Formal semantics has so far focused on three categories of quantifiers, to wit, Q-determiners (e.g. 'every'), Q-adverbs (e.g. 'always'), and Q-auxiliaries (e.g. 'would'). All three can be analyzed in terms of tripartite logical forms (LF). This paper presents evidence from verbs with distributive affixes (Q-verbs), in Kalaallisut, Polish, and Bininj Gun-wok, which cannot be analyzed in terms of tripartite LFs. It is argued that a Q-verb involves discourse reference to a distributive verbal dependency, i.e. an episode-valued function that sends different (...) semantic objects in a contextually salient plural domain to different episodes. (shrink)

The Eskimo language Kalaallisut (alias West Greenlandic) has traditionally been described as having a rich tense system, with three future tenses (Kleinschmidt 1851, Bergsland 1955, Fortescue 1984) and possibly four past tenses (Fortescue 1984). Recently however, Shaer (2003) has challenged these traditional claims, arguing that Kalaallisut is in fact tenseless.

In English, discourse reference to time involves grammatical tenses interpreted as temporal anaphors. Recently, it has been argued that conditionals involve modal discourse anaphora expressed by a parallel grammatical system of anaphoric modals. Based on evidence from Kalaallisut, this paper argues that temporal and modal anaphora can be just as precise in a language that does not have either grammatical category. Instead, temporal anaphora directly targets eventualities of verbs, without mediating tenses, while modal anaphora involves anaphoric moods and/or attitudinal verbs.

It has long been recognized that temporal anaphora in French and English depends on the aspectual distinction between events and states. For example, temporal location as well as temporal update depends on the aspectual type. This paper presents a general theory of aspect-based temporal anaphora, which extends from languages with grammatical tenses (like French and English) to tenseless languages (e.g. Kalaallisut). This theory also extends to additional aspect-dependent phenomena and to non-atomic aspectual types, processes and habits, which license anaphora to (...) proper atomic parts (cf. nominal pluralities and kinds). (shrink)

Most theories of conditionals and attitudes do not analyze either phenomenon in terms of the other. A few view attitude reports as a species of conditionals (e.g. Stalnaker 1984, Heim 1992). Based on evidence from Kalaallisut, this paper argues for the opposite thesis: conditionals are a species of attitude reports. The argument builds on prior findings that conditionals are modal topic-comment structures (e.g. Haiman 1978, Bittner 2001), and that in mood-based Kalaallisut English future (e.g. Ole will win) translates into a (...) factual report of a prospect-oriented attitudinal state (e.g. expectation or anxiety, see Bittner 2005). It is argued that in conditionals the antecedent introduces a topical subdomain of an input modal base (Kratzer 1981) and requires the consequent to comment. The comment is a factual report of an attitude to the topical antecedent sub-domain. [This paper was published in 2011 as "Time and modality without tenses or modals"]. (shrink)

Featured course on "Dynamic Semantics" at NASSLLI 2016. Day 1: Introduction. Abstract: Dynamic semantics is a family of semantic theories that seek to explicate the intuition that saying something changes the context for what follows. We survey the development of formal semantics from static to dynamic formalisms since 1970s. Throughout, we highlight natural language phenomena that motivate dynamic semantics, and the key pre-theoretical concepts -- information state, update, and discourse referent -- which can be implemented in different ways and thus (...) lead to various dynamic logics. (shrink)

Partee (1973) noted anaphoric parallels between English tenses and pronouns. Since then these parallels have been analyzed in terms of type-neutral principles of discourse anaphora. Recently, Stone (1997) extended the anaphoric parallel to English modals. In this paper I extend the story to languages of other types. This evidence also shows that centering parallels are even more detailed than previously recognized. Based on this evidence, I propose a semantic representation language (Logic of Change with Centered Worlds), in which the observed (...) parallels can be formally analyzed. (shrink)

