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A study of logics. (English) Zbl 0763.03003

Oxford Logic Guides. 18. Oxford: Clarendon Press. xiii, 417 p. (1991).
Not all books on logic can be appropriately titled: Introduction to such- and-such. Despite the fact the author may introduce some readers to a rigorous algebraic examination of logics as consequence relations, this book definitely cannot be called introductory. It demands mathematical sophistication, familiarity with standard axiomatic treatment of logic, insight into some of the history of foundational disputes, and to be read as a whole in the order written. For those with the requisite technical and philosophical background, this book is primarily a systematic series of studies of a variety of logics as consequence relations. Nonetheless, the author’s algebraic metalogic, which is developed systematically, along with his pluralistic philosophy gives the book a unity which makes it difficult to focus only on your favorite system. A seminar study may facilitate working through it. Those who work through it will be well rewarded by a deeper appreciation of how nicely the treatment of logics as consequence relations distinguishes the logical form from the material subject of theories, the significance of algebra in metalogic, truth value gaps, entailment logics, intuitionistic logics, modal logics and more. In addition, readers are rewarded with historical and philosophical observations throughout.

MSC:

03-02 Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations
03B22 Abstract deductive systems
03A05 Philosophical and critical aspects of logic and foundations
03G99 Algebraic logic
03Bxx General logic