Tractability and the computational mind

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 effective algorithms is hardly possible. Some problems need too much computational resource, e.g., time or memory, to be practically computable. Computational complexity theory is concerned with the amount of resources required for the execution of algorithms and, hence, the inherent difficulty of computational problems. An important goal of computational complexity theory is to categorize computational problems via complexity classes, and in particular, to identify efficiently solvable problems and draw a line between tractability and intractability. We survey how complexity can be used to study computational plausibility of cognitive theories. We especially emphasize methodological and mathematical assumptions behind applying complexity theory in cognitive science. We pay special attention to the examples of applying logical and computational complexity toolbox in different domains of cognitive science. We focus mostly on theoretical and experimental research in psycholinguistics and social cognition

‘Most’ vs ‘More Than Half’: An Alternatives Explanation

While \u27most\u27 and \u27more than half\u27 are generally assumed to be truth-conditionally equivalent, the former is usually interpreted as conveying greater proportions than the latter. Previous work has attempted to explain this difference in terms of pragmatic strengthening or variation in meanings. In this paper, we propose a novel explanation that keeps the truth-conditions equivalence. We support this explanation with a computational model of usage in the Rational Speech Act framework. We find that the difference in typical proportions associated with the two expressions can be explained with previously independently motivated semantic and pragmatic mechanisms

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Complexity/informativeness trade-off in the domain of indefinite pronouns

The vocabulary of human languages has been argued to support efficient communication by optimizing the trade-off between complexity and informativeness (Kemp & Regier 2012). The argument has been based on cross-linguistic analyses of vocabulary in semantic domains of content words such as kinship, color, and number terms. The present work extends this analysis to a category of function words: indefinite pronouns (e.g. someone, anyone, no-one, cf. Haspelmath 2001). We build on previous work to establish the meaning space and featural make-up for indefinite pronouns, and show that indefinite pronoun systems across languages optimize the complexity/informativeness trade-off. This demonstrates that pressures for efficient communication shape both content and function word categories, thus tying in with the conclusions of recent work on quantifiers by Steinert-Threlkeld (2019). Furthermore, we argue that the trade-off may explain some of the universal properties of indefinite pronouns, thus reducing the explanatory load for linguistic theories

A note on a generalization of the muddy children puzzle

ABSTRACT 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 active (satisfies a form of variety)

Logic in Cognitive Science: Bridging the Gap between Symbolic and Connectionist Paradigms

What can logic contribute to cognitive science? In the early days of cognitive science, logic was taken to play both a descriptive and a normative role in theories of intelligent behavior. Descriptively, human beings were taken to be fundamentally logical, or rational. Normatively, logic was taken t