This book takes concepts developed by researchers in theoretical computer science and adapts and applies them to the study of natural language meaning. Summarizing over a decade of research, Chris Barker and Chung-chieh Shan put forward the Continuation Hypothesis: that the meaning of a natural language expression can depend on its own continuation.

Using a vague predicate can make commitments about the appropriate use of that predicate in the remaining part of the discourse. For instance, if I assert that some particular pig is fat, I am committed to judging any fatter pig to be fat as well. We can model this update effect by recognizing that truth depends both on the state of the world and on the state of the discourse: the truth conditions of ‘This pig is fat’ rule out evaluation (...) points for which the pig in question in world w is thinner than the cutoff for fatness in the discourse d. Then disagreements about taste are disagreements about the discourse. Unlike disagreements about the world, disagreements about the discourse can be faultless, given that none of the discourse participants has privileged authority to make pronouncements about conventions for appropriate use of a predicate. Thus on the dynamic view developed here, whether or not a dispute about taste turns out to be faultless depends in part on predictable features of the previous discourse. On this account, faultless disagreement involving predicates of personal taste does not force relativizing truth to a judge or assessor. (shrink)

This book examines the hypothesis of "direct compositionality", which requires that semantic interpretation proceed in tandem with syntactic combination. Although associated with the dominant view in formal semantics of the 1970s and 1980s, the feasibility of direct compositionality remained unsettled, and more recently the discussion as to whether or not this view can be maintained has receded. The syntax-semantics interaction is now often seen as a process in which the syntax builds representations which, at the abstract level of logical form, (...) are sent for interpretation to the semantics component of the language faculty. In the first extended discussion of the hypothesis of direct compositionality for twenty years, this book considers whether its abandonment might have been premature and whether in fact direct compositionality is not after all a simpler and more effective conception of the grammar than the conventional account of the syntax-semantics interface in generative grammar. It contains contributions from both sides of the debate, locates the debate in the setting of a variety of formal theories, and draws on examples from a range of languages and a range of empirical phenomena. (shrink)

This paper proposes that the meanings of some natural language expressions should be thought of as functions on their own continuations. Continuations are a well-established analytic tool in the theory of programming language semantics; in brief, a continuation is the entire default future of a computation. I show how a continuation-based grammar can unify several aspects of natural language quantification in a new way: merely stating the truth conditions for quantificational expressions in terms of continuations automatically accounts for scope displacement (...) and scope ambiguity. To prove this claim, I exhibit a simple finite context-free grammar with a strictly compositional semantics in which quantificational NPs are interpreted in situ but take semantic scope over larger constituents. There is no Quantifier Raising (nor any use of a level of Logical Form distinct from overt syntax), no Cooper Storage (or similar mechanisms used in many recent HPSG, Categorial, or Type-logical treatments), and no need for type-shifting (as in Hendriks' Flexible Types account). Continuations also provide a natural account of generalized coordination that does not require either type-shifting or type polymorphism. Compositionality issues are discussed in some detail. (shrink)

I propose the first strictly compositional semantic account of same. New data, including especially NP-internal uses such as two men with the same name, suggests that same in its basic use is a quantificational element taking scope over nominals. Given type-lifting as a generally available mechanism, I show that this follows naturally from the fact that same is an adjective. Independently-motivated assumptions extend the analysis to standard examples such as Anna and Bill read the same book via a mechanism I (...) call PARASITIC SCOPE, in which the scope of same depends on the scope of some other scopetaking element in the sentence. Although I will initially discuss the analysis in terms of a familiar Quantifier Raising framework, I go on to implement the analysis within an innovative continuation-based Type-Logical Grammar. The empirical payoff for dealing in continuations is that a simple generalization of the basic analysis gives the first ever formal account of cases in which same distributes over objects other than NP denotations, as in the relevant interpretation of John hit and killed the same man. (shrink)