Crosslinguistically, causative constructions conform to the following generalization: If the causal relation is syntactically concealed, then it is semantically direct. Concealed causatives span a wide syntactic spectrum, ranging from resultative complements in English to causative subjects in Miskitu. A unified type-driven theory is proposed which attributes the understood causal relation—and other elements of constructional meaning—to type lifting operations predictably licensed by type mismatch at LF. The proposal has far-reaching theoretical implications not only for the theory of compositionality and causation, but (...) also for the underlying theory of events, space, and time, in natural language discourse. (shrink)

So far, we have focused on discourse reference to atomic individuals and specific times, events, and states. The basic point of the argument was that all types of discourse reference involve attention-guided anaphora (in the sense of Bittner 2012: Ch. 2). We now turn to discourses involving anaphora to and by quantificational expressions. Today, we focus on quantification over individuals but the analysis we develop will directly generalize to other semantic types. The basic idea is that quantification is one more (...) species of top-level anaphora--to wit, anaphora to top-ranked sets. (shrink)

Featured course on "Dynamic Semantics" at NASSLLI 2016. Day 2: Anaphora. Abstract: Cross-linguistic evidence shows that anaphora crucially involves context change. The logical representation system must be able to represent rank-based anaphora, because in every language the favorite anaphors -- e.g. Mandarin zeros, Kalaallisut inflections, English pronouns -- are restricted to refer to top-ranked antecedents (top-level anaphors, like Mandarin zeros or Kalaallisut inflections) or top- or 2nd-ranked antecedents (shallow anaphors, like English pronouns).

Natural languages exhibit a great variety of grammatical paradigms. For instance, in English verbs are grammatically marked for tense, whereas in the tenseless Eskimo-Aleut language Kalaallisut they are marked for illocutionary mood. Although time is a universal dimension of the human experience and speaking is part of that experience, some languages encode reference to time without any grammatical tense morphology, or reference to speech acts without any illocutionary mood morphology. Nevertheless, different grammatical systems are semantically parallel in certain respects. Specifically, (...) I propose that English tenses form a temporal centering system, which monitors and updates topic times, whereas Kalaallisut moods form a modal centering system, which monitors and updates modal discourse referents. To formalize these centering parallels I define a dynamic logic that represents not only changing information but also changing focus of attention in discourse (Update with Centering, formalizing Grosz et al 1995). Different languages can be translated into this typed logic by directly compositional universal rules of Combinatory Categorial Grammar (CCG) The resulting centering theory of tense and illocutionary mood draws semantic parallels across different grammatical systems. The centering generalizations span the extremes of the typological spectrum, so they are likely to be universal. In addition, the theory accounts for the translation equivalence of tense and illocutionary mood in a given utterance context. Following Stalnaker (1978) I assume that the very act of speaking up has a ‘commonplace effect’ on the context. It focuses attention on the speech act and thereby introduces default modal and temporal topics. These universal defaults complement language-specific grammars, e.g. English tenses and Kalaallisut moods. In a given utterance context the universal discourse-initial defaults plus language-specific grammatical marking may add up to the same truth conditions.. (shrink)

Rooth & Partee (1982) and Rooth (1985) have shown that the English-specific rule-by-rule system of PTQ can be factored out into function application plus two transformations for resolving type mismatch (type lifting and variable binding). Building on these insights, this article proposes a universal system for type-driven translation, by adding two more innovations: local type determination for gaps (generalizing Montague 1973) and a set of semantic filters (extending Cooper 1983). This system, dubbed Cross-Linguistic Semantics (XLS), is shown to account for (...) various phenomena — including scope relations in English and Greenlandic Eskimo, internally headed relative clauses in Lakhota, serial verbs in Yoruba and VP ellipsis in English. (shrink)

Featured course on "Dynamic Semantics" at NASSLLI 2016. Day 5: Quantification. Abstract: In discourse, quantifiers can function as antecedents or anaphors. We analyze a sample discourse in Dynamic Plural Logic (DPlL, van den Berg 1993, 1994), which represents not only current discourse referents, but also current relations by means of plural information states. This makes it possible to analyze quantification as structured discourse reference. Finally, the DPlL analysis is transposed into Update with Centering, to simplify the formalism and relate quantification (...) to earlier discussion in the course. (shrink)

This paper argues that indexical reference is a species of discourse reference, just like anaphora. Both varieties of discourse reference involve not only context dependence, but also context change. The act of speaking up focuses attention and thereby makes this very speech event available for discourse reference by indexicals. Mentioning something likewise focuses attention, making the mentioned entity available for subsequent discourse reference by anaphors. Empirical evidence is presented from grammatical centering in Kalaallisut and "shifty indexicals" in Slave attitude reports.

