If you believe that probability theory and machine learning are the true essence of artificial intelligence, or you insist that mathematical logic is the whole of logic, please stop reading anymore.
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Since the concept of "artificialintelligence" (AI) was proposed at the Dartmouth conference in 1956, thedevelopment of artificial intelligence has experienced several climaxes. Themost famous of these are symbolism from the 1950s to 1980s, and connectionism,which started intermittently in the 1980s and suddenly became hot in the 2010suntil today.
Symbolism, represented by knowledge baseand expert system, focuses on knowledge management. Connectionism, representedby machine learning and neural networks, lays emphasis on knowledge reasoningand prediction. Symbolism is mainly based on predicate logic in mathematicallogic, which is also called symbolic logic, hence the name of symbolism. And itis also called logicism. And connectionism has its roots in the theories ofneural networks and probability.
Mathematical Logic
Unlike traditional logic which isrepresented by Aristotle's deductive logic, mathematical logic takes abstractmathematical symbols as a tool to study logic. It should be said that theemergence of mathematical logic paradigm has fundamentally changed the researchof logic. It causes the research to deviate from the original and overall goalof logic, which is to provide normative models for reasoning processes ingeneral. Instead, most of its work focuses on mathematical reasoning,especially theorem proving.
Therefore, from the very beginning of itsemergence, mathematical logic was regarded as the authentic logic by themathematicians who pursued it, more authentic than traditional logic. In thefollowing one or two hundred years, with the continuous development of thediscipline and a large number of applications in the fields of communicationand computer, mathematical logic far surpassed traditional logic in terms ofboth the discipline status and attention. So that even in other areas of logicother than mathematical reasoning, mathematical logic is still widely regardedas a norm.
There is no doubt that computable logicalsymbols are needed in the fields of computing science and information science,but it does't work for human thinking. Psychologists have shown that thereasoning process of human daily thinking is not an abstract symbolic formsystem. The purpose of artificial intelligence is to build a "thinkingmachine" that thinks like human beings. Its application is not limited tothe scope of mathematics or its extension of disciplines, but to formalize thereasoning processes such as real-world reasoning, everyday reasoning orcommonsense reasoning. The limitations of mathematical logic in everydayreasoning, and the differences between it and the reality of human thinking,determine that it cannot provide a normative model for universal reasoning.
Probability Theory
Probability theory is a branch ofmathematics which studies the quantitative law of random phenomena. It is alsoa very important method of inductive logic.
Probability theory is the logical basis ofconnectionist artificial intelligence system reasoning. Every inference made bythe system is to infer different possibilities of various outcomes based onexisting data, so as to select the result with the highest or the mostconsistent probability. Such prediction method may be applicable to somereasoning scenarios with relatively clear and fixed rules or conditions, andcan also obtain prediction results with high accuracy. However, everydayreasoning of human thinking is not always in line with these scenarios afterall. When faced with scenarios of different patterns, or when the rules orconditions of such scenarios have changed (for example, there are somedifferences between the real world scene and the training scene of machinelearning), the results of such prediction methods are often not ideal.
In short, connectionism, which is based onprobability theory, only adopts the methodologies limited to the category ofinductive reasoning, while ignoring the key role that deductive logic can playin the process of knowledge reasoning and acquisition and in creatingtopological relationships among knowledge information. Therefore, it givespeople some impressions such as "the reasoning results are uncertain andunexplainable", "this is not like the way of human thinking",and so on.
Traditional Logic
Mathematical logic is a combination ofwestern traditional logic and mathematics.
The western traditional logic can be tracedback to the period of ancient Greece more than 2000 years ago. However, afterthe emergence of mathematical logic in the 18th and 19th century, traditionallogic was widely criticized by mathematical logicians. One of the importantreasons is that the study of traditional logic always exists only in the scopeof philosophy, which is not very practical and difficult to be directly appliedto the research of natural science.
On the other hand, despite thousands ofyears of development, traditional logic has not formed a complete system.Mathematics, which also started in the period of ancient Greece, had more orless formed some rigorous axiom systems in geometry, algebra, set and othersub-fields when mathematical logic appeared. But logic still had only asmall-scale and imperfect system like Aristotle's "major premise, minorpremise and conclusion" thousands of years ago, and the rest are mostlyvarious of different and scattered thoughts of philosophers. Even there arestill considerable divergences in the similarities, differences andrelationships between the most basic concepts such as "argument","reasoning" and "inference".
New Logicism
To figure out the reasons for thelimitation of traditional logic and the rapid rise of mathematical logic frombehind, One of the most important should be the difference relationship ofconcreteness and abstraction between the two disciplines logic and mathematics.Concreteness and abstraction are relative. For physics, chemistry and othernatural sciences, mathematics is abstract. But for logic, mathematics isrelatively concrete. Mathematics studies abstract things, but it studies withthe tools of representable numbers, symbols, mathematical formulas and so on.The abstract things studied by logic are the rules and forms of reasoning,which exist intangibly in the derivation and proof process of mathematicalformulas or other disciplines. As a result, it is more abstract, and moredifficult to be understood and studied.
I think that in order to build a moreperfect axiom system of logic, we should first clearly distinguish "reallogic" into two parts: basic logic and applied logic.
Basic logic, or called meta logic, is somebasic elements needed in the study of logic, mainly focusing on therelationships between logical elements such as "concept","proposition" and "argument". These elements and theirrelationships are inevitably involved in all reasoning paradigms, reasoningrules, or disciplines that apply these reasoning rules.
And applied logic is a variety of paradigmsof logical rules and reasoning rules, which is mainly seen in the combinationwith other disciplines. For example, mathematical logic means a separatediscipline that is created by mathematicians' combining the numbers and symbolscommonly used in mathematics with the logical rules of applied logic, ratherthan the product of the natural development of logic. And the currenttraditional logic research can be basically regarded as the combination ofvarious components in linguistics and applied logic. It's just not separatedand independent for thousands of years.
For the more universal artificial generalintelligence, it should be based on basic logic, rather than purely appliedlogic such as mathematical logic or traditional logic. Coupled with the basicelements in the field of information science related to knowledge managementand prediction, it can become a new combination of logical model andinformation model. That is "logical information model", which canprovide universality for artificial general intelligence.
It can be used as a new basic model ofknowledge representation to develop a new generation of knowledge base. When itis combined with the corresponding norms of applied logic, the correspondingexpert system or prediction system can be formed. When it can adaptively adjustand switch between different norms of applied logic, artificial generalintelligence will be achieved. The norms of applied logic here can be thesymbolism paradigm of mathematical logic, the connectionism paradigm of machinelearning, or even the unique everyday reasoning paradigm of each of us.
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New generation of knowledgerepresentation model (Logical Information Model)
->New generation of knowledge base (Logical Information Network)
->Artificial General Intelligence (AGI)
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