What is the communicative value of negative polarity? That is, why do so many languages maintain a stock of special indefinites that occur only in a proper subset of the contexts in which ordinary indefinites can appear? Previous answers include: marking the validity of downward inferences; marking the invalidity of veridical inferences; or triggering strengthening implications. My starting point for exploring a new answer is the fact that an NPI must always take narrow scope with respect to its licensing context. (...) In contrast, ordinary indefinites are notorious for taking wide scope. So whatever other functions NPIs may have, they at least serve as an utterly reliable signal that an indefinite is taking narrow scope. As also proposed in recent work of Kusumoto and Tancredi, I will show that NPIs are only licensed in contexts in which the wide scope construal of an indefinite fails to entail the narrow scope. In other words, weak NPIs occur only in contexts in which taking narrow scope matters for interpretation. Thus one part of the explanation for the ubiquity and robust stability of negative polarity is that it signals scope relations. (shrink)

We present a general theory of scope and binding in which both crossover and superiority violations are ruled out by one key assumption: that natural language expressions are normally evaluated (processed) from left to right. Our theory is an extension of Shan’s (2002) account of multiple-wh questions, combining continuations (Barker, 2002) and dynamic type-shifting. Like other continuation-based analyses, but unlike most other treatments of crossover or superiority, our analysis is directly compositional (in the sense of, e.g., Jacobson, 1999). In particular, (...) it does not postulate a level of Logical Form or any other representation distinct from surface syntax. One advantage of using continuations is that they are the standard tool for modeling order-of-evaluation in programming languages. This provides us with a natural and independently motivated characterization of what it means to evaluate expressions from left to right. We give a combinatory categorial grammar that models the syntax and the semantics of quantifier scope and wh-question formation. It allows quantificational binding but not crossover, in-situ wh but not superiority violations. In addition, the analysis automatically accounts for a variety of sentence types involving binding in the presence of pied piping, including reconstruction cases such as Whose criticism of hisi mother did each personi resent? (shrink)

Why ever assert clarity? If It is clear that p is true, then saying so should be at best superfluous. Barker and Taranto (2003) and Taranto (2006) suggest that asserting clarity reveals information about the beliefs of the discourse participants, specifically, that they both believe that p . However, mutual belief is not sufficient to guarantee clarity ( It is clear that God exists ). I propose instead that It is clear that p means instead (roughly) 'the publicly available evidence (...) justifies concluding that p '. Then what asserting clarity reveals is information concerning the prevailing epistemic standard that determines whether a body of evidence is sufficient to justify a claim. If so, the semantics of clarity constitutes a grammatical window into the discourse dynamics of inference and skepticism. (shrink)

What do terms such as the committee, the league, and the group of women denote? Pre-theoretically, group terms have a dual personality. On the one hand, the committee corresponds to an entity as ideosyncratic in its properties as any other object; for instance, two otherwise identical committees can vary with respect to the purpose for which they were formed. Call this aspect the group-as-individual. On the other hand, the identity of a group is at least partially determined by the properties (...) of its members; for instance, a committee will be a committee of women just in case each of its members is a woman. Call this aspect the group-as-set. Elaborating on suggestions in Link (1984) and Lasersohn (1988), I propose that group terms in English denote atomic individuals, that is, entities lacking internal structure. In particular, it is not possible to determine the membership of a group by examining the denotation of a group term. The proposed account correctly predicts that group terms systematically behave differently semantically (as well as syntactically) from plurals such as the men and conjunctions such as John and Bill. Thus the atomic analysis advocated here stands in sharp contrast to previous proposals, including Bennet (1975), Link (1984), and Landman (1989), in which group terms are considered of a piece semantically with plurals and conjunctions. Additional arguments come from the use of names of groups as rigid designators, from the parallel between group nouns and measure nouns, and from the distribution of group terms across two dialects of English. (shrink)