Featured course on "Dynamic Semantics" at NASSLLI 2016. Day 3: Indexicality. Abstract: Cross-linguistic evidence shows that indexicality, too, crucially involves context change. Speaking up focuses attention on that event and thereby makes it available for discourse reference (by "i", "you", etc). In Kalaallisut, this explains parallel grammatical marking of indexical reference and topic-oriented anaphora. Moreover, shiftable indexicals in Slavey show that certain expressions, e.g. attitude verbs, may update the top perspectival discourse referent from the speech event to an attitude state.

Featured course on "Dynamic Semantics" at NASSLLI 2016. Day 4: Temporality. Abstract: Cross-linguistic evidence shows that temporal reference likewise involves context change. In every language, temporal reference is similar to top-level nominal reference, except that instead of updating or referring to top-ranked individuals, temporal grammatical systems update or refer to top-ranked temporal referents (events, states, or times). We discuss and compare temporal reference in two sample languages: tense-based English and tenseless aspect-based Mandarin.

We analyze Case in terms of independent constraints on syntactic structures — namely, the Projection Principle (inherent Case), the ECP (marked structural Case), and the theory of extended projections (the nominative, a Caseless nominal projection). The resulting theory accounts for (1) the government constraint on Case assignment, (2) all major Case systems (accusative, ergative, active, three-way, and split), (3) Case alternations (passive, antipassive, and ECM), and (4) the Case of nominal possessors. Structural Case may correlate with pronominal agreement because the (...) former can, and the latter must, involve antecedent-government by a functional head. However, neither phenomenon implies the other. (shrink)

: This study describes a new field method, suited for investigating scope relations — and other aspects of truth conditional meaning — with native speaker consultants who may speak no other language and have no background in linguistics or logic. This method revealed a surprising scope contrast between the antipassive and the ergative construction in Greenlandic Eskimo. The results of this field work are described in detail and a crosslinguistic scope generalization is proposed based on Greenlandic Eskimo, Basque, Polish, Russian, (...) Finnish and English. (shrink)

I propose that Mandarin ｡-sentences (units marked by ｡) are aspectual topic-comment sequences, where an initial update (terminating in a pause) introduces a topic state for comment by one or more clauses. Each comment anaphorically refers to the topic state via the aspect feature of the verbal predicate. This proposal explains why Mandarin ｡-sentences have controversial boundaries, since speakers may disagree where one topic state ends and the next one begins. It also explains various manifestations of aspect-prominence and topic-prominence in (...) Mandarin discourse. In Bittner (2014), this proposal is formally implemented in Categorial Grammar and a new dynamic logic called Update with Centering. (shrink)

The central claim of this paper is that surface-faithful word-by-word update is feasible and desirable, even in languages where word order is supposedly free. As a first step, in sections 1 and 2, I review an argument from Bittner 2001a that semantic composition is not a static process, as in PTQ, but rather a species of anaphoric bridging. But in that case the context-setting role of word order should extend from cross-sentential discourse anaphora to sentence-internal anaphoric composition. This can be (...) spelled out as a two-part hypothesis. First, in all languages anaphoric composition derives incremental updates based on the topological order rather than the syntactic hierarchy. And secondly, rigid vs. free word order is simply rigid vs. free mapping from syntax to topology. To formalize this hypothesis, I first present, in section 3, Sevensorted Logic of Change with Centering. This makes it possible, in section 4, to articulate a system of constraints on basic meanings in Kalaallisut — a polysynthetic language with free word order, ideally suited to test the hypothesis of incremental update. The key assumptions about topology as the input to anaphoric composition are spelled out in section 5, which concludes the development of a general formal framework. This formal framework then serves, in sections 6 through 8, t o explicate topologically based incremental updates for increasingly more complex samples of an actual Kalaallisut text. This reveals ubiquitous patterns of prominence-guided anaphora, in all semantic domains, t o increasingly more complex types of discourse referents. These anaphoric patterns show that the context-setting role of word order indeed does extend from discourse to word-to-word anaphora. And this, in turn, strongly supports the hypothesis of topologically based anaphoric composition. Finally, in section 9 I adduce evidence from English that this hypothesis also holds for languages with rigid word order, albeit the fixed mapping keeps the topology close to the syntax. I conclude that both free and rigid word orders receive a natural account if semantic composition is viewed as topologically based anaphoric bridging.. (shrink)

