Vector models of language are based on the contextual aspects of language, the distributions of words and how they co-occur in text. Truth conditional models focus on the logical aspects of language, compositional properties of words and how they compose to form sentences. In the truth conditional approach, the denotation of a sentence determines its truth conditions, which can be taken to be a truth value, a set of possible worlds, a context change potential, or similar. In (...) the vector models, the degree of co-occurrence of words in context determines how similar the meanings of words are. In this paper, we put these two models together and develop a vector semantics for language based on the simply typed lambda calculus models of natural language. We provide two types of vector semantics: a static one that uses techniques familiar from the truth conditional tradition and a dynamic one based on a form of dynamic interpretation inspired by Heim’s context change potentials. We show how the dynamic model can be applied to entailment between a corpus and a sentence and provide examples. (shrink)

Contemporary natural-language semantics began with the assumption that the meaning of a sentence could be modeled by a single truth condition, or by an entity with a truth-condition. But with the recent explosion of dynamic semantics and pragmatics and of work on non- truth-conditional dimensions of linguistic meaning, we are now in the midst of a shift away from a truth-condition-centric view and toward the idea that a sentence’s meaning must be spelled out in terms (...) of its various roles in conversation. This communicative turn in semantics raises historical questions: Why was truth-conditional semantics dominant in the first place, and why were the phenomena now driving the communicative turn initially ignored or misunderstood by truth-conditional semanticists? I offer a historical answer to both questions. The history of natural-language semantics—springing from the work of Donald Davidson and Richard Montague—began with a methodological toolkit that Frege, Tarski, Carnap, and others had created to better understand artificial languages. For them, the study of linguistic meaning was subservient to other explanatory goals in logic, philosophy, and the foundations of mathematics, and this subservience was reflected in the fact that they idealized away from all aspects of meaning that get in the way of a one-to-one correspondence between sentences and truth-conditions. The truth-conditional beginnings of natural- language semantics are best explained by the fact that, upon turning their attention to the empirical study of natural language, Davidson and Montague adopted the methodological toolkit assembled by Frege, Tarski, and Carnap and, along with it, their idealization away from non-truth-conditional semantic phenomena. But this pivot in explana- tory priorities toward natural language itself rendered the adoption of the truth-conditional idealization inappropriate. Lifting the truth-conditional idealization has forced semanticists to upend the conception of linguistic meaning that was originally embodied in their methodology. (shrink)

The topic of temporal meaning in texts has received considerable attention in recent years from scholars in linguistics, logical semantics, cognitive science, and artificial intelligence. Representing Time in Natural Language offers a systematic and detailed account of how we use temporal information contained in a text or in discourse to reason about the flow of time, inferring the order in which events happened when this is not explicitly stated. A new representational system is designed to formalize an (...) appropriately context-dependent notion of situated inference. The Dynamic Aspect Tree, representing temporal dependencies, constitutes a novel and important dynamic temporal logic, one that makes it easy to see "what follows when" from the information given in an ordinary English text. (shrink)

Traditional approaches in deontic logic have focused on the so-called reportative reading of obligation sentences, by providing truth-functional semantics based on a primitive ideality order between possible worlds. Those approaches, however, do not take into account that, in natural language, obligation sentences primarily carry a prescriptive effect. The paper focuses precisely on that prescriptive character, and shows that the reportative reading can be derived from the prescriptive one. A dynamic, non truth-functional semantics for necessity deontic (...) modals is developed, in which the ideality relations among possible worlds can be updated. Finally, it is proven that the semantics solves several of the classic deontic paradoxes. (shrink)

This light piece reflects on analogies between two often disjoint streams of research: the logical semantics and pragmatics of natural language and dynamic logics of general information-driven agency. The two areas show significant overlap in themes and tools, and yet, the focus seems subtly different in each, defying a simple comparison. We discuss some unusual questions that emerge when the two are put side by side, without any pretense at covering the whole literature or at reaching (...) definitive conclusions. (shrink)

