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Dag Westerståhl

About me

I am Professor Emeritus in Theoretical Philosophy and Logic at Stockholm University, and Jin Yuelin Professor of Logic at Tsinghua University, Beijing.

 

 

Teaching

I currently teach (once a year) a course in Formal Semantics at Stockholm University, and a course Foundations of Logic: completeness, incompleteness, undecidability, at Tsinghua University.

Research

Most of my reasearch has been in the intersection of logic, philosophy of language, and linguistics. I have a monograph (OUP 2006, 510 pp, with Stanley Peters) on generalized quantifiers and natural language. My current reasearch is focused on issues about compositionality, and on logical constants and logical consequence.

Publications

A few additional publications (not from DIVA):

Monograph:

Quantifiers in Language and Logic (with Stanley Peters), OUP 2006, 2008, xix + 528 pp.

Papers:

The semantics of exceptives (with Stanley Peters), Linguistics and Philosophy, 2022 (to appear).

Carnap's problem in modal logic (with Denis Bonnay), Review of Symbolic Logic, 2020 (online first).

Compositionality I. Definitions and variants (with Peter Pagin), Philosophy Compass 5(3), 2010, 250-264.

Compositionality II. Arguments and problems (with Peter Pagin), Philosophy Compass 5(3), 2010, 265-282.

Generalized quantifiers in linguistics and logic (with Ed Keenan), in J. van Benthem and A. ter Meulen (eds.), Handbook of Logic and Language, 2010, Elesevier, Amsterdam, 859-910.

Decomposing generalized quantifiers, Review of Symbolic Logic 1:3, 2008, 355-371.

A selection from Stockholm University publication database

  • Generalized Quantifiers Meet Modal Neighborhood Semantics

    2021. Dag Westerståhl, Johan van Benthem. Hajnal Andréka and István Németi on Unity of Science

    Chapter

    In a mathematical perspective, neighborhood models for modal logic are generalized quantifiers, parametrized to points in the domain of objects/worlds. We explore this analogy further, connecting generalized quantifier theory and modal neighborhood logic. In particular, we find interesting analogies between conservativity for linguistic quantifiers and the locality of modal logic, and between the role of invariances in both fields. Moreover, we present some new completeness results for modal neighborhood logics of linguistically motivated classes of generalized quantifiers, and raise new types of open problem. With the bridges established here, many further analogies might be explored between the two fields to mutual benefit. 

    Read more about Generalized Quantifiers Meet Modal Neighborhood Semantics

  • Sameness

    2017. Dag Westerståhl. Feferman on foundations, 449-467

    Chapter

    I attempt an explication of what it means for an operation across domains to be the same on all domains, an issue that (Feferman, S.: Logic, logics and logicism. Notre Dame J. Form. Log. 40, 31–54 (1999)) took to be central for a successful delimitation of the logical operations. Some properties that seem strongly related to sameness are examined, notably isomorphism invariance, and sameness under extensions of the domain. The conclusion is that although no precise criterion can satisfy all intuitions about sameness, combining the two properties just mentioned yields a reasonably robust and useful explication of sameness across domains.

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  • Compositionality Solves Carnap's Problem

    2016. Denis Bonnay, Dag Westerståhl. Erkenntnis 81 (4), 721-739

    Article

    The standard relation of logical consequence allows for non-standard interpretations of logical constants, as was shown early on by Carnap. But then how can we learn the interpretations of logical constants, if not from the rules which govern their use? Answers in the literature have mostly consisted in devising clever rule formats going beyond the familiar what follows from what. A more conservative answer is possible. We may be able to learn the correct interpretations from the standard rules, because the space of possible interpretations is a priori restricted by universal semantic principles. We show that this is indeed the case. The principles are familiar from modern formal semantics: compositionality, supplemented, for quantifiers, with topic-neutrality.

    Read more about Compositionality Solves Carnap's Problem

  • Questions about compositionality

    2015. Dag Westerståhl. Logic, Methodology and Philosophy of Science: Logic and science facing the new technologies, 123-147

    Conference

    Compositionality is currently discussed mainly in computer science, linguistics, and the philosophy of language. In computer science, it is seen as a desirable design principle. But in linguistics and especially in philosophy it is an "issue". Most theorists have strong opinions about it. Opinions, however, vary drastically: from the view that compositionality is trivial or empty, or that it is simply false for natural languages, to the idea that it plays an important role in explaining human linguistic competence. This situation is unsatisfactory, and may lead an outside observer to conclude that the debate is hopelessly confused.

