Correct Grounded Reasoning with Presumptive Arguments

We address the semantics and normative questions for reasoning with presumptive arguments: How are presumptive arguments grounded in interpretations; and when are they evaluated as correct? For deductive and uncertain reasoning, classical logic and probability theory provide canonical answers to these questions. Staying formally close to these, we propose case models and their preferences as formal semantics for the interpretation of presumptive arguments. Arguments are evaluated as presumptively valid when they make a case that is maximally preferred. By qualitative and quantitative representation results, we show formal relations between deductive, uncertain and presumptive reasoning. In this way, the work is a step to the connection of logical and probabilistic approaches in AI.