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  1. Robert van Rooij, Notes.
    Definition 1. A Strict partial order is a structure X, P , with P a binary relation on X that is irreflexive (IR) and Transitive (TR): (IR) ∀x : ¬P (x, x). (TR) ∀x, y, v, w : (P (x, y) ∧ P (y, z)) → P (x, z).
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  2. Robert van Rooij, Vagueness and the Sorites.
    The principle of stability now says that if sentence ϕ is true/false in a model M, then ϕ has to stay true/false if M is getting more precise. Formally, let M = D, I be a refinement of M = D, I . Then it has to be the case that for all ϕ: (i) If VM(ϕ) = 1, then VM (ϕ) = 1. (ii) If VM(ϕ) = 0, then VM (ϕ) = 0.
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  3. Pablo Cobreros, Paul Egré, David Ripley & Robert van Rooij (forthcoming). Vagueness, Truth and Permissive Consequence. In T. Achourioti, H. Galinon, K. Fujimoto & J. Martínez-Fernández (eds.), Volume on Truth. Springer.
    We say that a sentence A is a permissive consequence of a set of premises Gamma whenever, if all the premises of Gamma hold up to some standard, then A holds to some weaker stan- dard. In this paper, we focus on a three-valued version of this notion, which we call strict-to-tolerant consequence, and discuss its fruitfulness toward a uni ed treatment of the paradoxes of vagueness and self-referential truth. For vagueness, st-consequence supports the principle of tolerance; for truth, it (...)
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  4. Pablo Cobreros, Paul Egre, Robert van Rooij & David Ripley (forthcoming). Reaching Transparent Truth. Mind:fzt110.
    This paper presents and defends a way to add a transparent truth predicate to classical logic, such that and A are everywhere intersubstitutable, where all T-biconditionals hold, and where truth can be made compositional. A key feature of our framework, called STTT (for Strict-Tolerant Transparent Truth), is that it supports a non-transitive relation of consequence. At the same time, it can be seen that the only failures of transitivity STTT allows for arise in paradoxical cases.
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  5. Rick Nouwen, Robert van Rooij, Uli Sauerland & Hans-Christian Schmitz (eds.) (forthcoming). Vagueness in Communication. Springer.
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  6. Pablo Cobreros, Paul Egré, David Ripley & Robert van Rooij (2013). Identity, Leibniz's Law and Non-Transitive Reasoning. Metaphysica 14 (2):253-264.
    Arguments based on Leibniz's Law seem to show that there is no room for either indefinite or contingent identity. The arguments seem to prove too much, but their conclusion is hard to resist if we want to keep Leibniz's Law. We present a novel approach to this issue, based on an appropriate modification of the notion of logical consequence.
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  7. Kris De Jaegher & Robert van Rooij (2013). Game-Theoretic Pragmatics Under Conflicting and Common Interests. Erkenntnis:1-52.
    This paper combines a survey of existing literature in game-theoretic pragmatics with new models that fill some voids in that literature. We start with an overview of signaling games with a conflict of interest between sender and receiver, and show that the literature on such games can be classified into models with direct, costly, noisy and imprecise signals. We then argue that this same subdivision can be used to classify signaling games with common interests, where we fill some voids in (...)
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  8. Peter Pagin, Robert van Rooij & Jonas Akerman (2013). Philosophy of Language and Mind. Synthese 190 (10):1731-1733.
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  9. Pablo Cobreros, Paul Egré, David Ripley & Robert van Rooij (2012). Tolerance and Mixed Consequence in the S'valuationist Setting. Studia Logica 100 (4):855-877.
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  10. David Ripley, Pablo Cobreros, Paul Egré & Robert van Rooij (2012). Tolerant, Classical, Strict. Journal of Philosophical Logic 41 (2):347-385.
    In this paper we investigate a semantics for first-order logic originally proposed by R. van Rooij to account for the idea that vague predicates are tolerant, that is, for the principle that if x is P, then y should be P whenever y is similar enough to x. The semantics, which makes use of indifference relations to model similarity, rests on the interaction of three notions of truth: the classical notion, and two dual notions simultaneously defined in terms of it, (...)
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  11. Robert Van Rooij (2012). The Propositional and Relational Syllogistic. Logique Et Analyse 55 (217):85.
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  12. Robert van Rooij & Tikitu de Jager (2012). Explaining Quantity Implicatures. Journal of Logic, Language and Information 21 (4):461-477.
    We give derivations of two formal models of Gricean Quantity implicature and strong exhaustivity in bidirectional optimality theory and in a signalling games framework. We show that, under a unifying model based on signalling games, these interpretative strategies are game-theoretic equilibria when the speaker is known to be respectively minimally and maximally expert in the matter at hand. That is, in this framework the optimal strategy for communication depends on the degree of knowledge the speaker is known to have concerning (...)
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  13. Robert van Rooij (2011). Revealed Preference and Satisficing Behavior. Synthese 179 (1):1-12.
    A much discussed topic in the theory of choice is how a preference order among options can be derived from the assumption that the notion of ‘choice’ is primitive. Assuming a choice function that selects elements from each finite set of options, Arrow (Economica 26:121–127, 1959) already showed how we can generate a weak ordering by putting constraints on the behavior of such a function such that it reflects utility maximization. Arrow proposed that rational agents can be modeled by such (...)
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  14. Pablo Cobreros, Paul Egré, David Ripley & Robert van Rooij (2010). Tolerant, Classical, Strict. Journal of Philosophical Logic 41 (2):347-385.
