Towards Context-Based Concurrent Formal Theories

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Abstract
We define a kind of simple actions of labelled transition systems. These actions cannot be atomic; consequently, their compositions cannot be inductive. Their informal meaning is that in one simple action we can suppose the maximum of its modifications. Such actions are called hybrid. Then we propose two formal theories on hybrid actions (the hybrid actions are defined there as non-well-founded terms and non-well-founded formulas): group theory and Boolean algebra. Both theories possess many unusual properties such as the following one: the same member of this group theory behaves as multiplicative zero in respect to one members and as multiplicative unit in respect to other members.

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