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444Tractability and the computational mindIn Mark Sprevak & Matteo Colombo (eds.), The Routledge Handbook of the Computational Mind, Routledge. pp. 339-353. 2018.We overview logical and computational explanations of the notion of tractability as applied in cognitive science. We start by introducing the basics of mathematical theories of complexity: computability theory, computational complexity theory, and descriptive complexity theory. Computational philosophy of mind often identifies mental algorithms with computable functions. However, with the development of programming practice it has become apparent that for some computable problems finding effecti…Read more
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191Computational Complexity of Polyadic Lifts of Generalized Quantifiers in Natural LanguageLinguistics and Philosophy 33 (3): 215-250. 2010.We study the computational complexity of polyadic quantifiers in natural language. This type of quantification is widely used in formal semantics to model the meaning of multi-quantifier sentences. First, we show that the standard constructions that turn simple determiners into complex quantifiers, namely Boolean operations, iteration, cumulation, and resumption, are tractable. Then, we provide an insight into branching operation yielding intractable natural language multi-quantifier expressions…Read more
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157Branching Quantification v. Two-way QuantificationJournal of Semantics 26 (4): 329-366. 2009.Next SectionWe discuss the thesis formulated by Hintikka (1973) that certain natural language sentences require non-linear quantification to express their meaning. We investigate sentences with combinations of quantifiers similar to Hintikka's examples and propose a novel alternative reading expressible by linear formulae. This interpretation is based on linguistic and logical observations. We report on our experiments showing that people tend to interpret sentences similar to Hintikka sentence …Read more
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157Semantic bounds for everyday languageSemiotica 2012 (188): 363-372. 2012.We consider the notion of everyday language. We claim that everyday language is semantically bounded by the properties expressible in the existential fragment of second–order logic. Two arguments for this thesis are formulated. Firstly, we show that so–called Barwise's test of negation normality works properly only when assuming our main thesis. Secondly, we discuss the argument from practical computability for finite universes. Everyday language sentences are directly or indirectly verifiable. …Read more
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136Comprehension of Simple Quantifiers: Empirical Evaluation of a Computational ModelCognitive Science 34 (3): 521-532. 2010.We examine the verification of simple quantifiers in natural language from a computational model perspective. We refer to previous neuropsychological investigations of the same problem and suggest extending their experimental setting. Moreover, we give some direct empirical evidence linking computational complexity predictions with cognitive reality.<br>In the empirical study we compare time needed for understanding different types of quantifiers. We show that the computational distinction betwe…Read more
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120Logic in Cognitive Science: Bridging the Gap between Symbolic and Connectionist ParadigmsJournal of the Indian Council of Philosophical Research (2): 279-309. 2010.This paper surveys applications of logical methods in the cognitive sciences. Special attention is paid to non-monotonic logics and complexity theory. We argue that these particular tools have been useful in clarifying the debate between symbolic and connectionist models of cognition.
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105Exploring the tractability border in epistemic tasksSynthese 191 (3): 371-408. 2014.We analyse the computational complexity of comparing informational structures. Intuitively, we study the complexity of deciding queries such as the following: Is Alice’s epistemic information strictly coarser than Bob’s? Do Alice and Bob have the same knowledge about each other’s knowledge? Is it possible to manipulate Alice in a way that she will have the same beliefs as Bob? The results show that these problems lie on both sides of the border between tractability (P) and intractability (NP-har…Read more
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98Quantifiers in TIME and SPACE. Computational Complexity of Generalized Quantifiers in Natural LanguageDissertation, University of Amsterdam. 2009.In the dissertation we study the complexity of generalized quantifiers in natural language. Our perspective is interdisciplinary: we combine philosophical insights with theoretical computer science, experimental cognitive science and linguistic theories. In Chapter 1 we argue for identifying a part of meaning, the so-called referential meaning (model-checking), with algorithms. Moreover, we discuss the influence of computational complexity theory on cognitive tasks. We give some arguments to tre…Read more
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86Quantifiers and Working MemoryIn Maria Aloni & Katrin Schulz (eds.), Amsterdam Colloquium 2009, LNAI 6042, Springer. 2010.The paper presents a study examining the role of working<br>memory in quantifier verification. We created situations similar to the<br>span task to compare numerical quantifiers of low and high rank, parity<br>quantifiers and proportional quantifiers. The results enrich and support<br>the data obtained previously in and predictions drawn from a computational<br>model.