    In this paper we investigate a semantics for first-order logic originally proposed by R. van Rooij to account for the idea that vague predicates are tolerant, that is, for the principle that if x is P, then y should be P whenever y is similar enough to x. The semantics, which makes use of indifference relations to model similarity, rests on the interaction of three notions of truth: the classical notion, and two dual notions simultaneously defined in terms of it, (...)
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  15. Robert van Rooij (2010). Introduction. Synthese 174 (1):1-3.
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  16. Robert Van Rooij (2010). Implicit Versus Explicit Comparatives. In Paul Egre & Nathan Klinedinst (eds.), Vagueness and Language Use. Palgrave Macmillan.
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  17. Robert van Rooij (2009). Review of Joseph Almog, Paolo Leonardi (Eds.), The Philosophy of David Kaplan. [REVIEW] Notre Dame Philosophical Reviews 2009 (9).
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  18. Krzysztof R. Apt & Robert van Rooij (eds.) (2008). New Perspectives on Games and Interactions. Amsterdam University Press.
    This volume is a collection of papers presented at the colloquium, and it testifies to the growing importance of game theory as a tool that can capture concepts ...
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  19. Robert van Rooij (2008). Games and Quantity Implicatures. Journal of Economic Methodology 15 (3):261-274.
    In this paper we seek to account for scalar implicatures and Horn's division of pragmatic labor in game?theoretical terms by making use mainly of refinements of the standard solution concept of signaling games. Scalar implicatures are accounted for in terms of Farrell's (1993) notion of a ?neologism?proof? equilibrium together with Grice's maxim of Quality. Horn's division of pragmatic labor is accounted for in terms of Cho and Kreps? (1987) notion of ?equilibrium domination? and their ?Intuitive Criterion?
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  20. Robert van Rooij, Optimality-Theoretic and Game-Theoretic Approaches to Implicature. Stanford Encyclopedia of Philosophy.
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  21. Robert van Rooij (2008). Towards a Uniform Analysis of Any. Natural Language Semantics 16 (4):297-315.
    In this paper, Universal any and Negative Polarity Item any are uniformly analyzed as ‘counterfactual’ donkey sentences (in disguise). Their difference in meaning is reduced here to the distinction between strong and weak readings of donkey sentences. It is shown that this explains the universal and existential character of Universal- and NPI-any, respectively, and the positive and negative contexts in which they are licensed. Our uniform analysis extends to the use of any in command and permission sentences. It predicts that (...)
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  22. Anton Benz & Robert van Rooij (2007). Optimal Assertions, and What They Implicate. A Uniform Game Theoretic Approach. Topoi 26 (1):63-78.
    To determine what the speaker in a cooperative dialog meant with his assertion, on top of what he explicitly said, it is crucial that we assume that the assertion he gave was optimal. In determining optimal assertions we assume that dialogs are embedded in decision problems (van Rooij 2003) and use backwards induction for calculating them (Benz 2006). In this paper, we show that in terms of our framework we can account for several types of implicatures in a uniform way, (...)
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  23. Gerhard Jäger & Robert van Rooij (2007). Language Structure: Psychological and Social Constraints. Synthese 159 (1):99 - 130.
    In this article we discuss the notion of a linguistic universal, and possible sources of such invariant properties of natural languages. In the first part, we explore the conceptual issues that arise. In the second part of the paper, we focus on the explanatory potential of horizontal evolution. We particularly focus on two case studies, concerning Zipf’s Law and universal properties of color terms, respectively. We show how computer simulations can be employed to study the large scale, emergent, consequences of (...)
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  24. Robert van Rooij (2007). The Stag Hunt and the Evolution of Social Structure. Studia Logica 85 (1):133-138.
  25. Katrin Schulz & Robert Van Rooij (2006). Pragmatic Meaning and Non-Monotonic Reasoning: The Case of Exhaustive Interpretation. [REVIEW] Linguistics and Philosophy 29 (2):205 - 250.
    In this paper an approach to the exhaustive interpretation of answers is developed. It builds on a proposal brought forward by Groenendijk and Stokhof (1984). We will use the close connection between their approach and McCarthy’s (1980, 1986) predicate circumscription and describe exhaustive interpretation as an instance of interpretation in minimal models, well-known from work on counterfactuals (see for instance Lewis (1973)). It is shown that by combining this approach with independent developments in semantics/pragmatics one can overcome certain limitations (...)
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  26. Robert van Rooij (2006). Pragmatic Value and Complex Sentences. Mind and Matter 4 (2):195-218.
    We investigate to what extent it is possible to determine a reasonable default pragmatic value of complex sentences in a compositional manner, and --when combined with a Boolean semantics --to see under which conditions it gives rise to reasonable predictions. We discuss several notions of pragmatic value, or relevance, and compare their behavior over complex sentences. Although the goal-oriented notions of relevance give rise to the same ordering relations between propositions,the conditions under which they behave 'compositionally' vary significantly.
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  27. Robert van Rooij & Katrin Schulz (2004). Exhaustive Interpretation of Complex Sentences. Journal of Logic, Language and Information 13 (4):491-519.
    In terms of Groenendijk and Stokhofs (1984) formalization of exhaustive interpretation, many conversational implicatures can be accounted for. In this paper we justify and generalize this approach. Our justification proceeds by relating their account via Halpern and Moses (1984) non-monotonic theory of only knowing to the Gricean maxims of Quality and the first sub-maxim of Quantity. The approach of Groenendijk and Stokhof (1984) is generalized such that it can also account for implicatures that are triggered in subclauses not entailed by (...)
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