[1]LIU Honglan,HAO Weidong.A probabilistic logic system as a Boolean algebra homomorphic with set algebra[J].CAAI Transactions on Intelligent Systems,2011,6(2):107-113.
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A probabilistic logic system as a Boolean algebra homomorphic with set algebra
CAAI Transactions on Intelligent Systems[ISSN 1673-4785/CN 23-1538/TP] Volume:
6
Number of periods:
2011 2
Page number:
107-113
Column:
学术论文—人工智能基础
Public date:
2011-04-25
- Title:
- A probabilistic logic system as a Boolean algebra homomorphic with set algebra
- Keywords:
- probabilistic propositional logic; set algebra; Boolean algebra; homomorphism; truth value function
- CLC:
- TP181
- DOI:
- -
- Abstract:
- Connectives are essentially operations on propositions, and only the true value functions applicable to all propositions can be used to define connectives. In probabilistic logic, any function on ［0,1］ is not completely applicable for the operation on all propositions, and the connectives of probabilistic propositional logic cannot be defined as a true value function because of propositional relativity in connotation. Every operator may be discussed and employed as a method of calculation, but not as a logic system. A probabilistic propositional logic system is the logical description of a probabilistic space, and is a Boolean algebra homomorphic with set algebra that is the event domain in the probabilistic space. All connectives which are compatible with those in classical twovalued logic and which accord with fact can be defined exactly by set functions on event domains. The classical formal system of propositional calculus is completely applicable to probabilistic propositional calculus.
- References:
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?LIU Honglan, GAO Qingshi, YANG Bingru. The two layers of propositional equivalence and the propositional calculus in probabilistic propositional logic［J］. Philosophical Researches, 2009, 10: 113.
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Last Update:
2011-05-19