Abstract
Many proposals for logic-based formalizations of argumentation consider an argument as a pair (Φ,α), where the support Φ is understood as a minimal consistent subset of a given knowledge base which has to entail the claim α. In most scenarios, arguments are given in the full language of classical propositional logic which makes reasoning in such frameworks a computationally costly task. For instance, the problem of deciding whether there exists a support for a given claim has been shown to be \(\Sigma^\mathrm{p}_2\)-complete. In order to better understand the sources of complexity (and to identify tractable fragments), we focus on arguments given over formulae in which the allowed connectives are taken from certain sets of Boolean functions. We provide a complexity classification for four different decision problems (existence of a support, checking the validity of an argument, relevance and dispensability) with respect to all possible sets of Boolean functions.
Supported by ANR Algorithms and complexity 07-BLAN-0327-04, WWTF grant ICT 08-028, and DFG grant VO 630/6-2.
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Creignou, N., Schmidt, J., Thomas, M., Woltran, S. (2010). Sets of Boolean Connectives That Make Argumentation Easier. In: Janhunen, T., Niemelä, I. (eds) Logics in Artificial Intelligence. JELIA 2010. Lecture Notes in Computer Science(), vol 6341. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15675-5_12
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DOI: https://doi.org/10.1007/978-3-642-15675-5_12
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