This paper introduces a framework for direct surface composition by online update. The surface string is interpreted as is, with each morpheme in turn updating the input state of information and attention. A formal representation language, Logic of Centering, is defined and some crosslinguistic constraints on lexical meanings and compositional operations are formulated.

Amele (Papuan, New Guinea) is a tense-mood-based language (in the typology of Bittner 2014) with an elaborate system of clause chaining, including switch reference (SR) and serial verb constructions (SVC). This draft analyzes two interlinear Amele texts (from Roberts 2007) in Update with Centering of Bittner (2014). The basic idea is that an SR-chain is a topic-comment sequence about a 'topical development' — i.e. a topic time framing a chain of causally linked events. In contrast, an SVC is a chain (...) of verbs that jointly introduce a single eventuality into discourse. (shrink)

In this paper, we discuss some rather puzzling facts concerning the semantics of Warlpiri expressions of cardinality, i.e. the Warlpiri counterparts of English expressions like one,two, many, how many. The morphosyntactic evidence, discussed in section 1, suggests that the corresponding expressions in Warlpiri are nominal, just like the Warlpiri counterparts of prototypical nouns, eg. child. We also argue that Warlpiri has no articles or any other items of the syntactic category D(eterminer). In section 2, we describe three types of readings— (...) "definite", "indefinite" and "predicative"—which are generally found with Warlpiri nouns, including those which correspond to English common nouns and cardinality expressions. A partial analysis of these readings is sketched i n section 3. Since Warlpiri has no determiner system, we hypothesize that the source of (in)definiteness in this language is semantic. More specifically, we suggest that Warlpiri nominals are basically interpreted as individual terms or predicates of individuals and that their three readings arise as a consequence of the interaction of their basic meanings, which are specific to Warlpiri, with certain semantic operations, such as type shifting (Rooth and Partee 1982, Partee and Rooth 1983, Partee 1986, 1987), which universally can or must apply in the process of compositional semantic interpretation. (shrink)

This paper describes quantificational structures in Greenlandic Eskimo (Kalaallisut), a language where familiar quantificational meanings are expressed in ways that are quite different from English. Evidence from this language thus poses some formidable challenges for cross-linguistic theories of compositional semantics.

Last time we introduced the notion of an illocutionary perspective . The basic idea is that the very act of speaking up introduces several discourse referents. The speech act itself (e ) is introduced as the central perspective point ( ε ). In addition, all the speech spheres (p ) where this speech act is realized, as well as the worlds of each sphere (w ∈p ) are introduced as modal topics ( Ω and  ω ).

Simple Mandarin Chinese texts translated into Update with Centering. Notes toward a directly compositional fragment of Mandarin Chinese, combining Categorial Grammar with Update with Centering, to appear in Bittner (in prep.) "Temporality: Universals and Variation".

