In the perception action cycle (PAC) all actions that an agent takes must be selecting some part of a possibility space. Rational agents have preferences which order the possibility space, and they maximize the satisfication of those preferences in their selection process.
Two general areas of mathematical study: mereology and order theory are particularily relevant to choice theory. Mereology studies the parts of general structures, which can be applied to study the parts of the possibility space and order theory studies ordering relations which can be applied to studying preferences.
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