    I believe there is something in the charge of confusion, but that compositionality is nevertheless an idea that deserves serious consideration, for logical as well as natural languages. In this paper I try to illustrate why, without presupposing extensive background knowledge about the issue.

    Read more about Questions about compositionality

  • Dynamic Versus Classical Consequence

    2014. Denis Bonnay, Dag Westerståhl. Johan van Benthem on Logic and Information Dynamics, 837-854

    Chapter

    The shift of interest in logic from just reasoning to all forms of information flow has considerably widened the scope of the discipline, as amply illustrated in Johan van Benthem's recent book Logical Dynamics of Information and Interaction. But how much does this change when it comes to the study of traditional logical notions such as logical consequence? We propose a systematic comparison between classical consequence, explicated in terms of truth preservation, and a dynamic notion of consequence, explicated in terms of information flow. After a brief overview of logical consequence relations and the distinctive features of classical consequence, we define classical and dynamic consequence over abstract information frames. We study the properties of information under which the two notions prove to be equivalent, both in the abstract setting of information frames and in the concrete setting of Public Announcement Logic. The main lesson is that dynamic consequence diverges from classical consequence when information is not persistent, which is in particular the case of epistemic information about what we do not yet know. We end by comparing our results with recent work by Rothschild and Yalcin on the conditions under which the dynamics of information updates can be classically represented. We show that classicality for consequence is strictly less demanding than classicality for updates. Johan van Benthem's recent book Logical Dynamics of Information and Interaction [8] can be seen as a passionate plea for a radically new view of logic. To be sure, the book is not a philosophical discussion of what logic is but rather an impressive series of illustrations of what logic can be, with presentations of numerous logical languages and a wealth of meta-logical results about them. The view is called simply Logical Dynamics, and contrasted with more traditional views of logic, and also with the earlier view from e.g. [5], now called Pluralism, in which logic was seen as the study of consequence relations. According to Logical Dynamics, logic is not only about reasoning, about what follows from what, but about all aspects of information flow among rational agents. Not just proof and inference, but observations, questions, announcements, communication, plans, strategies, etc. are first-class citizens in the land of Logic. And not only the output of these activities belong to logic, but also the processes leading up to it. This is a fascinating and inspiring view of logic. But how different is it from a more standard view? In particular, what does it change for the analysis of logical consequence, which had been the focus of traditional logical enquiry? This paper attempts some answers to the latter question, with a view to get clearer about the former.

    Read more about Dynamic Versus Classical Consequence

  • Negation and quantification: a new look at the square of opposition

    2013. Dag Westerståhl. Logic across the University: Foundations and Applications, 301-317

    Chapter

    We study the Aristotelian square of opposition from the modern perspective of generalized quantifiers. With a subtle but important change in the relations holding along the sides of the square, we show that it applies to all kinds of quantifiers, not just the four Aristotelian ones. We establish some of its logical properties, and give numerous examples of squares spanned by various quantifiers, in particular those expressed by possessive constructions.

    Read more about Negation and quantification: a new look at the square of opposition

  • The semantics of possessives

    2013. Dag Westerståhl, Stanley Peters. Language 89 (4), 713-759

    Article

    We investigate what possessives mean by examining a wide range of English examples, pre- and postnominal, quantified and non-quantified, to arrive at general, systematic truth conditions for them. In the process, we delineate a rich class of paradigmatic possessives having cross-linguistic interest, exploiting  characteristic semantic properties. One is that all involve (implicit or explicit) quantification over possessed entities. Another is that this quantification always carries existential import, even when the  quantifier over possessed entities itself doesn't. We show that this property, termed possessive existential import, is intimately related to the notion of narrowing \cite{barker95}. Narrowing has implications for compositionally analyzing possessives' meaning. We apply the proposed semantics to the issue of definiteness of possessives, negation of possessives, partitives and prenominal possessives, postnominal possessives and complements of relational nouns, freedom of the possessive relation, and the semantic relationship between pre- and postnominal possessives.

    Read more about The semantics of possessives

  • Classical vs. modern Squares of Opposition, and beyond

    2012. Dag Westerståhl. The Square of Opposition, 195-229

    Chapter

    The main difference between the classical Aristotelian square of oppo- sition and the modern one is not, as many seem to think, that the classical square has or presupposes existential import. The difference lies in the relations holding along the sides of the square: (sub)contrariety and sub- alternation in the classical case, inner negation and dual in the modern case. This is why the modern square, but not the classical one, applies to any (generalized) quantifier of the right type: all, no, more than three, all but five, most, at least two-thirds of the,... After stating these and other logical facts about quantified squares of opposition, we present a number of examples of such squares spanned by familiar quantifiers. Spe- cial attention is paid to possessive quantifiers, such Mary’s, at least two students’, etc., whose behavior under negation is more complex and in fact can be captured in a cube of opposition.