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85Computational complexity of some Ramsey quantifiers in finite modelsBulletin of Symbolic Logic 13 281--282. 2007.The problem of computational complexity of semantics for some natural language constructions – considered in [M. Mostowski, D. Wojtyniak 2004] – motivates an interest in complexity of Ramsey quantifiers in finite models. In general a sentence with a Ramsey quantifier R of the following form Rx, yH(x, y) is interpreted as ∃A(A is big relatively to the universe ∧A2 ⊆ H). In the paper cited the problem of the complexity of the Hintikka sentence is reduced to the problem of computational complexity …Read more
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84Hintikka's thesis revisitedBulletin of Symbolic Logic 13 273. 2007.We discuss Hintikka’s Thesis [Hintikka 1973] that there exist natural language sentences which require non–linear quantification to express their logical form.
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80A Computational Approach to Quantifiers as an Explanation for Some Language Impairments in SchizophreniaJournal of Communication Disorder 44 2011. 2011.We compared the processing of natural language quantifiers in a group of patients with schizophrenia and a healthy control group. In both groups, the difficulty of the quantifiers was consistent with computational predictions, and patients with schizophrenia took more time to solve the problems. However, they were significantly less accurate only with proportional quantifiers, like more than half. This can be explained by noting that, according to the complexity perspective, only proportional q…Read more
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79Tractable versus Intractable Reciprocal SentencesIn J. Bos & S. Pulman (eds.), Proceedings of the International Conference on Computational Semantics 9, . 2011.In three experiments, we investigated the computational complexity of German reciprocal sentences with different quantificational antecedents. Building upon the tractable cognition thesis (van Rooij, 2008) and its application to the verification of quantifiers (Szymanik, 2010) we predicted complexity differences among these sentences. Reciprocals with all-antecedents are expected to preferably receive a strong interpretation (Dalrymple et al., 1998), but reciprocals with proportional or numerical q…Read more
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74A remark on collective quantificationJournal of Logic, Language and Information 17 (2): 131-140. 2008.We consider collective quantification in natural language. For many years the common strategy in formalizing collective quantification has been to define the meanings of collective determiners, quantifying over collections, using certain type-shifting operations. These type-shifting operations, i.e., lifts, define the collective interpretations of determiners systematically from the standard meanings of quantifiers. All the lifts considered in the literature turn out to be definable in second-or…Read more
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72Characterizing Definability of Second-Order Generalized QuantifiersIn L. Beklemishev & R. de Queiroz (eds.), Proceedings of the 18th Workshop on Logic, Language, Information and Computation, Lecture Notes in Artificial Intelligence 6642, Springer. 2011.We study definability of second-order generalized quantifiers. We show that the question whether a second-order generalized quantifier $\sQ_1$ is definable in terms of another quantifier $\sQ_2$, the base logic being monadic second-order logic, reduces to the question if a quantifier $\sQ^{\star}_1$ is definable in $\FO(\sQ^{\star}_2,<,+,\times)$ for certain first-order quantifiers $\sQ^{\star}_1$ and $\sQ^{\star}_2$. We use our characterization to show new definability and non-definability r…Read more
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70This volume on the semantic complexity of natural language explores the question why some sentences are more difficult than others. While doing so, it lays the groundwork for extending semantic theory with computational and cognitive aspects by combining linguistics and logic with computations and cognition. -/- Quantifier expressions occur whenever we describe the world and communicate about it. Generalized quantifier theory is therefore one of the basic tools of linguistics today, studying th…Read more
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69Learnability and Semantic UniversalsSemantics and Pragmatics. forthcoming.One of the great successes of the application of generalized quantifiers to natural language has been the ability to formulate robust semantic universals. When such a universal is attested, the question arises as to the source of the universal. In this paper, we explore the hypothesis that many semantic universals arise because expressions satisfying the universal are easier to learn than those that do not. While the idea that learnability explains universals is not new, explicit accounts of lea…Read more
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66Contribution of Working Memory in the Parity and Proportional JudgmentsBelgian Journal of Linguistics 25 189-206. 2011.The paper presents an experimental evidence on differences in the sentence-picture verification under additional memory load between parity and proportional quantifiers. We asked subjects to memorize strings of 4 or 6 digits, then to decide whether a quantifier sentence is true at a given picture, and finally to recall the initially given string of numbers. The results show that: (a) proportional quantifiers are more difficult than parity quantifiers with respect to reaction time and accuracy; (b) mainta…Read more
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66We study a generalization of the Muddy Children puzzle by allowing public announcements with arbitrary generalized quantifiers. We propose a new concise logical modeling of the puzzle based on the number triangle representation of quantifiers. Our general aim is to discuss the possibility of epistemic modeling that is cut for specific informational dynamics. Moreover, we show that the puzzle is solvable for any number of agents if and only if the quantifier in the announcement is positively acti…Read more
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61Almost All Complex Quantifiers are SimpleIn C. Ebert, G. Jäger, M. Kracht & J. Michaelis (eds.), Mathematics of Language 10/11, Lecture Notes in Computer Science 6149, Springer. 2010.We prove that PTIME generalized quantifiers are closed under Boolean operations, iteration, cumulation and resumption.