This paper analyzes sluicing as anaphora to an anti-constituent (a continuation), that is, to the semantic remnant of a clause from which a subconstituent has been removed. For instance, in Mary said that [John saw someone yesterday], but she didn’t say who, the antecedent clause is John saw someone yesterday, the subconstituent targeted for removal is someone, and the ellipsis site following who is anaphoric to the scope remnant John saw ___ yesterday. I provide a compositional syntax and semantics on (...) which the relationship between the targeted subconstituent and the rest of the antecedent clause is one of scopability, not movement or binding. This correctly predicts that sluicing should be sensitive to scope islands, but not to syntactic islands. Unlike the currently dominant approaches to sluicing, there is no need to posit syntactic structure internal to the ellipsis site, nor is there any need for a semantic mutual-entailment requirement. Nevertheless, the fragment handles phenomena usually taken to suggest a close syntactic correspondence between the antecedent and the sluice, including case matching, voice matching, and verbal argument structure matching. In addition, the analysis handles phenomena exhibiting antecedent/sluice mismatches, including examples such as John remembers meeting someone, but he doesn’t remember who, , and especially so-called sprouting examples such as John left, but I don’t know when, in which there is no overt subconstituent to target for removal. In Sect. 5, I show how the analysis accounts for Andrews Amalgams such as Sally ate [I don’t know what] today, in which the antecedent surrounds the sluiced clause. Finally, in Sect. 6, I propose a new semantic constraint on sluicing: the Answer Ban, which says that the antecedent clause must not resolve, or even partially resolve, the issue raised by the sluiced interrogative. (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)

Using the programming-language concept of continuations, we propose a new, multimodal analysis of quantification in Type Logical Grammar. Our approach provides a geometric view of in-situ quantification in terms of graphs, and motivates the limited use of empty antecedents in derivations. Just as continuations are the tool of choice for reasoning about evaluation order and side effects in programming languages, our system provides a principled, type-logical way to model evaluation order and side effects in natural language. We illustrate with an (...) improved account of quantificational binding, weak crossover, wh-questions, superiority, and polarity licensing. (shrink)

This article pays close attention to Michel Foucault's theory that political regimes are enlightened through courageous free speech. A Foucaultian enlightenment occurs not when philosophical reason completely replaces superstition and enthusiasm in the public sphere, but instead when the parrhesiast partially organizes competing claims to know and to speak the truth. While much of the recent scholarly literature on Foucault’s later lectures emphasizes the political importance of the parrhesiast, less attention has been paid to the overlap and/or incompatibility between parrhesia (...) and the other modes of truth-telling. Below, I explain Foucault’s analysis of the basic modes of philosophical truth-telling: prophesy, philosophy, teaching, and parrhesia. I provide examples of speakers working within these modes in the ancient and modern world. I explain the overlap and tension between these modes, and I analyze Foucault’s partial organization of them through the image of the parrhesiast. I briefly compare Foucault’s position to the agonistic democratic theory of Chantal Mouffe and distinguish Foucault’s view from consensus-based views of public reason. Finally, I provide practical and theoretical examples of parrhesiastic activity in the contemporary world. (shrink)

An expression’s presuppositions must be satisfied by its local context, that is, by the utterance context updated with the content of expressions that have already been evaluated. Traditional dynamic approaches track local context by remaking clause denotations into context update functions. This requires crafting for each semantic operator an update recipe that is not fully determined by its truth conditions, failing to capture how local contexts depend only on truth conditions and order of evaluation. In other theories, computing local contexts (...) involves reasoning about the set of all possible grammatical syntactic completions, which relocates local contexts outside of the semantics. I show how to build local contexts systematically and uniformly as part of the composition of ordinary truth conditions. The result is a minimalist dynamic semantics in which the only thing that is dynamically tracked is the semantic content of what has already been said. (shrink)

