Talk about the evolution of calculation ideas to make machine certificates and reasoning ideas
----------- The possibility of the evolution proof and reasoning
Author: ESSAYS (percylee@126.com)
Abstract: This article discusses the possibility of making machine certificates and reasoning efforts by evolutionary calculation ideas, and proposes the concepts and preliminary frameworks of evolution proof and reasoning, and this is an overview of evolutionary proof and reasoning.
Keywords: machine certification and reasoning, evolutionary calculation, evolutionary certificate and reasoning, artificial intelligence
Certification and reasoning are intelligent advanced expressions; the machine proof and reasoning is one of the core areas of manual intelligence. In recent years, China has achieved impressive results, especially Mr. Wu Wenjun and his "Wu method", created a new situation of geometric theorem and even the machine certificate, and launched its " Dream of mathematical mechanization. Evolution calculation, as an emerging calculation model, its success is sufficient to become the basis of intelligent calculations. As a self-organized, adaptive system, evolutionary calculation based on random search strategies, has extensive adaptability. From a few months ago, according to the experience of the evolution calculation, with a little machine certificate, I started thinking about this question: Can you make a machine certificate and reasoning work according to the idea of evolutionary calculations? In this way, we can give one new definition, may wish to call evolution proof and reasoning. I have no detailed information on "Wu Method", only to find short descriptions, not enough to learn from. So the following discussion is naturally not deployed by the machine of the geometric theorem, but starts from the form system. Of course, from the form of a system, the proof and the reasoning process is to strictly logically reasoning the axiom and form rules, and the basic strategy of evolution is a random strategy, and how it is integrated, letting evolution calculate good for machine certificates What about the reasoning service? In other words, is this idea possible and effective? Below I started from the initial idea, I mainly talk about this problem, and in this process, some new definitions are given, trying to display the initial framework of evolution proof and reasoning.
Data expression form
The establishment of the form system is based on the formal language. The idea of evolution calculation is to do machine certificates and reasoning. The first question is: How to find a data expression form, you can fully express form language and form system, which can easily make evolution computing encoding?
If the evolution is proved to reason, such a problem is the first layer of the seed. Don't give a good answer, there are many impulses of ideas, but I don't know how to express it. Form language, we take the first-order language φ as an example, of course, we can join the modal operator □ and ◇, but it is still not necessary. When discussing the vocabulary process of human beings gives us an enlightenment, we will then introduce the proven sequence of modal logic. The first-order language φ, the main components are: 1, non-logical symbols (1) individual constant, such as C; (2) predicate variable elements, such as F; (3) function, such as F; 2, logic symbol ( 1) Individual variable elements, such as X; (2) quantifier symbol (action domain symbol), such as "with $; (3) link symbol, such as Ø, ∧, ∨, →, ↔, etc.; (4) auxiliary symbol, For example, ',', ',', ')', etc., on this basis, there is a definition of items and formulas, we will not repeat it again. Examples of two formulas are as follows: Equation 1: α → (β → α) ;
Equation 2: "x (α → β) → (" xα → "x β);
Obviously, the formal system Kφ of the first-order word logic calculation, which is axiom (K1) and (K6), respectively. These logical formulas are very rich. Don't consider others, we ask, what form is used as the form of our data expression? For mathematical discussions, use "string" is very good. But for our discussion, it is not the case, the algorithm design is too complicated, there are many problems to face. For example, formula (1) is a axiom, but its form is not unique, is also equivalent to the following formula: Formula 3: α → (β →) → α);
But if you want the machine to understand this, it is quite complicated to use the algorithm that uses a string. Never use more complex formulas. There is a more natural expression, which is the tree structure of "tree", formula (1) and formula (3): This seems to be very convenient (let's talk about it), and for evolutionary coding It is also very easy. However, the problem is coming soon, how is the formula (2) express? This limited domain information, how is it convenient to express, and take care of the evolution calculation coding efficiency?
This problem has plagued me before and after, I wanted to transform the tree structure, and I wanted to use a broad meter, and then I came back to transform the tree structure. Preliminary, we give the following expression system: It should be noted that P is a pointer, pointing to (3) contact or empty, and string_VAL in (3), can be as follows: String: "x1" x2 $ y. For the treatment of the predicate variable elements and the coupling words, the number of pointers that the latter point to the subtree is constant; and the processing of the individual constant and individual variable elements is also the same. Thus, we can express the formula (2) as follows: where the three defined domain contacts are: string_val1: "x; string_val2:" x; string_val3: "x., Α and β are formulas, essentially It is a subtree, so they are expressed as a node with a P pointer. Use this expression, we can basically solve the representation of the form system, if you want to change the logical form of the form of the form, such as we want to discuss modality Logic, the modal operator can be regarded as a monolithic logic operator, indicating similar to Ø. The following discussion is based on the expression of this data. Evolution proof and reasoning related definitions
In order to facilitate further discussion, we need to solve the following problems: the axiom and form rules of the form system, actually represent a class of formulas, how should we handle? How to express a certain relationship between the formula?
For example, for the axiom (k1), two conclusions have been shown in Figure 1 (note that we can see such a tree form as a brief form of the expression of Figure 2). How to determine that they are "the same"? We give the following definition. The formula tree T is based on the expression of Fig. 2, and the formula of the form system given, called the formula tree, remembers T. Figure 3 is a standard form of a formula tree, and Figure 1 is regarded as a corresponding simple form. Formula Tree Sign Set K If the formula tree is a form system, the formal rule or internal theorem, there is a unique equation to describe some of the node relationships in the tree, which represents the axiom, form rule or internal theorem. The essence of the connotation, we call the symbol set of the formula tree, remember to K. For example, for the axiom (K1), there are two different formula trees in Figure 1, the root of the tree is root, the left child is root-> leftchild, the right child is root-> rightchild, the formula tree sign Set as: {root = →, root-> rightchild = →, root-> leftchild = root-> rightchild-> rightchild}.
Arbitrary axiom, formal rules or internal theorem of the family H form system, all of its formula trees are in the same family, and such families correspond to their axiom, form rules or internal theorem is one or one, the family's logo For the logo set of the formula tree, the family is recorded as H. A collection of group O formula trees, if not a family, we call it a group, remember O. Tong family relationship ~ If the two formulas T1 and T2 are in the same family h, T1 and T2 have "same family relationship", remembered ~, after adding small brackets to indicate family name, namely: T1 ~ T2 (h) Equivalent to T1 ∈ H and T2 ∈ H. Thus, according to these concepts, we can write the two formula trees in Figure 1, that is, in the same family, if the formula (1) corresponds to the formula tree T1, the formula (2) corresponds to the formula tree T2 The axiom (K1) corresponds to the family H1, then: T1 to T2 (h1). <未 未> ----------------------------------------- Statement: This article retains All rights