    Read more about Classical vs. modern Squares of Opposition, and beyond

  • Compositionality in Kaplan style semantics

    2012. Dag Westerståhl. The Oxford Handbook of Compositionality, 192-219

    Chapter

    I investigate how the notion of compisitionality can be adapted to various kinds of semantics that take context dependence seriously.

    Read more about Compositionality in Kaplan style semantics

  • Explaining quantifier restriction

    2012. Dag Westerståhl. Logique et Analyse 55 (217), 109-120

    Article

    This is a reply to H. Ben-Yami, 'Generalized quantifiers, and beyond' (this journal,2009), where he argues that standard GQ theory does not explain why natural language quantifiers have a restricted domain of quantification. I argue, on the other hand, that although GQ theory gives no deep explanation of this fact, it does give a sort of explanation, whereas Ben-Yami's suggested alternative is no improvement.

    Read more about Explaining quantifier restriction

  • Consequence Mining Constants Versus Consequence Relations

    2012. Denis Bonnay, Dag Westerståhl. Journal of Philosophical Logic 41 (4), 671-709

    Article

    The standard semantic definition of consequence with respect to a selected set X of symbols, in terms of truth preservation under replacement (Bolzano) or reinterpretation (Tarski) of symbols outside X, yields a function mapping X to a consequence relation . We investigate a function going in the other direction, thus extracting the constants of a given consequence relation, and we show that this function (a) retrieves the usual logical constants from the usual logical consequence relations, and (b) is an inverse to-more precisely, forms a Galois connection with-the Bolzano-Tarski function.

    Read more about Consequence Mining Constants Versus Consequence Relations

  • Midpoints

    2012. Dag Westerståhl. Theories of Everything, 427-438

    Chapter

    I generalize Keenan's study of midpoints, generalized quantifiers equivalent to their own postcomplements (inner negations), focusing on the difference between a global and a local perspective of quantifiers.

    Read more about Midpoints

  • Compositionality

    2011. Peter Pagin, Dag Westerståhl. Semantics, 96-123

    Chapter

    This article is concerned with the principle of compositionality, i.e. the principle that the meaning of a complex expression is a function of the meanings of its parts and its mode of composition. After a brief historical background, a formal algebraic framework for syntax and semantics is presented. In this framework, both syntactic operations and semantic functions are (normally) partial. Using 20 the framework, the basic idea of compositionality is given a precise statement, and several variants, both weaker and stronger, as well as related properties, are distinguished. Several arguments for compositionality are discussed, and the standard arguments are found inconclusive. Also, several arguments against compositionality, and for the claim that it is a trivial property, are discussed, 25 and are found to be flawed. Finally, a number of real or apparent problems for compositionality are considered, and some solutions are proposed.

    Read more about Compositionality

  • From constants to consequence, and back

    2011. Dag Westerståhl. Synthese 187 (3), 957-971

    Article

    Bolzano’s definition of consequence in effect associates with each set X of symbols (in a given interpreted language) a consequence relation =>_X. We present this in a precise and abstract form, in particular studying minimal sets of symbols generating =>_X. Then we present a method for going in the other direction: extracting from an arbitrary consequence relation => its associated set C_=> of constants. We show that this returns the expected logical constants from familiar consequence relations, and that, restricting attention to sets of symbols satisfying a strong minimality condition, there is an isomorphism between the set of strongly minimal sets of symbols and the set of corresponding consequence relations (both ordered under inclusion).

    Read more about From constants to consequence, and back

  • Pure Quotation and General Compositionality

    2010. Peter Pagin, Dag Westerståhl. Linguistics and Philosophy 33 (5), 381-415

    Article

    Starting from the familiar observation that no straightforward treatment of pure quotation can be compositional in the standard (homomorphism) sense, we introduce general compositionality, which can be described as compositionality that takes linguistic context into account. A formal notion of linguistic context type is developed, allowing the context type of a complex expression to be distinct from those of its constituents. We formulate natural conditions under which an ordinary meaning assignment can be non-trivially extended to one that is sensitive to context types and satisfies general compositionality. As our main example we work out a Fregean treatment of pure quotation, but we also indicate that the method applies to other kinds of context, e.g. intensional contexts.

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