This book uses mathematical models of language to explain why there are certain gaps in language: things that we might expect to be able to say but can't. For instance, why can we say I ran for five minutes but not *I ran to the store for five minutes? Why is five pounds of books acceptable, but *five pounds of book not acceptable? What prevents us from saying *sixty degrees of water to express the temperature of the water in a (...) swimming pool when sixty inches of water can express its depth? And why can we not say *all the ants in my kitchen are numerous? The constraints on these constructions involve concepts that are generally studied separately: aspect, plural and mass reference, measurement, and distributivity. In this book, Lucas Champollion provides a unified perspective on these domains, connects them formally within the framework of algebraic semantics and mereology, and uses this connection to transfer insights across unrelated bodies of literature and formulate a single constraint that explains each of the judgments above. (shrink)

Based on a crowdsourced truth value judgment experiment, we provide empirical evidence challenging two classical views in semantics, and we develop a novel account of counterfactuals that combines ideas from inquisitive semantics and causal reasoning. First, we show that two truth-conditionally equivalent clauses can make different semantic contributions when embedded in a counterfactual antecedent. Assuming compositionality, this means that the meaning of these clauses is not fully determined by their truth conditions. This finding has a clear explanation in inquisitive semantics: (...) truth-conditionally equivalent clauses may be associated with different propositional alternatives, each of which counts as a separate counterfactual assumption. Second, we show that our results contradict the common idea that the interpretation of a counterfactual involves minimizing change with respect to the actual state of affairs. We propose to replace the idea of minimal change by a distinction between foreground and background for a given counterfactual assumption: the background is held fixed in the counterfactual situation, while the foreground can be varied without any minimality constraint. (shrink)

Davidsonian event semantics is often taken to form an unhappy marriage with compositional semantics. For example, it has been claimed to be problematic for semantic accounts of quantification Proceedings of the 16th Amsterdam Colloquium, 2007), for classical accounts of negation Semantics and contextual expression, 1989), and for intersective accounts of verbal coordination. This paper shows that none of this is the case, once we abandon the idea that the event variable is bound at sentence level, and assume instead that verbs (...) denote existential quantifiers over events. Quantificational arguments can then be given a semantic account, negation can be treated classically, and coordination can be modeled as intersection. The framework presented here is a natural choice for researchers and fieldworkers who wish to sketch a semantic analysis of a language without being forced to make commitments about the hierarchical order of arguments, the argument-adjunct distinction, the default scope of quantifiers, or the nature of negation and coordination. (shrink)

The main goal of this paper is to investigate the relation between the meaning of a sentence and its truth conditions. We report on a comprehension experiment on counterfactual conditionals, based on a context in which a light is controlled by two switches. Our main finding is that the truth-conditionally equivalent clauses (i) "switch A or switch B is down" and (ii) "switch A and switch B are not both up" make different semantic contributions when embedded in a conditional antecedent. (...) Assuming compositionality, this means that (i) and (ii) differ in meaning, which implies that the meaning of a sentential clause cannot be identified with its truth conditions. We show that our data have a clear explanation in inquisitive semantics: in a conditional antecedent, (i) introduces two distinct assumptions, while (ii) introduces only one. Independently of the complications stemming from disjunctive antecedents, our results also challenge analyses of counterfactuals in terms of minimal change from the actual state of affairs: we show that such analyses cannot account for our findings, regardless of what changes are considered minimal. (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)

Fine (J Philos Logic 46(6):625–674, 2017) develops a unilateral and a bilateral truthmaker semantics for propositional logic. The unilateral approach trades off the primitive exact falsification relation of the bilateral approach for a primitive exclusion relation between states, thereby raising the question if exclusion serves any purpose other than to avoid exact falsification. We argue that exclusion is motivated independently of its use in avoiding exact falsification, namely as a foundation for the reconstruction of modal notions such as possibility and (...) necessity. This reconstruction in turn motivates what we call _emergent exclusion_: an atomic state can exclude a sum of atomic states collectively without excluding any of these atomic states individually. Emergent exclusion is banned in Fine (2017a) in order to maintain exact equivalence in de Morgan’s law \(\lnot (P \wedge Q) \Leftrightarrow \lnot P \vee \lnot Q\) ; we argue that the two sides of this law are not exactly equivalent and discuss a variety of state spaces that feature emergent exclusion. This paper aims to be accessible to linguists without prior exposure to truthmaker semantics. We highlight points of contact with natural language semantics, such as event semantics and algebraic semantics of plurals and conjunction. (shrink)

