  The rich body of physical theories defines the foundation of our
understanding of the world. Its mathematical formulation is based on classical
Aristotelian (binary) logic. In the philosophy of science the ambiguities,
paradoxes, and the possibility of subjective interpretations of facts have
challenged binary logic, leading, among other developments, to Gotthard
G\"unther's theory of polycontexturality (often also termed 'transclassical
logic'). G\"unther's theory explains how observers with subjective perception
can become aware of their own subjectivity and provides means to describe
contradicting or even paradox observations in a logically sound formalism. Here
we summarize the formalism behind G\"unther's theory and apply it to two
well-known examples from physics where different observers operate in distinct
and only locally valid logical systems. Using polycontextural logic we show how
the emerging awareness of these limitations of logical systems entails the
design of mathematical transformations, which then become an integral part of
the theory. In our view, this approach offers a novel perspective on the
structure of physical theories and, at the same time, emphasizes the relevance
of the theory of polycontexturality in modern sciences.
