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  1. Dag Westerståhl & Johan van Benthem (forthcoming). Directions in Generalized Quantifier Theory. Studia Logica.
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  2. Juha Kontinen, Jouko Väänänen & Dag Westerståhl (2013). Editorial Introduction. Studia Logica 101 (2):233-236.
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  3. Denis Bonnay & Dag Westerståhl (2012). Consequence Mining: Constans Versus Consequence Relations. Journal of Philosophical Logic 41 (4):671-709.
    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 ⇒x. 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 (...)
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  4. Sten Lindström, Erik Palmgren & Dag Westerståhl (2012). Introduction: The Philosophy of Logical Consequence and Inference. Synthese 187 (3):817-820.
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  5. Dag Westerståhl (2012). Explaining Quantifier Restriction: Reply to Ben-Yami. Logique Et Analyse 55 (217):109-120.
    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.
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  6. Dag Westerståhl (2012). From Constants to Consequence, and Back. Synthese 187 (3):957-971.
    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 (...)
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  7. Alexander Almér & Dag Westerståhl (2010). Review of Relativism and Monadic Truth. [REVIEW] Linguistics and Philosophy 33 (1):37-50.
    This is a review of Herman Cappelen and John Hawthorne’s book Relativism and Monadic Truth (Oxford University Press, Oxford, 2009).
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  8. Peter Pagin & Dag Westerståhl (2010). Pure Quotation and General Compositionality. Linguistics and Philosophy 33 (5):381-415.
    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 (...)
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  9. Jouko Väänänen & Dag Westerståhl (2010). In memoriam: Per Lindström. Theoria 76 (2):100-107.
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  10. Dag Westerståhl (2008). Decomposing Generalized Quantifiers. Review of Symbolic Logic 1 (3):355-371.
    This note explains the circumstances under which a type 1 quantifier can be decomposed into a type 1, 1 quantifier and a set, by fixing the first argument of the former to the latter. The motivation comes from the semantics of Noun Phrases (also called Determiner Phrases) in natural languages, but in this article, I focus on the logical facts. However, my examples are taken among quantifiers appearing in natural languages, and at the end, I sketch two more principled linguistic (...)
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  11. Dag Westerståhl, Generalized Quantifiers. Stanford Encyclopedia of Philosophy.
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  12. Stanley Peters & Dag Westerståhl (2006). Quantifiers in Language and Logic. Clarendon Press.
    Quantification is a topic which brings together linguistics, logic, and philosophy. Quantifiers are the essential tools with which, in language or logic, we refer to quantity of things or amount of stuff. In English they include such expressions as no, some, all, both, and many. Peters and Westerstahl present the definitive interdisciplinary exploration of how they work - their syntax, semantics, and inferential role. Quantifiers in Language and Logic is intended for everyone with a scholarly interest in the exact treatment (...)
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  13. Dag Westerståhl (2005). On the Aristotelian Square of Opposition. In Felix Larsson (ed.), Kapten Mnemos Kolumbarium. Philosophical Communications.
    A common misunderstanding is that there is something logically amiss with the classical square of opposition, and that the problem is related to Aristotle’s and medieval philosophers’ rejection of empty terms. But [Parsons 2004] convincingly shows that most of these philosophers did not in fact reject empty terms, and that, when properly understood, there are no logical problems with the classical square. Instead, the classical square, compared to its modern version, raises the issue of the existential import of words like (...)
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  14. Dag Westerståhl (2004). On the Compositional Extension Problem. Journal of Philosophical Logic 33 (6):549-582.
    A semantics may be compositional and yet partial, in the sense that not all well-formed expressions are assigned meanings by it. Examples come from both natural and formal languages. When can such a semantics be extended to a total one, preserving compositionality? This sort of extension problem was formulated by Hodges, and solved there in a particular case, in which the total extension respects a precise version of the fregean dictum that the meaning of an expression is the contribution it (...)
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  15. Dag Westerståhl (2004). Perspectives on the Dispute Between Intuitionistic and Classical Mathematics. In Christer Svennerlind (ed.), Ursus Philosophicus. Essays dedicated to Björn Haglund on his sixtieth birthday. Philosophical Communications.
    It is not unreasonable to think that the dispute between classical and intuitionistic mathematics might be unresolvable or 'faultless', in the sense of there being no objective way to settle it. If so, we would have a pretty case of relativism. In this note I argue, however, that there is in fact not even disagreement in any interesting sense, let alone a faultless one, in spite of appearances and claims to the contrary. A position I call classical pluralism is sketched, (...)
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  16. Jouko Väänänen & Dag Westerståhl (2002). On the Expressive Power of Monotone Natural Language Quantifiers Over Finite Models. Journal of Philosophical Logic 31 (4):327-358.
    We study definability in terms of monotone generalized quantifiers satisfying Isomorphism Closure, Conservativity and Extension. Among the quantifiers with the latter three properties - here called CE quantifiers - one finds the interpretations of determiner phrases in natural languages. The property of monotonicity is also linguistically ubiquitous, though some determiners like an even number of are highly non-monotone. They are nevertheless definable in terms of monotone CE quantifiers: we give a necessary and sufficient condition for such definability. We further identify (...)
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  17. Peter Pagin & Dag Westerståhl (2001). Editorial: Compositionality: Current Issues. [REVIEW] Journal of Logic, Language and Information 10 (1):1-5.
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  18. Dag Westerståhl (2001). Quantifiers. In Lou Goble (ed.), The Blackwell Guide to Philosophical Logic. Blackwell Publishers. 437--460.