This book pursues the question of how and whether natural language allows for reference to abstract objects in a fully systematic way. By making full use of contemporary linguistic semantics, it presents a much greater range of linguistic generalizations than has previously been taken into consideration in philosophical discussions, and it argues for an ontological picture is very different from that generally taken for granted by philosophers and semanticists alike. Reference to abstract objects such as properties, numbers, (...) propositions, and degrees is considerably more marginal than generally held. (shrink)

A volume of studies in natural language semantics which brings together work by philosophers, logicians and linguists. The main topics treated are: quantification and reference in natural language; the relations between formal logic, programming languages and natural language; pragmatics and discourse meaning; surface syntax and logical meaning. The volume derives from a colloquium organised in 1973 by the Kings College Research Centre, Cambridge and the papers have been edited for publication by Professor Keenan. (...) It is hoped that the collection will make available some of the best work in this fast-moving field and will stimulate further progress by juxtaposing the different approaches and interests represented here. (shrink)

This paper adds evidence structure to standard models of belief, in the form of families of sets of worlds. We show how these more fine-grained models support natural actions of “evidence management”, ranging from update with external new information to internal rearrangement. We show how this perspective leads to new richer languages for existing neighborhood semantics for modal logic. Our main results are relative completeness theorems for the resulting dynamic logic of evidence.

Semantics of natural language; includes some Australian language examples.

Una Stojnić's Context and Coherence: The Logic and Grammar of Prominence offers a series of interesting criticisms of the classical dynamic paradigm in natural language semantics and offers a sophisticated alternative outlook, one that does recognize a dynamic, context change inducing dimension of meaning but at the same preserves the idea that (declarative) utterances express propositions in context. The purpose of this note is to set the record straight: existing dynamic analyses of modals and (...) conditionals compare favorably with Stojnić's dynamic propositionalism. (shrink)

a review of Keenan, ed. *Formal Semantics of Natural Language*.

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)

��We describe a comprehensive framework for text un- derstanding, based on the representation of context. It is designed to serve as a representation of semantics for the full range of in- terpretive and inferential needs of general natural language pro- cessing. Its most distinctive feature is its uniform representation of the various simple and independent linguistic sources that play a role in determining meaning: lexical associations, syntactic re- strictions, case-role expectations, and most importantly, contextual effects. Compositional syntactic (...) structure from a shallow parsing is represented in a neural net-based associative memory, where it then interacts through a Bayesian network with semantic associa- tions and the context or “gist” of the passage carried forward from preceding sentences. Experiments with more than 2000 sentences in different languages are included. (shrink)

Preface This book is about semantics and logic. More specifically, it is about the semantics and logic of natural language; and, even more specifically than ...

This book contains papers from a colloquium held in 1973 at Kings College, Cambridge. The contributions deal with the number of questions on which a great deal of current linguistic research and writing focus. These include the problem of quantification and reference in natural language; the application of formal logic to natural language semantics; the semantics of non-declarative sentences; the relation between natural language semantics and programming languages; the relation between sentences (...) and their contexts of use; discourse meaning; and the relation between surface syntax and logical meaning. An adequate treatment of these issues requires the interaction of a number of different linguistic approaches. As one of the contributors to the volume points out, there recently have developed three major new developments in areas of research into linguistic phenomena: transformational grammar, formal logic, and speech act theory. Although no one of these are represented singly in this volume, a number of the problems which are discussed involve issues which depend on the interfaces between these various approaches. (shrink)

In this paper we reexamine the question of whether questions areinherently intensional entities. We do so by proposing a novelextensional theory of questions, based on a re-interpretation of thedomain of t as a bilattice rather than the usual booleaninterpretation. We discuss the adequacy of our theory with respect tothe adequacy criteria imposed on the semantics of questionsby (Groenendijk and Stokhof 1997). We show that the theory is able to account in astraightforward manner for some complex issues in the (...) class='Hi'>semantics ofquestions including coordinated questions, combined indicative andinterrogative sentences, questions with quantifiers, and theimpossibility of negating questions. (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)