What licenses the use of a definite description? The formal and philosophical literature has approached this question in two ways. The uniqueness approach (Frege, 1892; Russell, 1905; Strawson, 1950) holds that we may use a definite determiner only if the property denoted by its complement holds of exactly one individual in some domain: Sentence (1) and (2) can only be true if there is exactly one king of France, and exactly one American governor, respectively. Since this is not the case (...) in the actual world, the sentences are either false or (on most modern accounts) fall prey to a presupposition failure. (shrink)

The traditional answer is: they must be atelic. But as we will see, this notion is imprecise. We will improve on it, without rejecting it. (Basically we’ll end up with temporally vs. spatially telic.).

The goal of this dissertation is twofold. First, we aim to identify the source of distributivity in natural language. Our hypothesis is that throughout the grammar, distributivity can be tracked down to a single operator. Two converging lines of reasoning help us identify this operator. One line emerges as a result of generalizing and unifying previously disparate treatments of distributivity in the domain of nominal quantifiers. The other line comes from analyzing the meaning of durative adverbials, with special attention to (...) their interaction with cumulative readings. Second, we aim to provide a unified formal semantic framework for the treatment of interactions between verbs and their arguments, most importantly aspect, plurality, and quantification, and to shed light on the way in which thematic arguments are associated with the verb in the lexicon and in the compositional process. Although existing frameworks deal with parts of this picture, no such unified framework exists to date. The theoretical results presented in this proposal include a novel argument in favor of a quantificational analysis of durative adverbials (Dowty, 1979; Moltmann, 1991); a novel account of cumulativity and distributivity that covers both the two-quantifier and three-quantifier case in the nominal domain, including readings prominently discussed by Schein (1993); a reason for severing not only the external, but also the internal argument from the semantics of the verb, in response to Kratzer (1996); and the first event-based semantics for Tree-adjoining grammar (TAG, Joshi et al., 1975). (shrink)

This paper presents a diagnostic for identifying distributive constructions and shows that it applies to pseudopartitives and for -adverbials. On this basis, a unified account is proposed for the parallels between the constructions involved. This account explains why for -adverbials reject telic predicates (*run to the store for five hours), why pseudopartitives reject count nouns (*five pounds of book ), and why both reject certain measure functions like temperature and speed (*30 of water, *drive for 5 mph). These restrictions all (...) follow from a general constraint on distributive constructions. Related concepts such as the D operator (Link, 1987), the subinterval property (Bennett and Partee, 1972), and divisive reference (Cheng, 1973) can be understood as formalizing special cases of this constraint. (shrink)

In this talk, I first systematize the analogies and complete the picture in some corners. Then, I formally relate the three constructions, and I derive their properties from a single operator. Previous analyses were not designed to account for all three constructions at the same time. Accordingly, I not only assess how well they generalize beyond their intended purpose, but I also evaluate them in their own right. Even so, this analysis improves on previous accounts in several ways. Although I (...) will not focus on this in the talk, the analysis of distributive quantification is compatible with more general analyses of cumulative and collective quantification such as Landman (2000). (shrink)

This document describes my dissertation proposal, “Aspect, plurality and quantification”, for a nonlinguist audience for the purposes of Penn’s SAS Dissertation Completion Fellowship. The dissertation proposal is available online on my website, http://www.ling.upenn.edu/~champoll/, as well as a handout with a description targeted at a linguist audience.

