just said?” or “It’s impossible for me to say I’m sorry.” However, humans don’t stop functioning when that happens, so obviously there is something to understand here.

The first breakthrough in this undertaking was in trying to understand if there were subsets of logic that would be useful while not being prone to the earlier problems found in using logic. Remember, Gödel showed that rich enough mathematics contains problematic statements. Well, he didn’t say it exactly like that, but we’ll keep it at that because his arguments had to do with a deep understanding of XIX^th and early XX^th Centuries mathematics, and we’ll spare the reader here. The issue became, was there, in the mathematics not rich enough, something that could be useful after all? Fortunately, the answer to that was positive, because by the end of the XX^th Century we were interested in new things like a formal description of content, something that was not the purpose of earlier mathematics. So was born a new field of science called description logic, which is wonderfully described in The Description Logic Handbook, edited by Franz Baader, Diego Calvanese, Deborah McGuinness, Danielle Nardi and Peter Patel-Schneider. Description logic allows the organization of vast amounts of data in such a way that we can reason on them without having to fear falling into inconclusive results. To come back to our previous example, descriptive logic allows us to teach a computer that children of the same parents are brothers and sisters. Now, if the computer learns that John, Mary and Virginia all have the same parents, it can deduce that John is the brother of Mary and Virginia. But, wait a minute? Isn’t the word description the same word we used earlier, when we saw that the Web community had found a way, the resource description framework, to represent relationships on the network? You got it, thanks to description logic, Artificial Intelligence and the Web would concur. Description logic provides the means to describe complex relationship and the resource description framework allows them to be established on a network of computers. Now, we are ready to have a unified, worldwide, reasoned representation of content.

That’s all fine and good, you’ll say, but what about the content itself. What’s in it? What do we represent? Is it limited to songs by Madonna and family relationships? Well, now computers and humans, for the first time, meet on even territory. Computers can now represent complex, human information. But, we know that even humans have difficulty representing their own information. It takes years of studies to barely master one subject of human knowledge; for instance, music or sociology. To really understand the rules of music that are eventually behind Madonna’s success, or to really understand how families flourish in society, clearly these is more than just stating than a song is on an album or that three children are siblings. That’s how we get to our next topic, that of ontology. This will probably one of the most difficult concepts presented in this book, so we’ll make an extra effort here.

Starting in the 1970’s, Artificial Intelligence researchers began thinking of a world where computers would collaborate on complex, human-like tasks. In a word, computers would be agents interacting to solve a given problem, just like humans do. For example, in a military environment some agents would be weapons specialists, some agents would be planning specialists and other agents would make decisions. This way, the researchers could concentrate on each task independently, working on how computers could fulfill the same tasks as a weapon specialist, a planning specialist or a decision maker. The idea then would be that wherever the computer can fulfill some task of the human, it replaces the human in that task. Wherever it cannot, the human stays in control. In time, that idea would become a tenet of automation, as described in Humans and Automation, by Thomas Sheridan. Now, we see that those computer agents, specialized in a domain, must talk to each other. Humans do that naturally, as collaborating on a task is something that language mediates reasonably well. But computers, how would they talk to each other since we don’t know yet how to teach them the language of

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