J. L. Austin, in "Ifs and Cans," proclaimed the common hope that we soon "may see the birth, through the joint labors of philosophers, grammarians, and numerous other students of language, of a true and comprehensive science of language." The problem has always been with the "joint labors" part. Philosophers have always been willing to issue linguists dictums and linguists have been happy to teach philosophers "plain facts." Austin’s general view of language, and his particular notion of (...) performative utterance, can be found in the writing of J. R. Firth, the most commanding British linguist of Austin’s generation, but Austin never refers to Firth. In the present volume, however, we find clear and exciting evidence of genuinely joint labors on the part of philosophers and linguists. They stem from a summer conference in 1969 rounded out with contributions from notables. To two thick issues of Synthese the editors have added a dazzling piece by Saul Kripke, two substantial pieces by James McCawley and J. R. Ross, a short paper by Paul Ziff, and a reprint of P. F. Strawson’s "Grammar and Philosophy." This is an invaluable book and the best book among the many now available concerning the interaction of linguistics and philosophy: worth the cost, which the contributors attempted to reduce through foregoing royalties. The philosophers in this volume hold, or hold intriguing, the view that the semantics of a natural language can and must, in effect, be a theory of truth for a language in much the manner that Tarski suggested, and provided, for artificial language: the recursive specification of biconditionals in which the left hand gives the structural description of an object language sentence and the right hand, the truth conditions in the metalanguage. In "homophonic" translation this requirement can be trivially satisfied simply by mentioning the sentence on the left that one uses on the right: one makes the requirement non-trivial by forcing enough into the recursive specification so that one captures the native speaker’s implicit semantic competence. In this volume, the "orthodox" Davidsonian program, which takes the syntax of the metalanguage to be standard predicate logic, is ably argued by John Wallace ; Richard Montague, David Lewis, and Jaakko Hintikka would want an intensional logic covering modality and propositional attitudes. The linguists who find this philosophical climate most appealing are called "generative semanticists": McCawley, Ross, George Lakoff and others argue that any proposed semantic rule will eventually prove necessary to syntax too and that, hence, the deepest level of syntactical form will be equivalent to semantic form. Whatever the ultimate fate of this joint program, it leads here to much exciting interaction between linguists and philosophers: linguists who welcome the machinery and conceptual standards of modern logic, and philosophers who try to grasp the specifics of crucial issues in recent linguistic theory. Even if Quine’s doubts, here sketched, and Chomsky’s currently unpublished more technical objections should be well-founded, nonetheless the joint labor will have been very much worthwhile. Aside from this general debate about semantics, there are several papers covering more specific issues. The papers of J. A. Fodor, Terence Parsons, and Ross concern adverbs and the logical form of action sentences; several papers, particularly B. H. Partee’s, examine "Opacity, Coreference, and Pronouns." In all these papers one notes the fulfillment of Austin’s hope that philosophic and linguistic arguments should become intermixed, if not at times properly indistinguishable. Perhaps the most enjoyable and exciting paper stands aside from linguistics: Saul Kripke’s "Naming and Necessity." Kripke here argues quite informally for the separation of analytic, a priori, and necessary that is required for a Kripke style, S5, modal logic with de re modalities. "Gold is a yellow metal," for example, turns out to be contingent, while "Heat is the motion of particles" is necessary but a posteriori ; and that philosopher’s stone of stones, "The morning star is the evening star," is discovered to be necessary but a posteriori.—J. L. (shrink)

Mathematics is a critical part of much scientific research. Physics in particular weaves math extensively into its instruction beginning in high school. Despite much research on the learning of both physics and math, the problem of how to effectively include math in physics in a way that reaches most students remains unsolved. In this paper, we suggest that a fundamental issue has received insufficient exploration: the fact that in science, we don’t just use math, we make meaning with it in (...) a different way than mathematicians do. In this reflective essay, we explore math as a language and consider the language of math in physics through the lens of cognitive linguistics. We begin by offering a number of examples that show how the use of math in physics differs from the use of math as typically found in math classes. We then explore basic concepts in cognitive semantics to show how humans make meaning with language in general. The critical elements are the roles of embodied cognition and interpretation in context. Then, we show how a theoretical framework commonly used in physics education research, resources, is coherent with and extends the ideas of cognitive semantics by connecting embodiment to phenomenological primitives and contextual interpretation to the dynamics of meaning-making with conceptual resources, epistemological resources, and affect. We present these ideas with illustrative case studies of students working on physics problems with math and demonstrate the dynamical nature of student reasoning with math in physics. We conclude with some thoughts about the implications for instruction. (shrink)

