Algebraic Logic

The popular literature on mathematical logic is rather extensive and written for the most varied categories of readers. College students or adults who read it in their free time may find here a vast number of thought-provoking logical problems. The reader who wishes to enrich his mathematical background in the hope that this will help him in his everyday life can discover detailed descriptions of practical (and quite often -- not so practical!) applications of logic. The large number of popular books on logic has given rise to the hope that by applying mathematical logic, students will finally learn how to distinguish between necessary and sufficient conditions and other points of logic in the college course in mathematics. But the habit of teachers of mathematical analysis, for example, to stick to problems dealing with sequences without limit, uniformly continuous functions, etc. has, unfortunately, led to the writing of textbooks that present prescriptions for the mechanical construction of definitions of negative concepts which seem to obviate the need for any thinking on the reader's part. We are most certainly not able to enumerate everything the reader may draw out of existing books on mathematical logic, however.

Contenu

1. Operations on Propositions.- 2. Logical Functions. Normal Forms.- 3. Law of Duality in Algebraic Logic.- 4. Arithmetic Operations in Algebraic Logic.- 5. Monotone Logical Functions.- 6. Functionally Closed Classes and Post's Theorem.- 7. The General Theory of Functionally Closed Classes.- 8. Networks of Functional Elements.- 9. Relay-Contact Networks. Estimating the Complexity of a Contact Network.- 10. Elements of Probabilistic Logic.- 11. Multi-Valued Logics.- 12. Predicate Logic.- Literature.