More Natural Derivations for Priest, An Introduction to Non-Classical Logic, 2nd ed

In [7] I produced natural derivation systems, including demonstration of soundness and completeness, for each of the logics described in the first edition of Priest, An Introduction to Non-Classical Logic [3]. The first edition of Priest’s book is Part I of the second edition. Eventually, I hope to complete the project, providing natural derivation systems for the quantified versions in Part II. In the meantime, without including parts for soundness and completeness, this document simply extends the previous paper to account for additions and changes in the first part of the new edition. Thus, as before, I provide an alternative or supplement to the semantic tableaux of his text. Some of the derivation systems may also be of interest in their own right. They are all Fitch-style systems on the model of [1, 6], and many other places. Though a classical system is presented for chapter 1, prior acquaintance with some such system is assumed. Associated goaldirected derivation strategies are discussed extensively in [6, chapter 6]. Except that some chapters are collapsed, there are sections for each chapter in the first part of Priest’s book, with an additional section on four-valued relevant logic. In each case, (i) the language is briefly described and key semantic definitions stated, and (ii) the derivation system is presented with a few examples given. For those with interest, demonstration of soundness and completeness should be straightforward given background and strategy from the published paper.
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