There is a prominent line of work in natural language semantics, rooted in the work of Hamblin, in which the meaning of a sentence is not taken to be a single proposition, but rather a set of propositions—a set of alternatives. This allows for a more fine-grained view on meaning, which has led to improved analyses of a wide range of linguistic phenomena. However, this approach also faces a number of problems. We focus here on two of these, in our (...) view the most fundamental ones. The first has to do with how meanings are composed, i.e., with the type-theoretic operations of function application and abstraction; the second has to do with how meanings are compared, i.e., the notion of entailment. Our aim is to reconcile what we take to be the essence of Hamblin’s proposal with the more orthodox type-theoretic framework rooted in the work of Montague in such a way that both the explanatory utility of the former and the solid formal foundations of the latter are preserved. Our proposal builds on insights from recent work on inquisitive semantics, and it also contributes to the further development of this framework by specifying how the inquisitive meaning of a sentence may be built up compositionally. (shrink)

Situation semantics was developed as an alternative to possible worlds semantics. In situation semantics, linguistic expressions are evaluated with respect to partial, rather than complete, worlds. There is no consensus about what situations are, just as there is no consensus about what possible worlds or events are. According to some, situations are structured entities consisting of relations and individuals standing in those relations. According to others, situations are particulars. In spite of unresolved foundational issues, the partiality provided by situation semantics (...) has led to some genuinely new approaches to a variety of phenomena in natural language semantics. In the way of illustration, this article includes relatively detailed overviews of a few selected areas where situation semantics has been successful: implicit quantifier domain restrictions, donkey pronouns, and exhaustive interpretations. It moreover addresses the question of how Davidsonian event semantics can be embedded in a semantics based on situations. Other areas where a situation semantics perspective has led to progress include attitude ascriptions, questions, tense, aspect, nominalizations, implicit arguments, point of view, counterfactual conditionals, and discourse relations. (shrink)

A free logical analysis of singular terms couched in terms of the semantic theory of Keenan and Faltz is shown to avoid problems with both Frege's and Russell's treatments. At its heart is the proposal of Keenan and Faltz to reverse the usual mode-theoretic conception of individuals and properties, taking the latter as primitive and the former as derived therefrom. A simple extension of the notion 'property' is then shown to enable a parallel treatment of definite generics.

Standard first-order logic plus quantifiers of all finite orders ("SFOLω") faces four well-known difficulties when used to characterize the behavior of certain English quantifier phrases. All four difficulties seem to stem from the typed structure of SFOLω models. The typed structure of SFOLω models is in turn a product of an asymmetry between the meaning of names and the meaning of predicates, the element-set asymmetry. In this paper we examine a class of models in which this asymmetry of meaning is (...) removed. The models of this class permit definitions of the quantifiers which allow a desirable flexibility in fixing the domain of quantification. Certain SFOLω type restrictions are thereby avoided. The resulting models of English validate all of the standard first-order logical truths and are free of the four deficiencies of SFOLω models. (shrink)

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

Formal semantic analyses often take words to be minimal building blocks for the purposes of compositionality. But various recent theories of morphology and syntax have converged on the view that there is no demarcation line corresponding to the word level. The same conclusion has emerged from the compositional semantics of superlatives. In the spirit of extending compositionality below the word level, this paper explores how a small set of particles (Japanese KA and MO, Chinese DOU, and Hungarian VALA/VAGY, MIND, and (...) IS) form quantifier words and serve as connectives, additive and scalar particles, question markers, and existential verbs. The main question is whether the meanings of these particles across the varied environments are highly regular, or they are lexicalized with a variety of different meanings that bear a family resemblance. This paper does not reach definitive conclusions, but it raises analytical possibilities using Boolean semantics and the semantics of alternatives. It also draws attention to systematic similarities and some differences between MO and DOU that have not been studied in the literature. (shrink)

