On an algebraic definition of laws

• Laws of nature can be formalized as many-sorted algebras of a special type.
• Algebraic representations of the laws form a special type of groups.
• For the case when measurement outcomes are real numbers an exhaustive classification of all possible laws can be achieved.

An algebraic definition of laws is formulated, motivated by analyzing points in Euclidean geometry and from considerations of two physical examples, Ohm’s law and Newton’s second law. Simple algebraic examples constructed over a field are presented.