The Logic of Entailment

What is it about?

This is the introduction to the book, The Logic of Entailment and its History. A logic of entailment is a logic that contains a connective that represents deducibility. A formula A->B is true if and only if B is deducible from A. The reason why we need an entailment connective is to be able to represent proof-plans. A proof-plan is a plan that says something like "If I can prove B from A, then if I can prove C from B, I will be able to prove C from A". This is represented in this logic by the formula, (A->B)->((B->C)->(A->C)). This chapter lays out the difficulties encountered by attempts to devise a logic of entailment and thus sets the stage for the rest of the book.

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Why is it important?

The topic is important both because the sort of reasoning studies is prevalent in mathematics and in any science in which deduction is used and because interesting problems appear when attempts are made to create a logic of entailment.