The traditional scope theory of intensionality (STI) (see Russell 1905; Montague 1973; Ladusaw 1977; Ogihara 1992, 1996; Stowell 1993) is simple, elegant, and, for the most part, empirically adequate. However, a few quite troubling counterexamples to this theory have lead researchers to propose alternatives, such as positing null situation pronouns (Percus 2000) or actuality operators (Kamp 1971; Cresswell 1990) in the syntax of natural language. These innovative theories do correct the undergeneration of the original scope theory, but at a cost: (...) the situation pronoun and operator theories overgenerate, as argued extensively by Percus (2000) and Keshet (2008). This paper presents new data that supports the STI over other analyses, such as structures where DPs lose their de re readings in positions where syntactic movement is blocked. These data point the way to a new theory of intensionality. This new theory, called split intensionality, is a modification of the STI which aims to solve the problems raised for the original scope theory without overgenerating. The proposal calls for an additional intensional abstraction operator that creates an expression denoting an intension from an expression denoting an extension. When a DP moves to a position above this operator, it is interpreted de re; otherwise it is de dicto. The crucial part of the new proposal is that a DP may move above this operator and yet remain, for instance, below an intentional verb or inside an if-clause. Therefore, a DP within an island for syntactic movement may be de re and yet not move out of the island when the intensional abstraction operator is also within the island. (shrink)

Second-order abstract categorial grammars (de Groote in Association for computational linguistics, 39th annual meeting and 10th conference of the European chapter, proceedings of the conference, pp. 148–155, 2001) and hyperedge replacement grammars (Bauderon and Courcelle in Math Syst Theory 20:83–127, 1987; Habel and Kreowski in STACS 87: 4th Annual symposium on theoretical aspects of computer science. Lecture notes in computer science, vol 247, Springer, Berlin, pp 207–219, 1987) are two natural ways of generalizing “context-free” grammar formalisms for string and tree (...) languages. It is known that the string generating power of both formalisms is equivalent to (non-erasing) multiple context-free grammars (Seki et al. in Theor Comput Sci 88:191–229, 1991) or linear context-free rewriting systems (Weir in Characterizing mildly context-sensitive grammar formalisms, University of Pennsylvania, 1988). In this paper, we give a simple, direct proof of the fact that second-order ACGs are simulated by hyperedge replacement grammars, which implies that the string and tree generating power of the former is included in that of the latter. The normal form for tree-generating hyperedge replacement grammars given by Engelfriet and Maneth (Graph transformation. Lecture notes in computer science, vol 1764. Springer, Berlin, pp 15–29, 2000) can then be used to show that the tree generating power of second-order ACGs is exactly the same as that of hyperedge replacement grammars. (shrink)

An overview of hyperintensionality is provided. Hyperintensional languages have expressions with meanings that are more fine-grained than necessary equivalence. That is, the expressions may necessarily co-apply and yet be distinct in meaning. Adequately accounting for theories cast in hyperintensional languages is important in the philosophy of language; the philosophy of mind; metaphysics; and elsewhere. This entry presents a number of areas in which hyperintensionality is important; a range of approaches to theorising about hyperintensional matters; and a range of debates that (...) attention to hyperintensional constructions has generated. (shrink)

The present paper deals with the semantics of locative expressions. Our approach is essentially model-theoretic, using basic geometrical properties of the space-time continuum. We shall demonstrate that locatives consist of two layers: the first layer defines a location and the second a type of movement with respect to that location. The elements defining these layers, called localisersand modalisers, tend to form a unit, which is typically either an adposition or a case marker. It will be seen that this layering is (...) not only semantically but in many languages also morphologically manifest. There are numerous languages in which the morphology is sufficiently transparent with respect to the layering. The consequences of this theory are manifold. For example, we shall show that it explains the contrast between English and Finnish concerning directionals, which is discussed in Fong (1997). In addition, we shall be concerned with the question of orientation of locatives, as discussed in Nam (1995). We propose that nondirectional locatives are oriented to the event, while directional locatives are oriented to certain arguments, called movers. (shrink)

Attitudinal propositionalism is the view that all mental attitude content is truth-evaluable. While attitudinal propositionalism is still silently assumed in large parts of analytic philosophy, recent work on objectual attitudes (i.e. attitudes like ‘fearing Moriarty’ and ‘imagining a unicorn’ that are reported through intensional transitive verbs with a direct object) has put attitudinal propositionalism under explanatory pressure. This paper defends propositionalism for a special subclass of objectual attitudes, viz. experiential attitudes. The latter are attitudes like seeing, remembering, and imagining whose (...) grammatical objects intuitively denote (events or) scenes. I provide a propositional analysis of experiential attitudes that preserves the merits of propositionalism. This analysis uses the possibility of representing the target-scenes of experiential attitudes by the intersection of all propositions that are true in these scenes. I show that this analysis makes available the usual (Russellian) account of intensionality and the common (Boolean) logic for entailments. (shrink)

