We investigate an aspect of defeasibility that has somewhat been overlooked by the nonmonotonic reasoning community, namely that of defeasible modes of reasoning. These aim to formalise defeasibility of the traditional notion of necessity in modal logic, in particular of its different readings as action, knowledge and others in specific contexts, rather than defeasibility of conditional forms. Building on an extension of the preferential approach to modal logics, we introduce new modal operators with which to formalise the notion of defeasible necessity and distinct possibility, and that can be used to represent expected effects, refutable knowledge, and so on. We show how KLM-style conditionals can smoothly be integrated with our richer language. We also propose a tableau calculus which is sound and complete with respect to our modal preferential semantics, and of which the computational complexity remains in the same class as that of the underlying classical modal logic.
Reference:
Britz, K. and Varzinczak, I. 2018. From KLM-style conditionals to defeasible modalities, and back. Journal of Applied Non-Classical Logics, vol. 28(1): 92-121
Britz, K., & Varzinczak, I. (2018). From KLM-style conditionals to defeasible modalities, and back. http://hdl.handle.net/10204/10755
Britz, K, and I Varzinczak "From KLM-style conditionals to defeasible modalities, and back." (2018) http://hdl.handle.net/10204/10755
Britz K, Varzinczak I. From KLM-style conditionals to defeasible modalities, and back. 2018; http://hdl.handle.net/10204/10755.
Copyright: 2018 Taylor & Francis. Due to copyright restrictions, the attached PDF file contains the postprint version of the published item. For access to the published version, kindly consult the publisher's website: https://www.tandfonline.com/doi/full/10.1080/11663081.2017.1397325