The standard way to represent anaphoric dependencies is to co-index the anaphor with its antecedent in the syntactic input to semantic rules, which then interpret such indices as variables. Dynamic theories (e.g. Kamp’s DRT, Heim’s File Change Semantics, Muskens’s Compositional DRT, etc) combine syntactic co-indexation with semantic left-to-right asymmetry. This captures the fact that the anaphor gets its referent from the antecedent and not vice versa. Formally, a text updates the input state of information to the output state. In particular, (...) an indexed antecedent updates the entity assigned to its index, and the output entity is then picked up as the referent by any subsequent co-indexed anaphor. (shrink)

Abstract According to an influential theory, English tenses are anaphoric to an aforementioned reference point. This point is sometimes construed as a time (e.g. Reichenbach 1947, Partee 1973, Stone 1997) and sometimes as an event (e.g. Kamp 1979, 1981, Webber 1988). Moreover, some researchers draw semantic parallels between tenses and pronouns (e.g. Partee 1973, 1984, Stone 1997), whereas others draw parallels between tenses and anaphorically anchored (in)definite descriptions (e.g. Webber 1988). This paper proposes a unified approach.

By this point, we have developed some articulated analyses of top-level temporal anaphora, including temporal quantification, in languages with grammatical tense and/or aspect systems, represented by English, Polish, and Mandarin. But it is still not clear how this approach might extend to temporal anaphora in a language such as Kalaallisut, which has neither grammatical tense nor grammatical aspect, but instead marks only grammatical mood and person. Most theories of mood and modal reference either ignore temporal reference or analyze modal and (...) temporal reference as unrelated phenomena. Such theories provide no inkling how temporal reference in a tenseless mood-based language can be as precise as in English. (shrink)

: The Hamblin-Karttunen approach has led to many insights about questions in English. In this article the results of this rule-by-rule tradition are reconsidered from a crosslinguistic perspective. Starting from the type-driven XLS theory developed in Bittner (1994a, b), it is argued that evidence from simple questions (in English, Polish, Lakhota and Warlpiri) leads to certain revisions. The revised XLS theory then immediately generalizes to complex questions — including scope marking (Hindi), questions with quantifiers (English) and multiple wh-questions (English, Hindi, (...) Japanese). Eliminating language- and construction-specific information from the compositional rules, in favor of universal semantic filters, leads to analyses that not only generalize across unrelated languages but are also empirically more accurate, not less. (shrink)

Day 1 of advanced course on "Temporal anaphora in tenseless languages" at 2006 ESSLLI.

Hamm, Kamp, and van Lambalgen 2006 (hereafter HLK) propose to relate NL discourse to cognitive representations that also deal with world knowledge, planning, belief revision, etc. Surprisingly, to represent human cognition they use an event calculus "which has found applications in robotics". This comment argues that the robotics-based theory of HLK attributes too much to world knowledge and not enough to the ontology, centering, and other universals of NL semantics. It is also too Anglo-centric to generalize to languages of other (...) linguistic types. (shrink)

Appendix to lecture notes on "Nominal (re)centering: From Kalaallisut to UC1". Day 2 of advanced course on "Cross-linguistic compositional semantics" at LSA Summer Institute 2009 at UC Berkeley.

This is the last of three lectures on anaphoric parallels between individuals and possibilities across languages (IMS, Stuttgart, 2000).

Day 3 of advanced course on "Crosslinguistic compositional semantics" at 2009 LSA Summer Institute at UC Berkeley. Plan for the day: (a) Introduction: Toward sun-sem typology (b) CCG+UC1 fragment of Kalaallisut, (c) Kalaallisut BA.TO.L-traits explained.

The first of three lectures on nominal and modal discourse reference across languages (IMS, Stuttgart, 2000).

Unlike English and Polish, Mandarin has no grammatical tense (TNS). Therefore, reference times are only introduced by temporal modifiers (contra Smith 1991/7, Wu 2003, Lin 2005, etc). In Mandarin discourse, the frequency of such modifiers (‘today’, ‘last night’, etc) is about the same (low) as in tensed languages (e.g. English, Polish) and plays a similarly marginal role in temporal discourse reference. This, however, does NOT mean that in tenseless Mandarin temporal relations between eventualities in discourse are in any way less (...) precise than in tensed languages. Rather, the issue is HOW temporal relations are established: indirectly , via reference times, or directly, without mediating reference times. Tensed English and Polish typically first introduce a topic time (by topic-setting TNS) and then locate verbal eventualities in relation to this temporal topic (by anaphoric TNS). (shrink)

Last time we saw that grammatical tenses anaphorically refer to top-ranked times or time-valued functions of top-ranked events, just like grammatical person markers anaphorically refer to top-ranked individuals or invididual-valued functions of top-ranked events. Today we extend this idea to grammatical aspect. Specifically, grammatical aspect marking in English and Polish is analyzed as discourse anaphora to top-ranked eventualities (states or events).

