RS-frames were introduced by Gehrke as relational semantics for substructural logics. They are two-sorted structures, based on RS-polarities with additional relations used to interpret modalities. We propose an intuitive, epistemic interpretation of RS-frames for modal logic, in terms of categorization systems and agents' subjective interpretations of these systems. Categorization systems are a key to any decision-making process and are widely studied in the social and management sciences. A set of objects together with a set of properties and an incidence relation connecting objects with their properties forms a polarity which can be 'pruned' into an RS-polarity. Potential categories emerge as the Galois-stable sets of this polarity, just like the concepts of Formal Concept Analysis. An agent's beliefs about objects and their properties (which might be partial) is modelled by a relation which gives rise to a normal modal operator expressing the agent's beliefs about category membership. Fixed-points of the iterations of the belief modalities of all agents are used to model categories constructed through social interaction.

Categorization systems are widely studied in psychology, sociology, and organization theory as information-structuring devices which are critical to decision-making processes. In the present paper, we introduce a sound and complete epistemic logic of categories and agents' categorical perception. The Kripke-style semantics of this logic is given in terms of data structures based on two domains: one domain representing objects (e.g. market products) and one domain representing the features of the objects which are relevant to the agents' decision-making. We use this framework to discuss and propose logic-based formalizations of some core concepts from psychological, sociological, and organizational research in categorization theory.Comment: In Proceedings TARK 2017, arXiv:1707.0825

Research Summary Game theory suggests that, in oligopolistic markets characterized by nonprice competition, dominant incumbents can use product proliferation to occupy a region of the product space (i.e., a subspace) and deter rivals from imitating their products. In part, this is because product proliferation makes the introduction of close substitutes comparatively less profitable; in part, it is because the strategy conveys a threat of retaliation to potential imitators. Yet this threat is only credible if the proliferator has high costs of exit from the occupied region of space. We hypothesize that complexity, as a property of product (sub)spaces, generates exit costs for the proliferator and increases the deterrent power of its strategy. We test this hypothesis by studying sequential product introductions in the U.S. recording industry, 2004–2014. Managerial Summary Differentiated‐product markets are often concentrated in the hands of a few dominant organizations, which strive to keep on equal footing by offering similar products. In these markets, a product proliferation strategy can help one of the dominant incumbents claim a particular submarket as its territory. Investing heavily in that submarket communicates a threat that the proliferator will retaliate against invaders to protect these investments. However, this threat is not credible enough to deter rivals unless the occupied submarket is sufficiently complex in terms of product attributes, as precisely this kind of complexity makes it harder for proliferators to back down if challenged. We find evidence of this mechanism in an analysis of product competition among major record companies and discuss implications for strategic decision‐making. RESOURCES This article has earned an Open Data badge for making publicly available the digitally‐shareable data necessary to reproduce the reported results. The data is available at https://github.com/piazzai/smj-18-19552. Learn more about the Open Practices badges from the Center for Open Science: https://osf.io/tvyxz/wiki.

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Michele (2018) 'Old at heart, young at the periphery : an age-dependence approach to resource partitioning.', Academy of management proceedings., 2018 (1). p. 11589.Further information on publisher's website:https://doi.org/10.5465/AMBPP.2018.31Publisher's copyright statement:Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details.