Abstract
Building on recent connections established between formal models used to study truth and argumentation, we define logics for reasoning about them that we then go on to axiomatize, relying on a link with three-valued Łukasiewicz logic. The first set of logics we introduce are based on formalizing so called skeptical reasoning, and our result shows that a range of semantics that are distinct for particular models coincide at the level of validities. Then, responding to the challenge that our logics do not capture credulous reasoning, we explore modal extensions, leading us to introduce models of three-valued belief induced by argument. We go on to take a preliminary look at some formal properties of this framework, offer a conjecture, then conclude by presenting some challenges for future work.
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Dyrkolbotn, S. (2014). On a Formal Connection between Truth, Argumentation and Belief. In: Colinet, M., Katrenko, S., Rendsvig, R.K. (eds) Pristine Perspectives on Logic, Language, and Computation. ESSLLI ESSLLI 2013 2012. Lecture Notes in Computer Science, vol 8607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44116-9_6
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