Daily Papers

A characteristic feature of human semantic cognition is its ability to not only store and retrieve the properties of concepts observed through experience, but to also facilitate the inheritance of properties (can breathe) from superordinate concepts (animal) to their subordinates (dog) -- i.e. demonstrate property inheritance. In this paper, we present COMPS, a collection of minimal pair sentences that jointly tests pre-trained language models (PLMs) on their ability to attribute properties to concepts and their ability to demonstrate property inheritance behavior. Analyses of 22 different PLMs on COMPS reveal that they can easily distinguish between concepts on the basis of a property when they are trivially different, but find it relatively difficult when concepts are related on the basis of nuanced knowledge representations. Furthermore, we find that PLMs can demonstrate behavior consistent with property inheritance to a great extent, but fail in the presence of distracting information, which decreases the performance of many models, sometimes even below chance. This lack of robustness in demonstrating simple reasoning raises important questions about PLMs' capacity to make correct inferences even when they appear to possess the prerequisite knowledge.

Strategies for the generation of periodic discrete structures with identical two-point correlation are developed. Starting from a pair of root structures, which are not related by translation, phase inversion or axis reflections, child structures of arbitrary resolution (i.e., pixel or voxel numbers) and number of phases (i.e., material phases/species) can be generated by means of trivial embedding based phase extension, application of kernels and/or phase coalescence, such that the generated structures inherit the two-point-correlation equivalence. Proofs of the inheritance property are provided by means of the Discrete Fourier Transform theory. A Python 3 implementation of the results is offered by the authors through the Github repository https://github.com/DataAnalyticsEngineering/EQ2PC in order to make the provided results reproducible and useful for all interested readers. Examples for the generation of structures are demonstrated, together with applications in the homogenization theory of periodic media.

This paper addresses the problem of formalizing and quantifying the concept of "intensional inheritance" between two concepts. We begin by conceiving the intensional inheritance of W from F as the amount of information the proposition "x is F " provides about the proposition "x is W. To flesh this out, we consider concepts F and W defined by sets of properties left{F_{1}, F_{2}, ldots, F_{n}right} and left{W_{1}, W_{2}, ldots, W_{m}right} with associated degrees left{d_{1}, d_{2}, ldots, d_{n}right} and left{e_{1}, e_{2}, ldots, e_{m}right}, respectively, where the properties may overlap. We then derive formulas for the intensional inheritance using both Shannon information theory and algorithmic information theory, incorporating interaction information among properties. We examine a special case where all properties are mutually exclusive and calculate the intensional inheritance in this case in both frameworks. We also derive expressions for P(W mid F) based on the mutual information formula. Finally we consider the relationship between intensional inheritance and conventional set-theoretic "extensional" inheritance, concluding that in our information-theoretic framework, extensional inheritance emerges as a special case of intensional inheritance.