In this paper we introduce a notion of context for Groenendijk & Stokhof's Dynamic Predicate Logic DPL. We use these contexts to give a characterization of the relations on assignments that can be generated by composition from tests and random resettings in the case that we are working over an infinite domain. These relations are precisely the ones expressible in DPL if we allow ourselves arbitrary tests as a starting point. We discuss some possible extensions of DPL and the way (...) these extensions interact with our notion of context. (shrink)

The development of the dynamic semantics of natural languagehas put issues of variable control on the agenda of formal semantics. Inthis paper we regard variables as names for stacks of values and makeexplicit several control actions as push and pop actions on stacks. Weapply this idea both to static and dynamic languages and compare theirfinite variable hierarchies, i.e., the relation between the number ofvariable stacks that is available and the expressivity of the language.This can be compared in natural languages with (...) relating the number ofpronouns available to the expressivity of the language.The results are obtained using techniques from static and dynamic modeltheory: model theoretic games, transition systems and bisimulation. (shrink)

In this paper we discuss the treatment of variables in dynamic semantics. Referent systems are introduced as a flexible mechanism for working with variables. In a referent system we carefully distinguish the variables themselves both from the machinery by which we manipulate them - their names - and from the information that we store in them - their values. It is shown that the referent systems provide a natural basis for dynamic semantics. The semantics with referent systems is compared with (...) the familiar formalisms in dynamic semantics, DRT and DPL. (shrink)

We consider substitutions in order sensitive situations, having in the back of our minds the case of dynamic predicate logic (DPL) with a stack semantics. We start from the semantic intuition that substitutions are move instructions on stacks: the syntactic operation [y/x] is matched by the instruction to move the value of the y-stack to the x-stack. We can describe these actions in the positive fragment of DPLE. Hence this fragment counts as a logic for DPL-substitutions. We give a calculus (...) for the fragment and prove soundness and completeness. (shrink)

A new system of dynamic logic is introduced and motivated, witha novel approach to variable binding for incremental interpretation. Thesystem is shown to be equivalent to first order logic and complete.The new logic combines the dynamic binding idea from DynamicPredicate Logic with De Bruijn style variable free indexing. Quantifiersbind the next available variable register; the indexing mechanismguarantees that active registers are never overwritten by newquantifiers actions. Apart from its interest in its own right, theresulting system has certain advantages over Dynamic (...) Predicate Logic orDiscourse Representation Theory. It comes with a more well behaved(i.e., transitive) consequence relation, it gives a more explicitaccount of how anaphoric context grows as text gets processed, and ityields new insight into the dynamics of anaphoric linking in reasoning.Incremental dynamics also points to a new way of handling contextdynamically in Montague grammar. (shrink)

1. Generic statements are some of the most intriguing statements we make. They are so central to our commonsense reasoning that every attested human language can express them (Dahl 1995; Cohen 2013...

Generic sentences are commonsense statements of the form ‘Fs are G,’ like ‘Bears have fur’ or ‘Rattlesnakes are poisonous.’ Kind theories hold that rather than being general statements about indivi...

Within natural language semantics, pronouns are often thought to correspond to variables whose values are contributed by contextual assignment functions. This paper concerns the application of this idea to cases where the antecedent of a pronoun is a plural quantifiers. The paper discusses the modelling of accessibility patterns of quantifier antecedents in a dynamic theory of interpretation. The goal is to reach a semantics of quantificational dependency which yields a fully semantic notion of pronominal accessibility. I argue that certain dependency (...) phenomena that arise in quantificationally created contexts require a representation of context wherein the labelling of antecedents is not rigid but rather dynamic itself. I propose a stack-based alternative to classic assignment functions, along the lines of Vermeulen (1993) and van Eijck (2001), and give a dynamic semantics of quantification which correctly accommodates the problematic anaphoric phenomena. (shrink)

This article points out problems in current dynamic treatments of anaphora and provides a new account that solves these by grafting Muskens' Compositional Discourse Representation Theory onto a partial theory of types. Partiality is exploited to keep track of which discourse referents have been introduced in the text (thus avoiding the overwrite problem) and to account for cases of anaphoric failure. Another key assumption is that the set of discourse referents is well-ordered, so that we can keep track of the (...) order in which they have been introduced, allowing a semantic characterization of anaphoric accessibility across stretches of discourse. Unlike other dynamic approaches, the system defines semantic values for unresolved anaphors. This leads to a clear separation of monotonic and non-monotonic content (in this case anaphoric resolution) and arguably provides a sound basis for a non-monotonic theory of anaphoric resolution. (shrink)

