The complexity of the warranted formula problem in propositional argumentation

Gorogiannis, Nikos ORCID: https://orcid.org/0000-0001-8660-6609 and Hirsch, Robin (2010) The complexity of the warranted formula problem in propositional argumentation. Journal of Logic and Computation, 20 (2) . pp. 481-499. ISSN 0955-792X [Article] (doi:10.1093/logcom/exp074)

Abstract

The notion of warrant or justification is one of the central concepts in formal models of argumentation. The dialectical definition of warrant is expressed in terms of recursive defeat: an argument is warranted if each of its counter-arguments is itself defeated by a warranted counter-argument. However, few complexity results exist on checking whether an argument is warranted in the context of deductive models of argumentation, i.e. models where an argument is a deduction of a claim from a set of premises using some logic. We investigate the computational complexity of checking whether a claim is warranted in propositional argumentation under two natural definitions of warrant and show that it is PSPACE-complete in both cases.

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