommodate the positive data and the negative data. While developing this view, we show how several previously developed semantics of generics may systematically accommodate both sets of data. One broad contribution of this paper is to show that, while they generate important desiderata, the positive and negative data cannot determine a unique semantics for generics. A further contribution of this paper is to highlight previously unnoted ways in which degree semantics may inform semantic theories of generic meaning. (shrink)

I explore constructions which contain an embedded disjunction ⌜p or q⌝which is interpreted as (p∨q) ∧♢p∧♢q, where ♢is a possibility modal whose flavor is epistemic, circumstantial, or deontic. I argue that no extant theory can account for these interpretations. I propose that the best way to do so is with a direct theory on which ⌜p or q⌝ simply means (p∨q) ∧♢p∧♢q. In addition to accounting for the novel cases I discuss, this theory explains both wide- and narrow-scope free choice (...) inferences, in a similar way as the theories of Zimmermann (2000); Geurts (2005); Goldstein (2019). It also accounts for recent observations about the relation between disjunction and possibility from Degano et al. 2025; Feinmann 2023. (shrink)

Research in formal theoretical semantics has recently expanded its scope to include gestural communication, focusing in particular on gestures that contribute to the content of an accompanying utterance, e.g., size gestures (LARGE, WIDE), pointing gestures, and gestures that depict objects (TELESCOPE) or actions (SLAP). At the same time, fruitful inquiries at the intersection of primatology and linguistics have given rise to the hypothesis that human and non-human great apes share a common set of directive (=imperative) gestures. Directive gestures such as (...) STOP or COME-CLOSER, pose non-trivial issues for a semantic analysis: we inherit the challenges that pertain to the analysis of imperative utterances (Come closer!), while adding a further challenge that stems from the underspecified mapping between a directive body movement and its potential counterparts in human language. We begin by outlining the problem and surveying the nascent state-of-the-art with regards to a formal semantics of directive gestures. Particular attention is given to the multifunctionality of directive gestures, which typically have different effects in different contexts; for example, a non-human ape gesture may communicate "Stop that" in some contexts and "Move away" in others, with similar patterns found in humans. We show that this multifunctionality can be derived from a single, rich abstract lexical entry, "Not…!", a candidate for a universal building block of meaning, shared by human and non-human great apes. "Not…!", which incorporates negation/rejection, temporal reference and presuppositionality is more explanatory in comparison to a minimal alternative. This chapter lays out the hypothesis space, addressing the foundational question of how to explain attested gestural overlap between human and non-human great apes. We conclude the chapter by reviewing potential expansions of the analysis to the pragmatic gestures of humans, which are thus placed on the primate gestural meaning continuum and connected to the directive gestures we share with our non-human relatives in the great ape family. (shrink)

Hobbs (2010) introduced ‘clause-internal coherence’ (CIC) to describe inferences in, e.g., ‘A jogger was hit by a car,’ where the jogging is understood to have led to the car-hitting. Cohen & Kehler (2021) argue that well-known pragmatic tools cannot account for CIC, motivating an enrichment account familiar from discourse coherence research. An outstanding question is how to compositionally derive CIC from coherence relations. This paper takes strides in answering this question. It first provides experimental support for the existence of CIC (...) via offline evidence that attributive (non-)deverbal adjectives can trigger the same causal inferences within clauses that their predicative counterparts can trigger across clauses, albeit more weakly. To explain the experimental results, we use tools in Segmented Discourse Representation Theory (SDRT), which allows us to show that causal inferences can be derived in various ways, depending on whether deverbal adjectives are used attributively or predicatively. If the former, they are presupposition triggers and the coherence relations Elaboration/Continuation compete with Background; if the latter, Explanation/Result compete with Background. These different competitions -- cashed out in terms of interaction between default axioms -- correlate with the difference in the relative salience of the causal inferences. (shrink)

A semantic universal, which we here dub the Veridical Uniformity Universal, has recently been argued to hold of responsive verbs (those that take both declarative and interrogative complements). This paper offers a preliminary explanation of this universal: verbs satisfying it are easier to learn than those that do not. This claim is supported by a computational experiment using artificial neural networks, mirroring a recent proposal for explaining semantic universals of quantifiers. This preliminary study opens up many avenues for future work (...) on explaining semantic universals more generally, which are discussed in the conclusion. (shrink)

One of the great successes of the application of generalized quantifiers to natural language has been the ability to formulate robust semantic universals. When such a universal is attested, the question arises as to the source of the universal. In this paper, we explore the hypothesis that many semantic universals arise because expressions satisfying the universal are easier to learn than those that do not. While the idea that learnability explains universals is not new, explicit accounts of learning that can (...) make good on this hypothesis are few and far between. We propose a model of learning — back-propagation through a recurrent neural network — which can make good on this promise. In particular, we discuss the universals of monotonicity, quantity, and conservativity and perform computational experiments of training such a network to learn to verify quantifiers. Our results are able to explain monotonicity and quantity quite well. We suggest that conservativity may have a different source than the other universals. (shrink)