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55The paper presents two case studies of multi-agent information exchange involving generalized quantifiers. We focus on scenarios in which agents successfully converge to knowledge on the basis of the information about the knowledge of others, so-called Muddy Children puzzle and Top Hat puzzle. We investigate the relationship between certain invariance properties of quantifiers and the successful convergence to knowledge in such situations. We generalize the scenarios to account for public announce…Read more
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55On theTractability of Comparing Informational StructuresIn J. van Eijck & R. Verbrugge (eds.), Proceedings of the Workshop 'Reasoning about other minds: Logical and cognitive perspectives, . 2011.
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49Pragmatic identification of the witness setsProceeding of the 8th Conference on Language Resources and Evaluation. 2012.Among the readings available for NL sentences, those where two or more sets of entities are independent of one another are particularly challenging from both a theoretical and an empirical point of view. Those readings are termed here as ‘Independent Set (IS) readings'. Standard examples of such readings are the well-known Collective and Cumulative Readings. (Robaldo, 2011) proposes a logical framework that can properly represent the meaning of IS readings in terms of a set-Skolemization of the …Read more
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44Improving Methodology of Quantifier Comprehension ExperimentsNeuropsychologia 47 (12): 2682--2683. 2009.Szymanik (2007) suggested that the distinction between first-order and higher-order quantifiers does not coincide with the computational resources required to compute the meaning of quantifiers. Cognitive difficulty of quantifier processing might be better assessed on the basis of complexity of the minimal corresponding automata. For example, both logical and numerical quantifiers are first-order. However, computational devices recognizing logical quantifiers have a fixed number of states while…Read more
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44The Computational Complexity of Quantified ReciprocalsIn Peter Bosch, David Gabelaia & Jérôme Lang (eds.), Lecture Notes on Artificial Intelligence 5422, Logic, Language, and Computation 7th International Tbilisi Symposium on Logic, Language, and Computation, Springer. 2009.We study the computational complexity of reciprocal sentences with quantified antecedents. We observe a computational dichotomy between different interpretations of reciprocity, and shed some light on the status of the so-called Strong Meaning Hypothesis.
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42Understanding Quantifiers in LanguageIn N. A. Taatgen & H. van Rijn (eds.), Proceedings of the 31st Annual Conference of the Cognitive Science Society, . 2009.We compare time needed for understanding different types of quantifiers. We show that the computational distinction between quantifiers recognized by finite-automata and pushdown automata is psychologically relevant. Our research improves upon hypothesis and explanatory power of recent neuroimaging studies as well as provides evidence for the claim that human linguistic abilities are constrained by computational complexity.
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36Parameterized Complexity of Theory of Mind Reasoning in Dynamic Epistemic LogicJournal of Logic, Language and Information 27 (3): 255-294. 2018.Theory of mind refers to the human capacity for reasoning about others’ mental states based on observations of their actions and unfolding events. This type of reasoning is notorious in the cognitive science literature for its presumed computational intractability. A possible reason could be that it may involve higher-order thinking. To investigate this we formalize theory of mind reasoning as updating of beliefs about beliefs using dynamic epistemic logic, as this formalism allows to parameteri…Read more
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36On the Identification of Quantifiers' Witness Sets: A Study of Multi-quantifier SentencesJournal of Logic, Language and Information 23 (1): 53-81. 2014.Natural language sentences that talk about two or more sets of entities can be assigned various readings. The ones in which the sets are independent of one another are particularly challenging from the formal point of view. In this paper we will call them ‘Independent Set (IS) readings’. Cumulative and collective readings are paradigmatic examples of IS readings. Most approaches aiming at representing the meaning of IS readings implement some kind of maximality conditions on the witness sets inv…Read more
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35A Note on some Neuroimaging Study of Natural Language Quantifiers ComprehensionNeuropsychologia 45 (9): 2158-2160. 2007.We discuss McMillan et al. (2005) paper devoted to study brain activity during comprehension of sentences with generalized quantifiers. According to the authors their results verify a particular computational model of natural language quantifier comprehension posited by several linguists and logicians (e. g. see van Benthem, 1986). We challenge this statement by invoking the computational difference between first-order quantifiers and divisibility quantifiers (e. g. see Mostowski, 1998). Moreover, we …Read more
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Philosophy of Language |
Logic and Philosophy of Logic |
Philosophy of Computing and Information |
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Generalized Quantifiers |