<p>We introduce a general rough set–based semantic framework for propositional logics that are not algebraizable in the sense of Blok–Pigozzi. The approach is based on the identification of a well-behaved algebraizable fragment of the language, which is interpreted as an <i>observational level</i> over the space of algebraic valuations. This restriction induces a natural indistinguishability relation and, consequently, non-trivial rough approximations in the sense of Pawlak. Within this setting, semantic indeterminacy emerges as a structural phenomenon generated by the loss of algebraic information under projection onto the chosen fragment. In particular, formulas whose semantic values cannot be reconstructed from the observational level give rise to non-empty rough boundaries. This motivates the notion of <i>rough indeterminacy</i>, which is defined and characterized independently of the derivability of explicit contradictions. The paraconsistent logic <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(C_\omega \)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mi>ω</mi> </msub> </math></EquationSource> </InlineEquation> is used as a motivating case study, illustrating how rough indeterminacy naturally arises when negation fails to be algebraically determined by the positive fragment. More generally, the proposed framework provides a structural and informational perspective on non-algebraizability and suggests a methodological tool for the semantic analysis of logics whose full language resists standard algebraic treatment.</p>