According to the DP hypothesis, the merger of a determiner and a noun yields a determiner phrase (DP) rather than a noun phrase (nP). Focusing on Spanish, I defend the DP hypothesis but reject the notion that argumenthood is contingent upon a DP layer. Instead, I maintain that arguments can be as small as nP provided that they are c-commanded by a verb or a preposition, in which case the variables that they introduce are bound through a last-resort operation of (...) existential closure. I then consider the ways in which functional projections above nP shape the denotation of nominal arguments and adopt Borer’s (2005) view that a division phrase (DivP) is responsible for countability. Nonplural indefinite expressions can either have mass or singular readings depending on the determiner ("mucho tomate" 'much tomato' versus "un tomate" 'a tomato'), whereas nonplural definite expressions can have both mass and singular readings no matter the determiner ("el/este/mi tomate" 'the/this/my tomato'). I attribute the systematic ambiguity of nonplural definite expressions to the absence of DivP in their structure and the maximality operator that is a component of definiteness. -/- Throughout the thesis, I explore the formal representation of φ-features and how their semantic behaviour is conditioned by their syntactic position. I propose that gender features have consequences for interpretation when they are hosted by Panagiotidis’s (2019) animacy phrase (AnimP) but not by nP and extend this argument to number features on DivP versus nP, thereby eliminating the need for "interpretable" and "uninterpretable" versions of the same feature. As for pronouns, it is not immediately apparent where they are generated in Spanish because they are not mutually exclusive with the definite article ("nosotros los cocineros" 'we the chefs'). After upholding Höhn’s (2016, 2017) claim that pronouns originate in a dedicated person phrase (πP) in languages that use the definite article in pronoun-noun constructions, I address the issue of the third-person gap ("ellos los cocineros" 'they the chefs') and argue that third-person pronouns are forms that realize π, D, Div, Anim, and n, a configuration that prevents other material from occupying these same heads. (shrink)

A hyperintensional epistemic logic would take the contents which can be known or believed as more fine-grained than sets of possible worlds. I consider one objection to the idea: Williamson’s Objection from Overfitting. I propose a hyperintensional account of propositions as sets of worlds enriched with topics: what those propositions, and so the attitudes having them as contents, are about. I show that the account captures the conditions under which sentences express the same content; that it can be pervasively applied (...) in formal and mainstream epistemology; and that it is left unscathed by the objection. (shrink)

This chapter develops a semantic theory for maps and situates it within the broader geography of meaning and semiotic significance. The discussion focuses on three central aspects of map semantics: the use of space, line marking, and linguistic tags. It is argued that the treatment of space in maps must be based on geometrical projection from a viewpoint rather than the traditional analysis in terms of spatial isomorphism. The chapter then shows how to integrate the projection-based semantics of maps and (...) the symbolic semantics of markers and tags, within the framework of possible-world semantics. The resulting account addresses issues of accuracy, viewpoint, orientation, and exhaustivity. (shrink)

What does ‘Smith knows that it might be raining’ mean? Expressivism here faces a challenge, as its basic forms entail a pernicious type of transparency, according to which ‘Smith knows that it might be raining’ is equivalent to ‘it is consistent with everything that Smith knows that it is raining’ or ‘Smith doesn’t know that it isn’t raining’. Pernicious transparency has direct counterexamples and undermines vanilla principles of epistemic logic, such as that knowledge entails true belief and that something can (...) be true without one knowing it might be. I re-frame the challenge in precise terms and propose a novel expressivist formal semantics that meets it by exploiting (i) the topic-sensitivity and fragmentation of knowledge and belief states and (ii) the apparent context-sensitivity of epistemic modality. The resulting form of assertibility semantics advances the state of the art for state-based bilateral semantics by combining attitude reports with context-sensitive modal claims, while evading various objectionable features. In appendices, I compare the proposed system to Beddor and Goldstein’s ‘safety semantics’ and discuss its analysis of a modal Gettier case due to Moss. (shrink)

When do two sentences say the same thing, that is, express the same content? We defend two-component (2C) semantics: the view that propositional contents comprise (at least) two irreducibly distinct constituents: (1) truth-conditions and (2) subject-matter. We contrast 2C with one-component (1C) semantics, focusing on the view that subject-matter is reducible to truth-conditions. We identify exponents of this view and argue in favor of 2C. An appendix proposes a general formal template for propositional 2C semantics.

