ArticleslgStudy

mathematics

Logic Theorist

Logic Theorist is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Logic Theorist rather than just read about it. In short: Logic Theorist is a computer program completed in 1956 by Allen Newell, Herbert A. Simon, and Cliff Shaw.

Key takeaways

  • Logic Theorist belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Logic Theorist to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Logic Theorist from memory before moving on to harder problems.

Reference excerpt

Logic Theorist is a computer program completed in 1956 by Allen Newell, Herbert A. Simon, and Cliff Shaw. It was the first program deliberately engineered to perform automated reasoning, and has been described as "the first artificial intelligence program". Logic Theorist proved 38 of the first 52 theorems in chapter two of Whitehead and Bertrand Russell's Principia Mathematica, and found a new and shorter proof for Theorem 2.85.

History In 1955, when Newell and Simon began to work on the Logic Theorist, the field of artificial intelligence did not yet exist; the term "artificial intelligence" would not be coined until the following summer. Simon was a political scientist who had previously studied the way bureaucracies function as well as developing his theory of bounded rationality (for which he would later win the Nobel Memorial Prize in Economic Sciences in 1978). He believed the study of business organizations requires, like artificial intelligence, an insight into the nature of human problem solving and decision making. Simon has stated that when consulting at RAND Corporation in the early 1950s, he saw a printer typing out a map, using ordinary letters and punctuation as symbols. This led him to think that a machine that could manipulate symbols could simulate decision making and possibly even the process of human thought. The program that printed the map had been written by Newell, a RAND scientist studying logistics and organization theory. For Newell, the decisive moment was in 1954 when Oliver Selfridge came to RAND to describe his work on pattern matching. Watching the presentation, Newell suddenly understood how the interaction of simple, programmable units could accomplish complex behavior, including the intelligent behavior of human beings. "It all happened in one afternoon," he would later say. It was a rare moment of scientific epiphany.

"I had such a sense of clarity that this was a new path, and one I was going to go down. I haven't had that sensation very many times. I'm pretty skeptical, and so I don't normally go off on a toot, but I did on that one. Completely absorbed in it—without existing with the two or three levels consciousness so that you're working, and aware that you're working, and aware of the consequences and implications, the normal mode of thought. No. Completely absorbed for ten to twelve hours." Newell and Simon began to talk about the possibility of teaching machines to think. Their first project was a program that could prove mathematical theorems like the ones used in Bertrand Russell and Alfred North Whitehead's Principia Mathematica. They enlisted the help of computer programmer Cliff Shaw, also from RAND, to develop the program. (Newell says "Cliff was the genuine computer scientist of the three".)

The first version was hand-simulated: they wrote the program onto 3x5 cards and, as Simon recalled:In January 1956, we assembled my wife and three children together with some graduate students. To each member of the group, we gave one of the cards, so that each one became, in effect, a component of the computer program ... Here was nature imitating art imitating nature. They succeeded in showing that the program could successfully prove theorems as well as a talented mathematician. Eventually Shaw was able to run the program on the computer at RAND's Santa Monica facility. In the summer of 1956, John McCarthy, Marvin Minsky, Claude Shannon and Nathan Rochester organized a conference on the subject of what they called "artificial intelligence" (a term coined by McCarthy for the occasion). Newell and Simon proudly presented the group with the Logic Theorist. It was met with a lukewarm reception. Pamela McCorduck writes "the evidence is that nobody save Newell and Simon themselves sensed the long-range significance of what they were doing." Simon confides that "we were probably fairly arrogant about it all" and adds:

They didn't want to hear from us, and we sure didn't want to hear from them: we had something to show them! ... In a way it was ironic because we already had done the first example of what they were after; and second, they didn't pay much attention to it. Logic Theorist soon proved 38 of the first 52 theorems in chapter 2 of the Principia Mathematica. The proof of theorem 2.85 was actually more elegant than the proof produced laboriously by hand by Russell and Whitehead. Simon was able to show the new proof to Russell himself who "responded with delight". They attempted to publish the new proof in The Journal of Symbolic Logic, but it was rejected on the grounds that a new proof of an elementary mathematical theorem was not notable, apparently overlooking the fact that one of the authors was a computer program. Newell and Simon formed a lasting partnership, founding one of the first AI laboratories at the Carnegie Institute of Technology and developing a series of influential artificial intelligence programs and ideas, including the General Problem Solver, Soar, and their unified theory of cognition.

Architecture The Logic Theorist is a program that performs logical processes on logical expressions. The Logic Theorist operates on the following principles:

Expressions An expression is made of elements. There are two kinds of memories: working and storage. Each working memory contains a single element. The Logic Theorist usually uses 1 to 3 working memories. Each storage memory is a list representing a full expression or a set of elements. In particular, it contains all the axioms and proven logical theorems. An expression is an abstract syntax tree, each node being an element with up to 11 attributes. For example, the logical expression ¬ P → ( Q ∧ ¬ P ) {\displaystyle \neg P\to (Q\wedge \neg P)} is represented as a tree with a root element representing → {\displaystyle \to } . Among the attributes of the root element are pointers to the two elements representing the subexpressions ¬ P {\displaystyle \neg P} and Q ∧ ¬ P {\displaystyle Q\wedge \neg P} .

Processes There are four kinds of processes, from the lowest to the highest level.

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Logic Theorist

Start with the simplest possible case. Write down what Logic Theorist claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Logic Theorist before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Logic Theorist ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Logic Theorist

In research
Logic Theorist appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Logic Theorist in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Logic Theorist is common in secondary-school and first-year university syllabi. It links to neighbouring topics History of artificial intelligence, Theorem proving software systems, so understanding it makes those chapters shorter.
In everyday life
Look for Logic Theorist outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Logic Theorist” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Logic Theorist in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Logic Theorist means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Logic Theorist out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Logic Theorist in simple terms?

Logic Theorist is a computer program completed in 1956 by Allen Newell, Herbert A. Simon, and Cliff Shaw.

Why does Logic Theorist matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Logic Theorist?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Logic Theorist.

Tags

  • History of artificial intelligence
  • Theorem proving software systems

Keep exploring