Brasoveanu (Linguist Philos 34:93–168, 2011) argues that “different” exhibits what he calls association with distributivity: a distributive operator such as “each” creates a two-part context that propagates through the compositional semantics in a way that can be accessed by a subordinate “different”. We show that Brasoveanu’s analysis systematically undergenerates, failing to provide interpretations of sentences such as “Every1 boy claimed every girl read a different1 poem”, in which “different” can associate with a non-local distributive operator. We provide a generalized version (...) of association with distributivity, implemented using de Groote’s (in: Proceedings of semantics and linguistic theory XVI, 2006) continuation-based dynamic semantics. We compare our analysis with the one in Brasoveanu (2011), drawing conclusions about computational tractability, scope of indefinites, and whether it is possible or even desirable to arrive at a unified analysis of internal and external readings of “different”. (shrink)

Lambek elegantly characterized part of natural language. As is well-known, his substructural logic L, and its non-associative version NL, handle basic function/argument composition well, but not scope taking and syntactic displacement—at least, not in their full generality. In previous work, I propose \, which is NL supplemented with a single structural inference rule.ion closely resembles the traditional linguistic rule of quantifier raising, and characterizes both semantic scope taking and syntactic displacement. Due to the unconventional form of the abstraction inference, there (...) has been some doubt that \ should count at a legitimate substructural logic. This paper argues that \ is perfectly well-behaved. In particular, it enjoys cut elimination and an interpolation result. In addition, perhaps surprisingly, it is decidable. Finally, I prove that it is sound and complete with respect to the usual class of relational frames. (shrink)

Let us suppose that thematic roles, or something very much like them, are needed to describe lexical and semantic patterns in the behavior of verbal predicates. But what about nouns? Is there evidence independent of verbal constructions motivating a system of nominal thematic relations? We suggest that the general problem of argument selection does in fact motivate a set of quintessentially nominal thematic proto-roles which we call Proto- Part and Proto-Whole. These nominal proto-roles are parallel to but distinct from the (...) verbal proto-roles of Proto-Agent and Proto-Patient proposed by Dowty (1991) to account for argument selection in verbal predicates. The resulting theory of nominal argument selection is properly semantic, that is, it distinguishes between argument positions purely on the basis of the semantic entailments of the predicates involved. Furthermore, it is non-dynamic, that is, it describes static patterns of lexicalization without hypothesizing any productive grammatical process that maps semantic arguments to syntactic arguments during the derivation of a sentence. (shrink)

Lambek elegantly characterized part of natural language. As is well-known, his substructural logic L, and its non-associative version NL, handle basic function/argument composition well, but not scope taking and syntactic displacement—at least, not in their full generality. In previous work, I propose \, which is NL supplemented with a single structural inference rule.ion closely resembles the traditional linguistic rule of quantifier raising, and characterizes both semantic scope taking and syntactic displacement. Due to the unconventional form of the abstraction inference, there (...) has been some doubt that \ should count at a legitimate substructural logic. This paper argues that \ is perfectly well-behaved. In particular, it enjoys cut elimination and an interpolation result. In addition, perhaps surprisingly, it is decidable. Finally, I prove that it is sound and complete with respect to the usual class of relational frames. (shrink)

SUMMARYThis paper examines the formal filters of the public's political will defended by JS Mill as consistent with the best form of representative government. Holding that institutions must adjust to democratic society, and that democratic society must be improved to achieve wise rule, Mill rejects secret ballots and electoral pledges, and advocates a constitutional council and graduated enfranchisement. He also recommends but does not require the indirect election of the President and a unicameral legislature. Mill's historically sensitive approach puts pressure (...) on interpreters to be sensitive to their own political and social context when applying Mill's ideas. In particular, obviously undemocratic measures such as plural voting should be adjusted to reflect Mill's view that the ratio between legitimacy and competence is constantly changing. The continual readjustment between the powers of masses and elites is the way that Mill's Considerations on Representative Government manage to avoid the now-traditional charge of expertocracy. (shrink)