The term 'covert mixed quotation' describes cases in which linguistic material is interpreted in the manner of mixed quotation — that is, used in addition to being mentioned — despite the superficial absence of any commonly recognized conventional devices indicating quotation. After developing a novel theory of mixed quotation, I show that positing covert mixed quotation allows us to give simple and unified treatments of a number of puzzling semantic phenomena, including the projective behavior of conventional implicature items embedded in (...) indirect speech reports and propositional attitude ascriptions, so-called 'c-monsters,' metalinguistic negation, metalinguistic negotiation, and 'in a sense' constructions. (shrink)

The similarity approach to conditionals (Stalnaker 1968; Lewis 1973) predicts Reciprocity to be valid: whenever A > B, B > A and A > C are true, B > C is true too (where A > B denotes if A would B). We ran an experiment to test the validity of this rule. Strikingly, half of our participants judged the rule invalid, i.e. judged in at least one scenario that it does not preserve truth. Our data also challenge Kratzer’s (2012) (...) and Fine’s (2012) semantics of conditionals, but we show that McHugh’s (2022; 2023) aboutness approach can account for our data. (shrink)

Generics have historically proven difficult to analyse using the tools of formal semantics. In this paper, I argue that an influential theory of the meaning of generics due to Sarah-Jane Leslie, the Psychological Theory of Generics, is best interpreted not as a theory of their meaning, but as a theory of the psychological heuristics that we use to judge whether or not generics are true. I argue that Leslie’s methodology is not well-suited to producing a theory of the meaning of (...) generics, since it takes speakers’ judgments at face value and ignores the non-semantic factors that might affect these judgments. Leslie’s theory therefore overfits the data of our linguistic intuitions. I present a reconceptualised version of the Psychological Theory of Generics as a theory of how heuristics affect our judgements of the truth values of generics and discuss the application of this reconceptualised theory to some of the puzzles posed by generics, including their apparent content-sensitivity, their inferential asymmetry and their association with stereotyping and prejudice. (shrink)

This paper highlights a small selection of cases where crosslinguistic insights have been important to big questions in the theory of semantics and the syntax/semantics interface. The selection includes (i) the role and representation of Speaker and Addressee in the grammar; (ii) mismatches between form and interpretation motivating high-placed silent operators for functional elements; and (iii) the explanation of semantic universals, including universals pertaining to inventories, in terms of learnability and the trade-off between informativeness and simplicity.

Given any set _E_ of expressions freely generated from a set of atoms by syntactic operations, there exist trivially compositional functions on _E_ (to wit, the injective and the constant functions), but also plenty of non-trivially compositional functions. Here we show that within the space of non-injective functions (and so _a fortiori_ within the space of non-injective and non-constant functions), compositional functions are not sufficiently abundant in order to generate the consequence relation of every propositional logic. Logical consequence relations thus (...) impose substantive constraints on the existence of compositional functions when coupled with the condition of non-injectivity (though not without it). We ask how the _apriori_ exclusion of injective functions from the search space might be justified, and we discuss the prospects of claims to the effect that any function can be “encoded” in a compositional one. (shrink)

I investigate whether Wittgenstein’s “weakly exclusive” Tractarian semantics (as reconstructed by Rogers and Wehmeier) is compositional. In both Tarskian and Wittgensteinian semantics, one has the choice of either working exclusively with total variable assignments or allowing partial assignments; the choice has no bearing on the compositionality of Tarskian semantics, but turns out to make a difference in the Wittgensteinian case. Some philosophical ramifications of this observation are discussed.

_Framing effects_ concern the having of different attitudes towards logically or necessarily equivalent contents. Framing is of crucial importance for cognitive science, behavioral economics, decision theory, and the social sciences at large. We model a typical kind of framing, grounded in (i) the structural distinction between beliefs activated in working memory and beliefs left inactive in long term memory, and (ii) the topic- or subject matter-sensitivity of belief: a feature of propositional attitudes which is attracting growing research attention. We introduce (...) a class of models featuring (i) and (ii) to represent, and reason about, agents whose belief states can be subject to framing effects. We axiomatize a logic which we prove to be sound and complete with respect to the class. (shrink)

We introduce an expected-value theory of linguistic modality that makes reference to expected utility and a likelihood-based confirmation measure for deontics and epistemics, respectively. The account is a probabilistic semantics for deontics and epistemics, yet it proposes that deontics and epistemics share a common core modal semantics, as in traditional possible-worlds analysis of modality. We argue that this account is not only theoretically advantageous, but also has far-reaching empirical consequences. In particular, we predict modal versions of reasoning fallacies from the (...) heuristics and biases literature. Additionally, we derive the modal semantics in an entirely transparent manner, as it is based on the compositional semantics of Korean modal expressions that are morphosyntactically decomposed into a conditional and an evaluative predicate. (shrink)