Non formal description of calculus, what is formalization? What is a formal model

Formal methods generally describe software in a rigorous, precise way (usually in mathematical language) and model software.

You can think of it as something like UML modeling. It's just that the formal method is more difficult to learn, and you can understand it as various conventions and formulas in discrete mathematics. A formal model is a model that you build using formal methods, which can be analogous to UML models, mathematical modeling, or even programming (programming is also an accurate description of software requirements in a programming language).

The origin of types and type systems, as well as research and development, are independent of OOP. The type system was already used as a means of type checking in the Fortran compiler implementations of the fifties. A generalized type is generally defined as a constraint, i.e., a logical formula.

In the process of studying types, a variety of methods have been generated, such as [C&W 1985] and so on. The algebraic approach is a very good way to establish a formal specification of types. A type in algebra corresponds to a series of elements on which algebraic operations are defined.

At the same time, on this basis, second-order calculus has been used for inheritance and models supported by templates. In both approaches, a type is considered to be a series of elements that satisfy a certain constraint, and in a more abstract way, a type can be treated as a constraint, and the better the constraint we specify, the more precise the set of corresponding defined elements, so logical formulas are the most appropriate tools to describe the characteristics of a type. Here, we don't want to go into the different mathematical models of type theory, what we need to understand is that the connotation of type and type theory, a concept often used in programming languages, is extremely rich, and the development of its own theory is not limited to OOP, but when the two are combined, it has a huge impact on our program view.

1. The definitions are different.

Formal logic: the study of the laws of thinking in the intellectual stage of human cognition, in the narrow sense refers to deductive logic, and in the broad sense, it also includes inductive logic. The law of thinking in formal logic is also the unity of the form of thinking and the content of thinking.

Non-formal logic: Generally refers to logical theories that can be used to analyze, evaluate, and improve non-formal reasoning and argumentation in interpersonal communication, advertising, political debates, court debates, and in newspapers, television, the Internet, and other popular applications.

2. The development history is different.

Formal logic: It has gone through a history of more than 2,000 years, formal logic before the middle of the 19th century is mainly traditional logic, and modern formal logic developed after the middle of the 19th century, commonly known as mathematical logic, also known as symbolic logic.

Non-formal logic: emerged in North America in the 70s of the 20th century, founded by Ralph Johnson and Anthony Blair. They co-authored The Self-Defense of Logic in 1977, an early introductory work that emphasized concrete examples of nonformal reasoning.

In 1978, they organized the first International Symposium on Nonformal Logic and the Institute's Nonformal Logic Newsletter (later renamed Nonformal Logic), marking the formal birth of non-formal logic as an independent discipline.

3. Research is different.

Formal logic: In terms of research methods, formal logic attempts to extend the form of thinking based on a limited content of thinking to the whole of thinking, which is obviously impossible. To prove this, it is useful to assume that formal logic is indeed sound logic.

It is not difficult to find that this kind of logic, which claims to be a model of human logic, does not take into account human emotions and likes and dislikes, and this logic that thinks it is the best at explaining actually uses the theological statement that "because theory A does not meet the requirements of formal logic, it is wrong", which is essentially "because it is wrong", or "because it does not conform to me, it is wrong", and this logic of aspiring to be all-encompassing is at least pale in the face of life events. It can be concluded that this is by no means a logic that can fully reflect the human mind.

Non-formal logic: The main object of study of non-formal logic is the real arguments used by ordinary people in real life. Argumentation is an important carrier for people to communicate, disseminate and express ideas, a powerful tool to persuade and influence the views and positions of others, and the main form of deepening understanding rationally.

Good arguments are persuasive and irrefutable, while bad arguments pale in comparison. Some arguments seem to be reasonable, but they are very confusing, but in fact they cannot stand scrutiny and are logically untenable. Non-formal logic is committed to discovering, analyzing, and developing the standards, procedures, and patterns that people use and analyze arguments in their daily lives, and it does not inherently reject formal methods, but in view of the extremely limited application of formal methods in the daily lives of ordinary people, the formal orientation of non-formal logic and traditional logic research is naturally very different.