The paper investigates an elliptical construction, Clarification Ellipsis, that occurs in dialogue. We suggest that this provides data that demonstrates that updates resulting from utterances cannot be defined in purely semantic terms, contrary to the prevailing assumptions of existing approaches to dynamic semantics. We offer a computationally oriented analysis of the resolution of ellipsis in certain cases of dialogue clarification. We show that this goes beyond standard techniques used in anaphora and ellipsis resolution and requires operations on highly structured, linguistically (...) heterogeneous representations. We characterize these operations and the representations on which they operate. We offer an analysis couched in a version of Head-Driven Phrase Structure Grammar combined with a theory of information states (IS) in dialogue. We sketch an algorithm for the process of utterance integration in IS which leads to grounding or clarification. The account proposed here has direct applications to the theory of attitude reports, an issue which is explored briefly in the concluding remarks of the paper. (shrink)

A globally expressivist analysis of the indicative conditional based on the Ramsey Test is presented. The analysis is a form of ‘global’ expressivism in that it supplies acceptance and rejection conditions for all the sentence forming connectives of propositional logic (negation, disjunction, etc.) and so allows the conditional to embed in arbitrarily complex sentences (thus avoiding the Frege–Geach problem). The expressivist framework is semantically characterized in a restrictor semantics due to Vann McGee, and is completely axiomatized in a logic dubbed (...) ICL (‘Indicative Conditional Logic’). The expressivist framework extends the AGM (after Alchourron, Gärdenfors, Makinson) framework for belief revision and so provides a categorical (‘yes’–‘no’) epistemology for conditionals that complements McGee’s probabilistic framework while drawing on the same semantics. The result is an account of the semantics and acceptability conditions of the indicative conditional that fits well with the linguistic data (as pooled by linguists and from psychological experiments) while integrating both expressivist and semanticist perspectives. (shrink)

This paper presents a new take on how argument dependencies in natural language are established and constrained. The paper starts with a rather standard view that (quantificational) argument dependencies are operator-variable dependencies. The interesting twist the paper offers is to eliminate the need for syntax that serves to enforce what the operator-variable dependencies are. Instead the role of ensuring grammatical and generally unambiguous forms is taken up by semantics imposing what are dependency requirements for any interpretation to go through at (...) evaluation time. With this viewpoint there emerges an essential need for localities as the hiding of (embedded) expression material, together with a (limited) form of garbage collection to release grammatical resources used in the current locality for reuse in subsequent localities. (shrink)

This paper develops a semantics with control over scope relations using Vermeulen’s stack valued assignments as information states. This makes available a limited form of scope reuse and name switching. The goal is to have a general system that fixes available scoping effects to those that are characteristic of natural language. The resulting system is called Scope Control Theory, since it provides a theory about what scope has to be like in natural language. The theory is shown to replicate a (...) wide range of grammatical dependencies, including options for, and constraints on, ‘donkey’, ‘binding’, ‘movement’, ‘Control’ and ‘scope marking’ dependencies. (shrink)

The paper proposes the first unified account of deictic/sentence-external and sentence-internal readings of singular different . The empirical motivation for such an account is provided by a cross-linguistic survey and an analysis of the differences in distribution and interpretation between singular different , plural different and same (singular or plural) in English. The main proposal is that distributive quantification temporarily makes available two discourse referents within its nuclear scope, the values of which are required by sentence-internal uses of singular different (...) to be distinct, much as its deictic uses require the values of two discourse referents to be distinct. Thus, we take sentence-internal readings to be a form of ‘association with distributivity’ that is similar to association with focus. The contrast between singular different , plural different and same is explained in terms of several kinds of quantificational distributors that license their internal readings. The analysis is executed in a stack-based dynamic system couched in type logic, so we get compositionality in the usual Montagovian way. Quantificational subordination and dependent indefinites in various languages provide additional motivation for the account. Investigating the connections between items with sentence-internal readings and the quantificational licensors of these readings opens up a larger project of formally investigating (i) the typology of quantificational distributors and distributivity-dependent items and (ii) the fine-grained contexts of evaluation needed to capture this typological variation. (shrink)

In this paper we describe a framework for the construction of entities that can serve as interpretations of arbitrary contiguous chunks of text. An important part of the paper is devoted to describing stacking cells, or the proposed meanings for bracket-structures.

This paper discusses three potential varieties of update: updates to the common ground, structuring updates, and updates that introduce discourse referents. These different types of update are used to model different aspects of natural language phenomena. Not-at-issue information directly updates the common ground. The illocutionary mood of a sentence structures the context. Other updates introduce discourse referents of various types, including propositional discourse referents for at-issue information. Distinguishing these types of update allows a unified treatment of a broad range of (...) phenomena, including the grammatical evidentials found in Cheyenne (Algonquian) as well as English evidential parentheticals, appositives, and mood marking. An update semantics that can formalize all of these varieties of update is given, integrating the different kinds of semantic contributions into a single representation of meaning. (shrink)