In Kalaallisut (Eskimo-Aleut:Greenland) verbs inflect for illocutionary mood (declarative, interrogative, imperative, or optative). In addition, the language has an evidential (reportative) clitic which is compatible with all illocutionary moods and gives rise to a variety of readings. These<br>lecture notes exemplify the attested combinations and readings by means of a representative sample of mini-discourses and mini-dialogs.

Day 6 of advanced course on "Crosslinguistic compositional semantics" at 2009 LSA Summer Institute at UC Berkeley. Plan for today: (a) Review: scope prediction, Kalaallisut data, (b) Analysis of Kalaallisut data, (c) Questions & discussion.

Day 4 of advanced course on "Crosslinguistic compositional semantics" at 2009 LSA Summer Institute at UC Berkeley. Plan to today: (a) Introduction (syn-sem traits of English vs. Kalaallisut, scope corollary), (b) UC1 + event (re)centering = UC2, (c) English and Kalaallisut in CCG+UC2, (d) Analysis of Kalaallisut BA.TO.L (review) vs. English SA.SU.S (new).

Day 5 of advanced course on "Crosslinguistic compositional semantics" at 2009 LSA Summer Institute at UC Berkeley. Plan for today: (a) Introduction: scope prediction (SA vs. BA), sample data (English vs. Kalaallisut), (b) Analysis of English data.

Ergative languages make up a substantial percentage of the world’s languages. They have a case system which distinguishes the subject of a transitive verb from that of an intransitive, grouping the latter with the object — that is, the object of a transitive verb and the subject of an intransitive verb are in the same case, which we refer to as the nominative. However, ergative languages differ from one another in important ways. In Greenlandic Eskimo the nominative, whether it is (...) a subject or an object, is syntactically prominent in the clause, much like a subject in English; but in Warlpiri, the nominative is not prominent, more like an object. The variable prominence of the nominative manifests itself as well in the semantics, e.g., default scope of indefinite and quantified nominals. Using data from Greenlandic Eskimo and Warlpiri, and from Hindi, which represents a split ergative system, this paper develops a general theory of case which explains the observed differences amongst ergative languages. In addition, the theory is designed to account for the accusative language type, represented by English. (shrink)

Tuesday evening, December 27, 1983 …I did go skiing today, though, which is what I want to write about. The temperature is down to –10°C again, on my thermometer, which probably means –12 to –13°C, in real terms. The visibility is still very poor though the wind has stopped. I set off at 2 pm and got home at about 4 pm, which meant skiing in the dark all the time. This wouldn’t have bothered me except that I had an (...) unpleasant adventure in Torssukataq fiord, on the intended route for me New Year’s hike. No more and no less but one of my ski poles went through the ice. I am not sure whether it would have continued all the way down, but it went in deeper than I liked, and I heard and saw water coming up around where it had gone in. I didn’t feel like probing any further, especially in the dark, [so I] just turned in my tracks and, carefully testing the ice with my ski poles, went back as fast as I could. (shrink)

This book surveys the ways in which languages of different types refer to past, present, and future events and how these referents are related to the knowledge and attitudes of discourse participants. The book is the culmination of fifteen years of research by the author. Four major language types are examined in-depth: tense-based English, tense-aspect-based Polish, aspect-based Chinese, and mood-based Kalaallisut. Each contributes to a series of logical representation languages, which together define a common logical language that is argued to (...) underlie all language types. The four types differ in whether they choose to grammaticalize discourse reference to times (tense), events (aspect), and/or attitudes (mood), and how non-grammaticalized elements are inferred. The common logical language is a dynamic update logic, building on DRT and Centering Theory, but with a novel architecture—e.g. the distinction between focal vs. peripheral attention plays a key role, parallel to focal vs. peripheral vision. (shrink)