•  408
    Tractability and the computational mind
    with Rineke Verbrugge
    In 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
  •  186
    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
  •  143
    Semantic bounds for everyday language
    Semiotica 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
  •  138
    Branching Quantification v. Two-way Quantification
    Journal 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
  •  133
    Comprehension of Simple Quantifiers: Empirical Evaluation of a Computational Model
    with Marcin Zajenkowski
    Cognitive 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
  •  107
    Logic in Cognitive Science: Bridging the Gap between Symbolic and Connectionist Paradigms
    Journal 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.
  •  92
    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
  •  86
    Exploring the tractability border in epistemic tasks
    with Cédric Dégremont and Lena Kurzen
    Synthese 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
  •  80
    Quantifiers and Working Memory
    with Marcin Zajenkowski
    In Maria Aloni & Katrin Schulz (eds.), Amsterdam Colloquium 2009, LNAI 6042, Springer. 2010.
    The paper presents a study examining the role of working&lt;br&gt;memory in quantifier verification. We created situations similar to the&lt;br&gt;span task to compare numerical quantifiers of low and high rank, parity&lt;br&gt;quantifiers and proportional quantifiers. The results enrich and support&lt;br&gt;the data obtained previously in and predictions drawn from a computational&lt;br&gt;model.
  •  80
    Computational complexity of some Ramsey quantifiers in finite models
    Bulletin 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
  •  80
    Hintikka's thesis revisited
    Bulletin 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.
  •  74
    A Computational Approach to Quantifiers as an Explanation for Some Language Impairments in Schizophrenia
    with Marcin Zajenkowski and Rafał Styła
    Journal 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
  •  73
    Tractable versus Intractable Reciprocal Sentences
    with Oliver Bott and Fabian Schlotterbeck
    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
  •  65
    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
  •  65
    This 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
  •  62
    Contribution of Working Memory in the Parity and Proportional Judgments
    with Marcin Zajenkowski
    Belgian 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
  •  60
    Learnability and Semantic Universals
    Semantics 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
  •  60
    We 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
  •  59
    A remark on collective quantification
    with Juha Kontinen
    Journal 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
  •  53
    Almost All Complex Quantifiers are Simple
    In 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.
  •  49
    The 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
  •  44
    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.
  •  42
    Understanding Quantifiers in Language
    with Marcin Zajenkowski
    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.
  •  42
    Pragmatic identification of the witness sets
    with Livio Robaldo
    Proceeding 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
  •  42
    Improving Methodology of Quantifier Comprehension Experiments
    with Marcin Zajenkowski
    Neuropsychologia 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
  •  35
    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
  •  33
    Conjoining Meanings: Semantics without Truth Values
    Philosophical Review 130 (1): 171-175. 2021.
  •  32
    On the Identification of Quantifiers' Witness Sets: A Study of Multi-quantifier Sentences
    with Livio Robaldo and Ben Meijering
    Journal 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
  •  31
    Parameterized Complexity of Theory of Mind Reasoning in Dynamic Epistemic Logic
    with Iris van de Pol and Iris van Rooij
    Journal 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