Graded properties are ubiquitous in human discourse and reasoning. They are characterized by the fact that they may apply with different intensity to different objects. Typical examples are vague properties (e.g. “tall” or “rich”), that is, those that do not establish a clear distinction between objects that satisfy them and those that do not, and hence have blurry boundaries and borderline cases, and generate sorites paradoxes. But also many properties with well-defined boundaries can be seen as graded (e.g. “acute angle” or “guilty”). Seen as a science of correct reasoning, Logic should, in particular, explain the notion of consequence in scenarios involving graded properties. We aim at developing a logical framework for reasoning with graded properties that, by employing formal tools from mathematical fuzzy logic, goes beyond the simple classical bivalent analysis. In particular, we plan a new analysis of sorites paradoxes, a study of relations to other graded theories in linguistics, and an account of counterfactual and defeasible reasoning with graded notions.