Chapter 5 Propositions and Inference

For when I am presented with a false theorem, I do not need to examine or even to know the demonstration, since I shall discover its falsity a posteriori by means of an easy experiment, that is, by a calculation, costing no more than paper and ink, which will show the error no matter how small it is …

And if someone would doubt my results, I should say to him: “Let us calculate, Sir,” and thus by taking to pen and ink, we should soon settle the question.

– Gottfried Wilhelm Leibniz [1677]

This chapter considers simple forms of reasoning in terms of propositions – statements that can be true or false. Some reasoning includes model finding, finding logical consequences, and various forms of hypothetical reasoning. Semantics forms the foundations of specification of facts, reasoning, and debugging.