Quantitative Claim-Centric Reasoning in Logic-Based Argumentation

Argumentation is a well-established formalism for nonmonotonic reasoning with popular frameworks being Dung's abstract argumentation (AFs) or logic-based argumentation (Besnard-Hunter's framework). Structurally, a set of formulas forms support for a claim if it is consistent, subsetminimal, and implies the claim. Then, an argument comprises a support and a claim. We observe that the computational task (ARG) of asking for support of a claim in a knowledge base is "brave", since many claims with a single support are accepted. As a result, ARG falls short when it comes to the question of confidence in a claim, or claim strength. In this paper, we propose a concept for measuring the (acceptance) strength of claims, based on counting supports for a claim. Further, we settle classical and structural complexity of counting arguments favoring a given claim in propositional knowledge bases (KBs). We introduce quantitative reasoning to measure the strength of claims in a KB and to determine the relevance strength of a formula for a claim.