Basic Logic: Core Notions
In these series we will introduce some of the concepts behind the tech of Tau, the first-ever platform that will be able to take the thoughts, advice, and knowledge of its users and update its own software in real-time by having its users write in logical languages that both machines and people can read and understand.
You will not need to be able to apply logic in order to enjoy Tau, but it is useful to familiarize yourself with its foundations in order to understand why we as a team are so passionate about Logical AI and the power it will give to Tau and you, the future tauists.
Just as with many other modern-day widely used concepts, there is not a single definition of Logical AI, but many proposed definitions. As expected, some people are better at defining it than others; those are the people who actually work hands-on in the field and/or have contributed to its creation and development. John McCarthy, the computer and cognitive scientist in one who actually co-authored the coinage of the term “Artificial Intelligence”, wrote in 2000:
Logical AI involves representing knowledge of an agent’s world, its goals and the current situation by sentences in logic. The agent decides what to do by inferring that a certain action or course of action is appropriate to achieve the goals. (McCarthy, 2000)
If we tell you that John McCarthy was the recipient in 1971 of the prestigious Turing Award, given yearly by the Association for Computing Machinery (ACM) and internationally recognized as the highest distinction in computer science, then you know that we chose just the right guy to define what Logical AI, or Logic-based AI, is.
We can extract two keywords from the above quotation, to wit, “knowledge representation” and “inference.” Let us start with inference. Everybody learned in high school that given two or more sentences you may infer another sentence if there is a logical connection between them. One of the simplest rules for this is called modus ponens*: Suppose you are given the sentences (1) “If device X is not turned on, then ask the user to turn device X on.” and (2) “Device X is not turned on.” If you apply the modus ponens logical rule, then you output (3) “Ask the user to turn device X on.”
You apply modus ponens all the time, often automatically, but think twice if you assume this is trivial; in fact, as Allen Newell, another recipient of the Turing Award (in 1975 jointly with Herbert A. Simon), did put it, this is big magic. Where does the big magic lie, you may wonder. Well, just think that your agent is a machine, and not a human; your machine needs to be able to identify device X among all the many internal and external hardware items that constitute both itself and its environment (its world), and it needs to be able to detect that device X is turned off, or is not turned on (while this might sound the same to you, it involves logical negation, which can be very messy, especially in databases).
Moreover, when not malfunctioning, your machine does not apply modus ponens spontaneously as, say, following an inspiration; there must be a goal to be accomplished in its world that prompts the application of this rule. Suppose you gave the machine the instruction to print a document and that device X is the printer connected to your machine; it will only go to the extra step of informing you that you must turn the printer on if it represents its knowledge of the current state of its world as “Device X is the printer” and “The printer is not turned on”, and thus the request cannot be fulfilled without your intervention.
So, remember these two keywords, “inference” and “knowledge representation”, because they will feature profusely in our future articles; they are, so to say, the core concepts of Logical AI.
* The modus ponens rule (also: affirming the antecedent) is a logical rule of the form: (1) If A, then B.; (2) A. If one has sentences (1) and (2), then one can infer sentence (3) B.
McCarthy, J. (2000). Concept of logical AI. In J. Minker (ed.), Logic-based artificial intelligence (pp. 37–56). Kluwer.