The application and prospect of artificial intelligence logic and mathematical logic? 50

Artificial intelligence (AI) is an interdisciplinary discipline that integrates computer science, physiology, and philosophy. The research topics of artificial intelligence cover a wide range of fields, from machine vision to expert systems. The common basic feature is that machines learn to "think".

In order to distinguish whether a machine "thinks" or not, it is necessary to give a definition of "intelligence". To what extent is "thinking" called intelligence? For example, solving complex problems, or being able to generalize and find associations?

What else is "perception", what is "comprehension", and so on? The study of learning processes, language, and sensory perception has helped scientists build intelligent machines. One of the biggest challenges facing AI experts today is how to construct a system that mimics the behavior of a human brain made up of tens of billions of neurons to think about the most complex problems in the universe.

Perhaps the best measure of machine intelligence is the experiment of British computer scientist Alan Turing. He argues that if a computer can trick people into believing that it is a human and not a machine, then it should be called intelligent.

Mathematical Logic" classification. There are 64 entries in this category. *Mathematical Logic .

Sentences (Mathematical Logic).Can. Computability logic · Reliability theorem.

Combine. Oneness · Combination formula. Life.

Propositional Variables · Propositional Logic. Elder brother. Gödel's Incompleteness Theorem · Gödel's Completeness Theorem ...

Quantification (Mathematical Logic).Zero. Zero-order logic.

The development status of artificial intelligence is in the growth period, and due to the relatively small number of related talents, the talent market for artificial intelligence is vacant, and there is a situation where supply exceeds demand. In addition, the state has issued relevant policies to promote the development of artificial intelligence; Some provinces are also paying more attention to the development of artificial intelligence.

Since the establishment of the discipline of mathematical logic, it has developed relatively rapidly, and there are many factors that promote its development. For example, the establishment of non-Euclidean geometry has prompted people to study the non-contradiction between non-Euclidean geometry and Euclidean geometry.

The emergence of set theory is a major event in the development of modern mathematics, but in the process of researching set theory, there is a so-called third major crisis in the history of mathematics. The crisis was caused by the discovery of the paradox of set theory. What is a paradox?

A paradox is a logical contradiction. Set theory is originally a branch of rigorous argumentation and is recognized as the foundation of mathematics.

In 1903, Russell, a British idealist philosopher, logician and mathematician, proposed the "Russell paradox" named after him for set theory, which shook almost the entire foundation of mathematics.

There are many examples of Russell's paradox, one of which is the "barber's paradox": there is a barber in a certain village, and one day he declares that he should only shave those who don't shave himself.

Then the question arises: does the barber shave himself? If he shaves himself, he is the one who shaves himself, and according to his principles, he should not shave himself; If he doesn't shave himself, then he is the one who doesn't shave himself, and according to his principle, he should shave himself.

This creates a contradiction.

The proposition of paradox prompted many mathematicians to study the non-contradiction problem of set theory, which gave rise to an important branch of mathematical logic, axiomatic set theory.

The emergence of non-Euclidean geometry and the discovery of the paradox of set theory show that there are still many problems in mathematics itself, and in order to study the non-contradictory problem of mathematical system, it is necessary to take the concepts, propositions, and proofs of mathematical theoretical systems as the research objects, and study the logical structure of mathematical systems and the laws of proof, so that another branch of mathematical logic is born-proof theory.

Mathematical logic has recently developed many new branches, such as recursive theory and model theory. Recursive theory mainly studies the theory of computability, which is closely related to the development and application of computers. Model theory is the study of the relationship between formal systems and mathematical models.

Mathematical logic has developed particularly rapidly in recent years, mainly because this discipline has had a significant impact on the development of other branches of mathematics such as set theory, number theory, algebra, topology, etc., especially the development of the newly formed computer science. In turn, the development of other disciplines has also promoted the development of mathematical logic.

Because it is a newly emerging and rapidly developing discipline, it also has many problems that need to be studied in depth. Many mathematicians are now working on the problems of mathematical logic itself.

In short, the importance of this discipline has become very obvious, and it has attracted the attention and attention of many people.