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  19. Dag Westerståhl (1999). Scope of the Journal. Journal of Logic, Language, and Information 8:129-134.
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  20. Dag Westerståhl (1998). On Mathematical Proofs of the Vacuity of Compositionality. Linguistics and Philosophy 21 (6):635-643.
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  21. Dag Westerstahl (1998). Review: G. Y. Sher, Partially-Ordered (Branching) Generalized Quantifiers: A General Definition. [REVIEW] Journal of Symbolic Logic 63 (4):1614-1615.
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  22. Dag Westerståhl & Maarten de Rijke (1998). Editorial: Special Issues – the Ground-Rules. [REVIEW] Journal of Logic, Language and Information 7 (2):3-4.
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  23. Lauri Hella, Jouko Väänänen & Dag Westerståhl (1997). Definability of Polyadic Lifts of Generalized Quantifiers. Journal of Logic, Language and Information 6 (3):305-335.
    We study generalized quantifiers on finite structures.With every function : we associate a quantifier Q by letting Q x say there are at least (n) elementsx satisfying , where n is the sizeof the universe. This is the general form ofwhat is known as a monotone quantifier of type .We study so called polyadic liftsof such quantifiers. The particular lifts we considerare Ramseyfication, branching and resumption.In each case we get exact criteria fordefinability of the lift in terms of simpler quantifiers.
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  24. Jerry Seligman & Dag Westerståhl (eds.) (1996). Logic, Language and Computation. Csli Publications, Stanford.
  25. Dag Westerståhl (1996). Editorial. Journal of Logic, Language and Information 5 (1).
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  26. Dag Westerståhl (1996). Self-Commuting Quantifiers. Journal of Symbolic Logic 61 (1):212-224.
    We characterize the generalized quantifiers Q which satisfy the scheme $QxQy\phi \leftrightarrow QyQx\phi$ , the so-called self-commuting quantifiers, or quantifiers with the Fubini property.
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  27. Dag Westerstahl & Jeremy Seligman (eds.) (1996). Language, Logic, and Computation: The 1994 Moraga Proceedings. CSLI.
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  28. Johan van Benthem & Dag Westerståhl (1995). Directions in Generalized Quantifier Theory. Studia Logica 55 (3):389-419.
    We give a condensed survey of recent research on generalized quantifiers in logic, linguistics and computer science, under the following headings: Logical definability and expressive power, Polyadic quantifiers and linguistic definability, Weak semantics and axiomatizability, Computational semantics, Quantifiers in dynamic settings, Quantifiers and modal logic, Proof theory of generalized quantifiers.
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  29. Dag Westerståhl (1995). Quantifiers in Natural Language A Survey of Some Recent Work. In. In M. Krynicki, M. Mostowski & L. Szczerba (eds.), Quantifiers: Logics, Models and Computation. Kluwer Academic Publishers. 359--408.
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  30. Dag Prawitz, Brian Skyrms & Dag Westerståhl (eds.) (1994). Logic, Methodology, and Philosophy of Science Ix: Proceedings of the Ninth International Congress of Logic, Methodology, and Philosophy of Science, Uppsala, Sweden, August 7-14, 1991. [REVIEW] Elsevier.
    This volume is the product of the Proceedings of the 9th International Congress of Logic, Methodology and Philosophy of Science and contains the text of most of ...
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  31. Dag Prawitz & Dag Westerståhl (eds.) (1994). Logic and Philosophy of Science in Uppsala. Kluwer.
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  32. Peter Pagin & Dag Westerståhl (1993). Predicate Logic with Flexibly Binding Operators and Natural Language Semantics. Journal of Logic, Language and Information 2 (2):89-128.
    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.
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  33. Dag Westerståhl, Björn Haglund & Torbjörn Lager (1993). A Situation-Theoretic Representations of Text Meaning: Anaphora, Quantification, and Negation'. In Peter Aczel, David Israel, Yosuhiro Katagiri & Stanley Peters (eds.), Situation Theory and its Applications Vol. Csli. 375--408.
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  34. Dag Westerståhl (1990). Parametric Types and Propositions in First-Order Situation Theory. In Robin Cooper, Kuniaki Mukai & John Perry (eds.), Situation Theory and its Applications Vol. 1. Csli.
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  35. Dag Westerståhl (1989). Aristotelian Syllogisms and Generalized Quantifiers. Studia Logica 48 (4):577-585.
    The paper elaborates two points: i) There is no principal opposition between predicate logic and adherence to subject-predicate form, ii) Aristotle's treatment of quantifiers fits well into a modern study of generalized quantifiers.
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  36. Dag Westerståhl (1989). Quantifiers in Formal and Natural Languages. In. In Dov Gabbay & Franz Guenthner (eds.), Handbook of Philosophical Logic. Kluwer. 1--131.
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  37. Dag Westerståhl (1987). Branching Generalized Quantifiers and Natural Language. In. In Peter Gärdenfors (ed.), Generalized Quantifiers. Reidel Publishing Company. 269--298.
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  38. Dag Westerståhl (1985). Determiners and Context Sets. In Generalized Quantifiers in Natural Language. Foris Publications. 45--71.
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  39. Dag Westerståhl (1985). Logical Constants in Quantifier Languages. Linguistics and Philosophy 8 (4):387 - 413.
  40. Dag Westerståhl (1984). Some Results on Quantifiers. Notre Dame Journal of Formal Logic 25 (2):152--169.
  41. Dag Westerståhl (1976). Some Philosophical Aspects of Abstract Model Theory. Dissertation, University of Gothenburg
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