Quantifiers in Language and Logic (QLL) is a major contribution to natural language semantics, specifically to quantification. It integrates the extensive recent work on quantifiers in logic and linguistics. It also presents new observations and results. QLL should help linguists understand the mathematical generalizations we can make about natural language quantification, and it should interest logicians by presenting an extensive array of quantifiers that lie beyond the pale of classical logic. Here we focus on those aspects of QLL we judge (...) to be of specific interest to linguists, and we contribute a few musings of our own, as one mark of a worthy publication is whether it stimulates the reader to seek out new observations, and QLL does. QLL is long and fairly dense, so we make no attempt to cover all the points it makes. But QLL has a topic index, a special symbols index and two tables of contents, a detailed one and an overview one, all of which help make it user friendly. QLL is presented in four parts: I, "The Logical Conception of Quantifiers and Quantification" with an introductory section "Quantification". II, "Quantifiers of Natural Language", the most extensive section in the book and of the most direct interest to linguists. III, "Beginnings of a Theory of Expressiveness, Translation, and Formalization" introduces notions of expressive power and definability, and IV, presents recent work and techniques concerning quantifier definability over finite domains, making accessible to linguists recent work in finite model theory. (shrink)

The Strongest Meaning Hypothesis of Dalrymple et al (1994,1998), which was originally proposed as a principle for the interpretation of reciprocals, is extended in this paper into a general principle of plural predication. This principle applies to complex predicates that are composed of lexical predicates that hold of atomic entities, and determines the pluralities in the extension of the predicate. The meaning of such a complex predicate is claimed to be the truth-conditionally strongest meaning that does not contradict lexical properties (...) of the simple predicates it contains. Weak interpretations of reciprocals (as in the books are stacked on top of each other), plural predicate conjunction (e.g. the books are old and new) and ’atomic’ distributivity in general are derived by a unified mechanism, which ’weakens’ the basic universal meanings of strong reciprocals, boolean conjunction and quantification over atomic entities. (shrink)

The exclusive component of unembedded disjunctions is standardly derived as a conversational implicature by assuming that or forms a lexical scale with and. It is well known, however, that this assumption does not suffice to determine the required scalar competitors of disjunctions with more than two atomic disjuncts (McCawley, Everything that linguists have always wanted to know about logic* (But were ashamed to ask). Chicago University Press, Chicago, 1993, p. 324; Simons, “Or”: Issues in the semantics and pragmatics of disjunction. (...) Ph.D. thesis, Cornell University, Ithaca, NY, 1998). To solve this, Sauerland (Linguist Philos 27(3): 367–391, 2004) assumes that or forms a lexical scale with two otherwise unattested silent connectives ( ${\mathbb{L}}$ and ${\mathbb{R}}$ ) that retrieve the left and right terms of a disjunction. A number of recent works have proposed an Alternative Semantics for indefinites and disjunction to account for their interaction with modals and other propositional operators (Kratzer and Shimoyama, In: Otsu Y (ed) The Proceedings of the Third Tokyo Conference on Psycholinguistics. Hituzi Syobo, Tokyo, pp. 1–25, 2002; Aloni, In: Weisgerber M (ed) Proceedings of the Conference “SuB7—Sinn und Bedeutung”. Arbeitspapier Nr. 114. Konstanz, pp. 28–37, 2003; Simons, Nat Lang Semantics 13: 271–316, 2005; Alonso-Ovalle, Disjunction in alternative semantics. Ph.D. thesis, University of Massachusetts, Amherst, MA, 2006). We note that the McCawley–Simons problem does not arise in an Alternative Semantics, if we assume that the set of pragmatic competitors to a disjunction is the closure under intersection of the set of propositions that it denotes. An adaptation of the strengthening mechanism presented in Fox (In: Sauerland U, Stateva P (eds) Presupposition and implicature in compositional semantics. MacMillan, Palgrave, pp. 71–120, 2007) allows for the derivation of the exclusive component of disjunctions with more than two atomic disjuncts without having to rely on the ${\mathbb{L}}$ and ${\mathbb{R}}$ operators. The proposal extends to the case of disjunctions with logically dependent disjuncts. (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)

This paper discusses the semantics of intensional transitive verbs such as 'need', 'want','recognize', 'find', and 'hire'. It proposes new linguistic criteria for intensionality and defends two semantic analyses for two different classes of intensional verbs. The paper also includes a systematic classification of intensional verbs according to the type of lexical meaning they involve.