Semantic noise, the effect ensuing from the denotative and thus functional variability exhibited by different terms in different contexts, is a common concern in natural language processing (NLP). While unarguably problematic in specific applications (e.g., certain translation tasks), the main argument of this paper is that failing to observe this linguistic matter of fact as a generative effect rather than as an obstacle, leads to actual obstacles in instances where language model outputs are presented as neutral. Given (...) that a common and long-standing challenge in NLP is the interpretation of ambiguous – i.e., semantically noisy – cases, this article focuses on an exemplar ambiguity-resolution task in NLP: the problem of anaphora in Winograd schemas. The main question considered is: to what extent is the standard approach to disambiguation in NLP subject to a stagnant “image of language”? And, can a transdisciplinary, dynamic approach combining linguistics and philosophy elucidate new perspectives on these possible conceptual shortcomings? In order to answer these questions we explore the term and concept of noise, particularly in its presentation as semantic noise. Owing to its definitional plurality, and sometimes even desirable unspecificity, the term noise is thus used as proof of concept for semantic generativity being an inherent characteristic in linguistic representation, and its concept is used to interrogate assumptions admitted in the resolution of Winograd schemas. The argument is speculative and theoretical in method, and the result is an analysis which provides an account of the fundamentally dialogical and necessarily open-ended effects of semantic noise in natural language. (shrink)

We propose to represent the syntax and semantics of natural languages with labelled proof nets in the implicative fragment of intuitionistic linear logic. Resource-sensitivity of linear logic is used to express all dependencies between the syntactic constituents of a sentence in the form of a proof net. Phonological and semantic labelling of the proof net from its inputs to the unique output are used to produce the well-formed phonological form and the semantic representation of a sentence from entries (...) of a lexicon. In this way we obtain a linguistic model of great flexibility because labelling is not completely determined logically: it is used to introduce linguistic constraints which go beyond the underlying logic. (shrink)

This paper adds evidence structure to standard models of belief, in the form of families of sets of worlds. We show how these more fine-grained models support natural actions of “evidence management”, ranging from update with external new information to internal rearrangement. We show how this perspective leads to new richer languages for existing neighborhood semantics for modal logic. Our main results are relative completeness theorems for the resulting dynamic logic of evidence.

Introduction -- Basic concepts -- Previous approaches -- Semantic expressions: introduction -- Formal issues -- Semantic expressions: basic features -- Advanced features -- Applications: capture -- Three little pigs -- Applications: creation.

Prof. Ruth Barcan Marcus created quantified modal logic in 1946. She extended the Lewis calculus S2 to cover quantification. Quantified modal logic became an essential tool for the rigorous study of natural language in the hands of R. Montague in the late sixties. Some complex phenomena cannot be properly handled at the level of sentences. Recent researches in formal semantics have concentrated on discourse and led to a rich amount of results. Logical theories introduced for the logical (...) study of programs play an important role in these developments. We shall present a detailed account of the connection between dynamic logic and “static” logic. The core of the paper will be the translation of dynamic logic into S5. Developping an insight due to Prof. J. van Eijck, We shall offer a simplified version of the latter translation. The paper also relates to P. Gärdenfors' Knowledge in Flux. (shrink)

A new formalism for predicate logic is introduced, with a non-standard method of binding variables, which allows a compositional formalization of certain anaphoric constructions, including donkey sentences and cross-sentential anaphora. A proof system in natural deduction format is provided, and the formalism is compared with other accounts of this type of anaphora, in particular Dynamic Predicate Logic.

