A New Approach to Quantum Logic

. The reason for including this chapter is to make the book as selfcontained as possible. It should in particular be accessible to physicists, who normally have no training in formal logic. We present the basics of classical propositional logic and non-monotonic logic. In fact, it is possible to provide the reader with all the logical equipment he needs in order to understand the logical investigations in later chapters. The material covered by the introduction to classical propositional logic comprises the following: The language of classical propositional logic The notion of a consequence relation, monotonic or not Presenting classical consequence in (old fashioned) Hilbert style Truth functional semantics Soundness and Completeness Theorem Compactness theorem Deduction theorem The Lindenbaum (-Tarski) algebra This is, in particular, sufficient to enable the reader to understand the logical investigations in the chapters 6, 7 94and10. Basics of Nonmonotonic Logic ¥ 2.1 Basics of Classical Propositional Logic All the reader needs to know about classical propositional logic is: • The Deduction Theorem • The Soundness and Completeness Theorem • The Compactness Theorem • The Concept of a Lindenbaum (-Tarski) Algebra