Further Topics in First-Order Logic

We introduce this subject with a parable about two scholars, named Oren and Nero, who were visiting an archaeologist and were shown a recently discovered tablet, the contents of which are reproduced in Figure 4.1. They soon realized that the figures on the tablet were truth tables, and they set about translating them into more familiar notations. (Before proceeding further, the reader is advised to do this for himself for at least a few of the tables.) Oren produced the translation in Figure 4.2, and Nero produced that in Figure 4.3. As they started to show their translations to the archaeologist, Nero modestly remarked “That was really quite easy, as soon as I realized that ⊕ denoted conjunction”. “But you’re wrong!” exclaimed Oren. “⊕ denoted disjunction!” They argued for some time, and neither was able to persuade the other that he was wrong. All they could agree on was that ⊖ denoted negation.