Logicians have always found inspiration for new research in the ordinary language that is used on a daily basis and acquired naturally in childhood. Whereas the logical issues in the foundations of mathematics motivated the development of mathematical logic with its emphasis on notions of proof, validity, axiomatization, decidability, consistency, and completeness, the logical analysis of natural language motivated the development of philosophical logic with its emphasis on semantic notions of presupposition, entailment, modality, conditionals, and intensionality. The (...) relation between research programs in both mathematical and philosophical logic and natural language syntax and semantics as branches of theoretical linguistics has increased in importance throughout the last fifty years. This chapter reviews the development of one particularly interesting and lively area of interaction between formal logic and linguistics—the semantics of natural language. Research in this emergent field has proved fruitful for the development of empirically, cognitively adequate models of reasoning with partial information, sharing or exchanging information, dynamic interpretation in context, belief revision and other cognitive processes. (shrink)

Objective. Conceptualization of the definition of space as a semantic unit of language consciousness. -/- Materials & Methods. A structural-ontological approach is used in the work, the methodology of which has been tested and applied in order to analyze the subject matter area of psychology, psycholinguistics and other social sciences, as well as in interdisciplinary studies of complex systems. Mathematical representations of space as a set of parallel series of events (Alexandrov) were used as the initial theoretical basis of (...) the structural-ontological analysis. In this case, understanding of an event was considered in the context of the definition adopted in computer science – a change in the object properties registered by the observer. -/- Results. The negative nature of space realizes itself in the subject-object structure, the components interaction of which is characterized by a change – a key property of the system under study. Observer’s registration of changes is accompanied by spatial focusing (situational concretization of the field of changes) and relating of its results with the field of potentially distinguishable changes (subjective knowledge about «changing world»). The indicated correlation performs the function of space identification in terms of recognizing its properties and their subjective significance, depending on the features of the observer`s motivational sphere. As a result, the correction of the actual affective dynamics of the observer is carried out, which structures the current perception of space according to principle of the semantic fractal. Fractalization is a formation of such a subjective perception of space, which supposes the establishment of semantic accordance between the situational field of changes, on the one hand, and the worldview, as well as the motivational characteristics of the observer, on the other. -/- Conclusions. Performed structural-ontological analysis of the system formed by the interaction of the perceptual function of the psyche and the semantic field of the language made it possible to conceptualize the space as a field of changes potentially distinguishable by the observer, structurally organized according to the principle of the semantic fractal. The compositional features of the fractalization process consist in fact that the semantic fractal of space is relevant to the product of the difference between the situational field of changes and the field of potentially distinguishable changes, adjusted by the current configuration of the observer`s value-needs hierarchy and reduced by his actual affective dynamics. (shrink)

Approaches to anaphora generally seek to explain the potential for a DP to covary with a pronoun in terms of a combination of factors, such as the inherent semantics of the antecedent DP, its scope properties, and its structural position. A case in point is Reinhart’s classic condition on bound anaphora, paraphrasable as A DP can antecede a pronoun pro only if the DP c-commands pro at S-structure, supplemented with some extra machinery to allow indefinites to covary with pronouns (...) beyond their c-command domains. In the present paper, I explore a different take. I propose that anaphora is governed not by DPs and their properties; it is governed by predicates and their properties. To use a metaphor from dynamic semantics: discourse referents can only be ‘activated’ by predicates, never by DPs. This conceptually simple assumption is shown to have far-reaching consequences. For one, it yields a new take on weak crossover, arguably worthy of consideration. Moreover, it leads to a further general “restatement of the anaphora question”, in Reinhart’s words. (shrink)

Mental Spaces is the classic introduction to the study of mental spaces and conceptual projection, as revealed through the structure and use of language. It examines in detail the dynamic construction of connected domains as discourse unfolds. The discovery of mental space organization has modified our conception of language and thought: powerful and uniform accounts of superficially disparate phenomena have become available in the areas of reference, presupposition projection, counterfactual and analogical reasoning, metaphor and metonymy, and time (...) and aspect in discourse. The present work lays the foundation for this research. It uncovers simple and general principles that lie behind the awesome complexity of everyday logic. (shrink)