A type quantifier F is symmetric iff F ( X, X )( Y ) = F ( Y, Y )( X ). It is shown that quantifiers denoted by irreducible binary determiners in natural languages are both conservative and symmetric and not only conservative.

DP hypothesis of Abney (1987), the syntactic unit that had formerly been known as noun phrase should in fact be analyzed as a phrase headed by a determiner, hence the label DP. Quite independently of this syntactic development, Partee (1987) proposed a type shifting paradigm for the semantic analysis of nominals (now called DPs). In Partee's proposal DPs are ambiguous between a referential reading of type e, a predicative reading of type et and a quantificational reading of type (et)t. DP (...) meanings can flexibly move between their different readings due to covert application of semantic operators. The present paper proposes some strong relationships between these syntactic and semantic paradigms. It is argued that the structure of the DP affects its semantics in that the NP level within the DP is purely predicative and the DP level itself is purely quantificational. However, the intermediate D' level is flexible between the predicate/quantifier semantic categories, due to the covert application of semantic operators at this level. Partee's assumption, adopted from Discourse Representation Theory and more traditional approaches in philosophical logic, that some DPs need to have a (discourse) referential reading, is withdrawn. Instead of Partee's type shifting operators between the three semantic categories she assumes, two operators are used between predicates and quantifiers. The choice function operation of Reinhart (1997) and Winter (1997) is used as a general operator from predicates to quantifiers. The minimum operator of Winter (1996) is used as a general operator from quantifiers to predicates. These two operations, referred to as category shifting operators , account for most of the Partee data and substantially extend the theory of flexibility to treat some intricate phenomena in the domains of coordination, plurality and scope. (shrink)

The phenomenon of inverse linking, where a noun phrase embedded within another behaves with respect to binding as though it were structurally independent, has proven challenging for theories of the syntax–semantics interface. In this paper I show that, using an LF-movement style approach to the syntax–semantics interface, we can derive all and only the appropriate meanings for such constructions using no semantic operations other than function application and composition. The solution relies neither on a proliferation of lexical ambiguity nor on (...) abandoning the idea that pronouns denote variables, but rather on a straightforward (and standard) reification of assignment functions, which allows us to define abstraction operators within our models. (shrink)

We revisit a typological puzzle due to Horn (Doctoral Dissertation, UCLA, 1972) regarding the lexicalization of logical operators: in instantiations of the traditional square of opposition across categories and languages, the O corner, corresponding to ‘nand’ (= not and), ‘nevery’ (= not every), etc., is never lexicalized. We discuss Horn’s proposal, which involves the interaction of two economy conditions, one that relies on scalar implicatures and one that relies on markedness. We observe that in order to express markedness and to (...) account for a bigger typological puzzle, namely the absence of lexicalizations of ‘XOR’ (= exclusive or), ‘all-or-none’, and many other imaginable logical operators, one must restrict the basic lexicalizable elements to a small set of primitives. We suggest that an ordering based perspective, following Keenan and Faltz (Boolean semantics for natural language, 1985), makes the stipulated primitives that we arrive at more natural. We also propose a modification to Horn’s proposal, based on recent work on implicatures, in which only the implicature condition is operative and in which markedness is part of the definition of the alternatives for scalar implicatures rather than an independent condition. (shrink)

The paper presents both new data and a new analysis of the semantic and pragmatic properties of the class of absolute scalar adjectives within an extension of a well-known logical framework for the analysis of gradable predicates: the delineation semantics framework . It has been long observed that the context-sensitivity, vagueness and gradability features of absolute scalar predicates give rise to certain puzzles for their analysis within most, if not all, modern formal semantic frameworks. While there exist proposals for solving (...) these puzzles within other major frameworks , it has been argued that some of their aspects are particularly challenging for the analysis of absolute scalar predicates within the delineation approach. By combining insights into the relationship between context-sensitivity and scalarity from the DelS framework with insights into the relationship between tolerance/similarity relations and the Sorites paradox from Cobreros et al.’s Tolerant, Classical, Strict framework, I propose a new logical system, called Delineation TCS , in which to set analyses of four classes of adjectival predicates. I argue that this new framework allows for an analysis of absolute scalar adjectives that answers these challenges for delineation-based frameworks, while still preserving the heart of the Klein-ian approach. (shrink)