Approximate reasoning mode algorithm based on propositional logic probability assignment

Abstract

The invention discloses an approximate reasoning mode algorithm based on a propositional logic probability assignment. Compared to the prior art, by using the method in the invention, an assignment domain of a classic proposition logic is extended to a given probability space from a binary value {0,1}; and a probability assignment of a propositional formula is introduced, wherein the probability assignment is promotion of a classic proposition logic binary value assignment and various kinds of true degree concepts. Through using the probability assignment, a probability truth degree, an unreliable degree, a probability truth degree based on an independent event assignment set and other concepts of the propositional formula is introduced. A property of the probability truth degree is discussed so as to prove that a truth degree set of all the proposition formulas based on the independent event assignment set does not have an isolated point in [0,1]. In proposition logic form deduction, an unreliable degree of an effective inference conclusion does not exceed a product sum of an unreliable degree of each precondition and a necessary degree. Based on the probability assignment, an a.e. conclusion, a conclusion in probability, a truth degree conclusion in probability and other concepts of a proposition formula set are introduced; connection between the concepts is discussed and two different types of approximate reasoning modes are provided.

Description

technical field [0001] The invention relates to a calculation method, in particular to an approximate reasoning model algorithm based on propositional logic probability assignment. Background technique [0002] Classical logic based on binary values ​​has achieved great success in the research of axiomization and formal reasoning. Therefore, in order to meet the needs of applications, scholars have promoted classical logic from different directions according to different problems discussed, and established various forms of non-classical logic theories. Probability logic is the logical representation of probability space, and probability logic is On the basis of classical logic and probability theory, it studies how to use the language of logic to carry out probability reasoning. Probability theory is the mathematical basis of uncertainty reasoning, although it has been used in many kinds of uncertainty reasoning such as subjective Bayes method, evidence theory, etc. However...

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Problems solved by technology

[0002] Classical logic based on binary values ​​has achieved great success in the research of axiomization and formal reasoning. Therefore, in order to meet the needs of applications, scholars have promoted classical logic from different directions according to different problems discussed, and established various forms of non-classical logic theories. Probability logic is the logical representation of probability space, and probability logic is On the basis of classical logic and probability theory, it studies how to use the language of logic to carry out probability reasoning. Probability theory is the mathematical basis of uncertainty reasoning, although it has been used in many kinds of uncertainty reasoning such as subjective Bayes method, evidence theory, etc. However, how to carry out probabilistic reasoning within the logical framework is a problem worth studying. A common feature of classical logic and fuzzy logic is that propositional connectives are truth functions, and they all start with {0,1} or [ 0,1] to explain the connectives in the form of truth function, but its ideas and methods are somewhat inappropriate when applied to probabilistic logic. The truth value of compound propositions in probabilistic logic is related to the truth value of constituent propositions and The connotation of the proposition is related. For example, the formula v(p∨q)=v(p)+v(q)-v(p∧q) means that the truth value v(p∨q) of p∨q is not only related to v(p ) is related to v(q), and also related to v(p∧q). Therefore, the connectives of probability logic cannot be explained by truth functions.

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