The difference between formal logic and non-formal logic is that the definitions are different.

Formal logic is a doctrine that studies the laws of thinking in the intellectual stage of human cognition, which refers to deductive logic in the narrow sense and inductive logic in the broad sense. Non-formal logic: Generally refers to logical theories that can be used to analyze, evaluate, and improve non-formal reasoning and argumentation in interpersonal communication, advertising, political debates, court debates, and in newspapers, television, the Internet, and other popular applications.

Non-formal logic is a branch of logic whose task is to describe the non-formal criteria, scales, and procedures for analyzing, explaining, evaluating, critiquing, and arguing the construction of everyday life.

Difference Between Formal Logic and Dialectical Logic:

1. Dialectical logic.

Dialectical logic is a doctrine that studies the laws of thinking in the stage of human understanding and rationality, including two types or two stages of contradictory logic and symmetrical logic.

Dialectical logic generalizes, approximates, but is an essential reflection of the external world through abstract forms of concept, judgment, reasoning, etc. (see Dialectics of Thinking Forms). Its basic characteristic is to look at the object as a whole, to examine the object in terms of the movement and change of internal contradictions and the interconnection of its various aspects. This logic is different both from the metaphysical way of thinking that sees objects as static and isolated, and from the traditional logic of knowing objects from a static point of view in a pre-made, definite form of thought (see Formal Logic).

The dialectical logic of science, like the revolutionary change of Marxist philosophy in philosophy, is also a major change in the science of thinking. Its emergence is not only a revolution in the metaphysical way of thinking, but also a breakthrough in the traditional concept of logic. It is distinct from and interrelated with Marxist dialectics, epistemology (see dialectical materialist epistemology), and formal logic, thus constituting its own unique nature and function.

2. Formal logic.

The so-called "formal logic" refers to traditional logic, deductive logic in the narrow sense, and inductive logic in the broad sense. The so-called logic is the law of thinking, logic is the doctrine of the law of thinking, and the law of thinking is the unity of the content of thinking and the "form" of thinking. The logic of "form" is also a doctrine that studies the laws of thinking from the unity of content and "form", so it is by no means a pure "formal" logic.

Concept, judgment, and reasoning are the three basic elements of formal logic. The two aspects of the concept are extension and connotation, extension refers to the scope of things included in the concept, and connotation refers to the meaning and nature of the concept; Judgments are qualitatively divided into positive judgments and negative judgments, and quantitatively divided into full-name judgments, special judgments and singular judgments. Reasoning is the highest form of thinking, concepts constitute judgment, judgment constitutes reasoning, and in general, human thinking is determined by these three elements.

It requires thinking to satisfy the law of identity, the law of contradiction, the law of exclusion, and the law of sufficient reason. These four laws require that thinking must be deterministic, non-contradictory, consistent and demonstrative.

Formal logic is either/or, and logical contradictions cannot be allowed.

Formal logic is reasoning according to certain rules of logical reasoning and following certain steps, while non-formal logic is the logical thinking reasoning commonly used in our daily life.

Formal logic is to talk about how correct thinking comes about, and it is a summary and summary of human correct thinking.

Non-formal logic is wrong thinking, and it is the rhetoric of Western religion to criticize and oppose formal logic in order to fool and deceive the common people. For example, the sun revolves around the earth, 1+1=3, referring to a deer as a horse, etc., are all non-formal logic.

The formal methods used to develop computer systems are mathematically based techniques that describe the properties of the system, and such formal methods provide a framework within which the system can be described, developed, and validated in a systematic, rather than ad hoc way. If a method has a good mathematical foundation, then it is formalized, typically given in formal specification language. This foundation provides a range of precisely defined concepts, such as:

consistency and completeness, as well as the implementation and correctness of the definition specification. The essence of a formal method is a technique that is based on a mathematical approach to describe the properties of a target software system. Different formal methods have different mathematical foundations, some are based on set theory and first-order predicate calculus (e.g., z and VDM), and some are based on temporal logic.

Formal methods require the support of the formal specification description language.