We develop a framework for natural language semantics which handles intensionality via metalogical constructions and deals with degree truth values in an integrated way. We take an axiomatic set theory, ZF, as the foundation for semantic representations, but we make ZF a metalanguage for part of itself by embedding a language ℒ within ZF which is basically a copy of the part of ZF consisting of set expressions. This metalogical set-up is used for handling propositional attitude (...) verbs (limited to believe in this paper). We define a truth function τ which determines the truth value τ(p, T) of an ℒ-proposition p with respect to a theory T. Theories are sets of ℒ-propositions with associated truth values, and can be viewed as a (much more well-defined) replacement for possible worlds. We develop a mechanism for defining belief worlds as theories. We simultaneously develop two different versions of our system - a Boolean version where the set Ω of truth values is {0, 1}, and a degree-truth version where Ω is the interval [0, 1] of real numbers. We use degrees of truth in handling a broad class of semantic predicates that we call base-focus predicates, which include generalized quantifiers as well as many adverb and adjective senses and certain discourse-level predicates. (shrink)

This handbook comprises, in three volumes, an in-depth presentation of the state of the art in linguistic semantics from a wide variety of perspectives. It contains 112 articles written by leading scholars from around the world. These articles present detailed, yet accessible, introductions to key issues, including the analysis of specific semantic categories and constructions, the history of semantic research, theories and theoretical frameworks, methodology, and relationships with related fields; moreover, they give expert guidance on topics of debate within (...) the field, on the strengths and weaknesses of existing theories, and on the likely directions for the future development of semantic research. In many cases, the articles written for this handbook promise to become the standard references on the topics they cover. This work will provide an essential reference for both advanced students and researchers in semantics and related fields within linguistics, psychology, philosophy, and other areas. (shrink)

SECTION I In 1972, Donald Davison and Gilbert Hannan wrote in the introduction to the volume Semantics of Natural Language: "The success of linguistics in treating natural languages as formal ~yntactic systems has aroused the interest of a number of linguists in a parallel or related development of semantics. For the most part quite independently, many philosophers and logicians have recently been applying formal semantic methods to structures increasingly like natural languages. While differences in (...) training, method and vocabulary tend to veil the fact, philosophers and linguists are converging, it seems, on a common set of interrelated problems. " Davidson and Harman called for an interdisciplinary dialogue of linguists, philosophers and logicians on the semantics of natural language, and during the last ten years such an enterprise has proved extremely fruitful. Thanks to the cooperative effort in these several fields, the last decade has brought about striking progress in our understanding of the semantics of natural language. This work on semantics has typically paid little attention to psychological aspects of meaning. Thus, psychologists or computer scientists working on artificial intelligence were not invited to join the forces in the influential introduction of Semantics of Natural Language. No doubt it was felt that while psychological aspects of language are important in their own right, they are not relevant to our immediate semantic concerns. In the last few years, several linguists and logicians have come to question the fundamental anti-psychological assumptions underlying their theorizing. (shrink)

Paul M. Pietroski, University of Maryland I had heard it said that Chomsky’s conception of language is at odds with the truth-conditional program in semantics. Some of my friends said it so often that the point—or at least a point—finally sunk in.

The essay "Semantics for Natural Languages" is here translated from a collection of Davidson's essays published under the title "Inquiries into Truth and Interpretation", Claredon Press, Oxford 1984.

This handbook comprises, in three volumes, an in-depth presentation of the state of the art in linguistic semantics from a wide variety of perspectives. It contains 112 articles written by leading scholars from around the world. These articles present detailed, yet accessible, introductions to key issues, including the analysis of specific semantic categories and constructions, the history of semantic research, theories and theoretical frameworks, methodology, and relationships with related fields; moreover, they give expert guidance on topics of debate within (...) the field, on the strengths and weaknesses of existing theories, and on the likely directions for the future development of semantic research. In many cases, the articles written for this handbook promise to become the standard references on the topics they cover. This work will provide an essential reference for both advanced students and researchers in semantics and related fields within linguistics, psychology, philosophy, and other areas. (shrink)

I. Foundations of semantics 1. Meaning in linguistics 1. 2. 3. 4. 5. 6. Introduction Truth Compositionality Context and discourse Meaning in contemporary ...