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Symmetry plays an important role in human reasoning about physical systems. Symmetry has been used as a constraint when deriving models for specific systems (as in dimensional analysis) as well as for physical laws. After reviewing human reasoning by symmetry in physics, this paper formalizes a symmetry-based reasoning. In dimensional analysis, only the scale symmetry for unit of measure of independent dimension is used to derive models. Symmetry-based reasoning is considered to be a generalization of dimensional analysis in the sense that it can take any symmetry and that it can deal with equations of physical laws as well as models of specific systems. Symmetry-based reasoning can be viewed as a symbolic version of finding fixed points where constraints are also given by symmetries represented by a symbolic level. In contrast to finding numerical fixed points of a given function, there are no systematic procedures for finding an invariant form. However, heuristics based on the strength of symmetry is given for efficiency. This symmetry-based reasoning system has been implemented as a symbolic-processing system with a production system and a formula-processing system.
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