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Titlebook: Quantifiers and Cognition: Logical and Computational Perspectives; Jakub Szymanik Book 2016 Springer International Publishing Switzerland

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Algorithmic Theory of Meaningof quantifier sentences in various situations. I sometimes refer to the meaning understood in such a way as referential meaning to distinguish it from other possible aspects of meaning. This chapter overviews philosophical and methodological motivations behind the theoretical framework explored in this book.
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Basic Generalized Quantifier Theorygames. Then, I discuss a linguistic question: which of the logically possible quantifiers are actually realized in natural language. In order to provide an answer, I introduce various linguistic properties of quantifiers, including the key semantic notion of monotonicity.
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Algorithmic Theory of Meaningo give a short historical overview of this idea. The procedural approach to meaning seems reasonable for a large part of natural language in many different contexts. Even though the results of the book are independent from philosophical theories of meaning, my research perspective is very much inspi
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Computing Simple Quantifiers with a procedural approach to semantics, given a quantified sentence and a finite model, a semantic automaton computes the truth-value of this sentence in that model. In order to build the semantic automata theory, I first show how to encode finite models as strings of symbols, translating between
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Cognitive Processing of Quantifierstruth-value of sentences with simple quantifiers (like ‘some’, ‘an even number of’, ‘more than 7’, ‘less than half’). As the exact strategies people use to verify quantifier sentences are mostly uncertain, I study optimal (computationally minimal) algorithms that can handle the tasks, i.e., semantic
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Standard Polyadic Liftsrst, I show how to compositionally construct the meaning of such sentences from the meaning of single quantifiers using special semantic operations known as ., i.e., iteration, cumulation, and resumption. Next, I discuss how to extend semantic automata model to cover some of the polyadic quantifiers
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