Law-thinking is an approach in which action and reasoning are thought to have theoretical criteria (laws) specifying the optimal actions and belief adjustments in any given situation. These criteria may be impossible to apply to a situation directly, and one may be forced to use only rough approximations. But one can still evaluate the approximations based on how well they match the optimal criteria.
The relationship between laws and approximations resembles that of between physics and engineering. Physics specify the laws by which the world works, while engineering tries to find practical solutions as constrained by those laws.
Some concepts which have been used as theoretical criteria in law-thinking:
Bayes Theorem is a law of probability that describes the proper way to incorporate new evidence into prior probabilities to form an updated probability estimate.
Decision Theory studies the general laws for choosing between actions in any given situation.
Solomonoff Induction is a theoretically optimal way of arriving at true beliefs, though impossible to use directly. AIXI is an AI design based on Solomonoff Induction; it is also impossible to build directly, but some approximations exist.
Note that one can make use of e.g. Bayes Theorem or decision theory without being a law-thinker. Thus, articles covering the above topics do not automatically fall under this tag. A “toolbox-thinker” may use such tools if that seems warranted, without considering them normative standards to compare things against. This difference is discussed in Toolbox-thinking and Law-thinking.