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Maximality of the Minimal R-Logic

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Karczewska A. M.

Logic and Logical Philosophy

2018

vol. 27

issue 2

193-203

The minimal system of the connective of realization – T. Jarmużek and A. Pietruszczak’s MR– is examined. The single-index rule is defined. Then it is claimed that if a single– index rule non-derivable in MR is derivable in a strengthening of MR, then the strengthening is inconsistent. This property may be called the single-index maximality.

A Generalisation of a Refutation-related Method in Paraconsistent Logics

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Trybus A.

Logic and Logical Philosophy

2018

vol. 27

issue 2

235-261

This article describes a refutation method of proving maximality of three-valued paraconsistent logics. After outlining the philosophical background related to paraconsistent logics and the refutation approach to modern logic, we briefly describe how these two areas meet in the case of maximal paraconsistent logics. We focus on a method of proving maximality introduced in [34] and [37] that has the benefit of being simple and effective. We show how the method works on a number of examples, thus emphasising the fact that it provides a unifying approach to the search for maximal paraconsistent logics. Finally, we show how the method can be generalised to cover a wide range of paraconsistent logics. We also conduct a small experimental setting that confirms the theoretical results.

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2 Logic and Logical Philosophy

1 Karczewska A. M.

1 Trybus A.

2 2018

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Maximality of the Minimal R-Logic

A Generalisation of a Refutation-related Method in Paraconsistent Logics