We introduce LTAG-spinal, a novel variant of traditional Lexicalized Tree Adjoining Grammar (LTAG) with desirable linguistic, computational and statistical properties. Unlike in traditional LTAG, subcategorization frames and the argument-adjunct distinction are left underspecified in LTAG-spinal. LTAG-spinal with adjunction constraints is weakly equivalent to LTAG. The LTAG-spinal formalism is used to extract an LTAG-spinal Treebank from the Penn Treebank with Propbank annotation. Based on Propbank annotation, predicate coordination and LTAG adjunction structures are successfully extracted. The LTAG-spinal Treebank makes explicit semantic relations (...) that are implicit or absent from the original PTB. LTAG-spinal provides a very desirable resource for statistical LTAG parsing, incremental parsing, dependency parsing, and semantic parsing. This treebank has been successfully used to train an incremental LTAG-spinal parser and a bidirectional LTAG dependency parser. (shrink)

An NP-hardness proof for non-local Multicomponent Tree Adjoining Grammar (MCTAG) by Rambow and Satta (1st International Workshop on Tree Adjoining Grammers 1992 ), based on Dahlhaus and Warmuth (in J Comput Syst Sci 33:456–472, 1986 ), is extended to some linguistically relevant restrictions of that formalism. It is found that there are NP-hard grammars among non-local MCTAGs even if any or all of the following restrictions are imposed: (i) lexicalization: every tree in the grammar contains a terminal; (ii) dominance links: (...) every tree set contains at most two trees, and in every such tree set, there is a link between the foot node of one tree and the root node of the other tree, indicating that the former node must dominate the latter in the derived tree. This is the version of MCTAG proposed in Becker et al. (Proceedings of the 5th conference of the European chapter of the Association for Computational Linguistics 1991 ) to account for German long-distance scrambling. This result restricts the field of possible candidates for an extension of Tree Adjoining Grammar that would be both mildly context-sensitive and linguistically adequate. (shrink)

Psycholinguistic experiments show that pronouns tend to be resolved differently depending on whether they occur in main or subordinate clauses. If a pronoun in a subordinate clause has more than one potential antecedent in the main clause, then the pronoun tends to refer to the antecedent which has a certain thematic role (depending on the verb and on the subordinating conjunction). In contrast, pronouns in main clauses tend to refer back to the subject of the previous main clause, and this (...) tendency is not affected by any verbs or conjunctions. In natural language processing, these findings have recently led to a proposal that pronoun resolution systems should have a split architecture, i.e. that they should use different mechanisms for pronoun resolution in the two cases. With the help of two parsed and coreference-annotated corpora, this paper estimates the impact of the split-architecture proposal. The findings of this work are as follows: (1) Subject pronouns in authentic texts behave the same way in main and subordinate clauses. (2) The number of sentences in which a split architecture would behave differently than a system that treats both cases the same way is close to zero. Therefore, a separate treatment of resolution within and across units is unlikely to improve the performance of any system. This result casts a doubt on the split-architecture proposal, and more generally on approaches that directly incorporate psycholinguistic results into performance-oriented algorithms for anaphora resolution without assessing the relative importance of the phenomena that underlie them. (shrink)

• Beaver and Condoravdi (2007): NO “In Davidsonian Event Semantics the analysis of quantification is problematic: either quantifiers are treated externally to the event system and quantified in (cf. Landman, 2000), or else the definitions of the quantifiers must be greatly (and non-uniformly) complicated (cf. Krifka, 1989)”.

This is a description of the collection of scripts which I'm submitting as a term project for the CIS530 course, what their purpose is, and how to use them. Note that at the moment I'm writing this, the tool is installed on alpha.nlp.liniac.upenn.edu in the directory /home/champoll/tblplus. It will most likely not run anywhere else at the moment, though it can be adapted easily if the relevant packages (especially fnTBL) are installed. See below fore more details.

This paper provides a unification-based implementation of Binding Theory (BT) for the English language in the framework of feature-based lexicalized tree-adjoining grammar (LTAG). The grammar presented here does not actually coindex any noun phrases, it merely outputs a set of constraints on co- and contraindexation that may later be processed by a separate anaphora resolution module. It improves on previous work by implementing the full BT rather than just Condition A. The main technical innovation consists in allowing lists to appear (...) as values of semantic features. (shrink)

(1) adapted from (Higginbotham, 2006): (black instead of red) a. Do you see the man in (or: wearing) the black hat? b. #Do you see the man in (or: wearing) a black hat?