Proposition relativity and logic calculation in probabilistic logic
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摘要: 原子命題是數理邏輯研究的基本單位.分析了原子命題的相關性與邏輯運算之間的關系.在經典二值邏輯中,命題邏輯運算結果的真值只與參與運算的命題的真值有關,而與命題的具體內容無關;在概率邏輯中,命題邏輯運算由命題的關系決定,真值相同的不同命題,邏輯運算結果不一定相同.定義了與經典二值邏輯相容的蘊涵聯結詞,克服了條件概率不能用于推理的缺點.Abstract: Atom propositions are the basic unit of symbolic logic. The relationship between atom propositions' relativity and logic calculation was analyzed. In classical two-valued logic, the truth value of the proposition logic calculation result only bears on the truth value of the proposition which participates in the logic calculation, but is independent of the idiographic content in the proposition. In probabilistic logic, proposition logic calculation is decided by the relationship of propositions. The different propositions with the same truth value can not have the same logic calculation result. Implication connectives which are compatible with classical two-valued logic were defined, and they overcome the shortcoming that conditional probability can not be used to inference.
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Key words:
- probabilistic logic /
- two-valued logic /
- set /
- logic calculation
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