An introduction to non-classical logic (Q2748497)

This welcome book provides, in unified format, treatments of a variety of different propositional logics. We begin with the presumed familiar classical logic, introducing the tableau method of proof for it, and proceed to various systems of modal logic, conditional logics, intuitionist logic, many-valued logics, first-degree entailment, relevant and other paraconsistent logics, and fuzzy logics (including fuzzified relevant logics, p. 222). For each class of logics we have an introduction, semantics (in terms of possible, or in some cases impossible, worlds), rules for tableau-style proofs (except for the fuzzy logics from \({\L}_\aleph)\), a general discussion of some of the distinctive features and of relations among the different logics of the class, examples and counter-examples illustrating these, a starred (omissible) section giving proofs of the appropriate soundness and completeness theorems, a brief (sometimes too brief) history of the circumstances in which logics of that class were introduced, suggestions for further reading, and some (well-devised) problems. There is a recurrent focus on how conditionals behave in each logic, which gives a unity to the project. Using the tableau methods simplifies soundness and (even more so) completeness proofs, and working through them will give the student a good feel for what is, and what is not, valid in each different logic. This book deserves to become the standard textbook in its field.