Charles Peirce's method of studying semiotics is:

Charles Peirce's method of studying semiotics is described as semi-scientific.

His logic-based, systematic study of signs sought rigour yet stopped short of a full natural science.

Calling it experimental wrongly implies laboratory manipulation, which his sign theory did not employ.

Labelling it historical misreads it as a study of past development rather than a logic of signs.

Terming it semi-legal has no bearing on his triadic theory of signs and their signification.

His semiotics, grounded in logic and classification of signs, is thus best called semi-scientific.

Peirce's triad of icon, index and symbol underpins this approach.