Depicting Falsifiability in Algebraic Modelling

One key distinction between science and pseudoscience lies in whether a theory can, at least in principle, be falsified by empirical measurements. In physics, in particular, the prevailing view is that reality is defined by what can be measured. All minimal theories that are consistent with observed data are regarded as equally valid. However, the possibility that two objects could differ despite sharing all currently measurable properties is often overlooked. As a result, many theories may be considered non-minimal when viewed from a micrological perspective. In this initial attempt, we introduce an algebraic framework to represent minimalist modeling assumptions. From a physical perspective, we explore and analyze weakened forms of the associative and commutative laws. From a mathematical standpoint, we demonstrate that assuming the existence of a weak neutral element leads to the emergence of several transversal algebraic laws. Each of these laws is individually weaker than the combination of associativity and commutativity, but any two of them together are equivalent this combination.