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Borel probabilistic and quantitative logic

Science China(Information Sciences) 2011年第9期54卷 1843-1854页

作者： ZHOU HongJun & WANG GuoJun College of Mathematics and Information Science,Shaanxi Normal University,Xi’an 710062,China College of Mathematics and Information Science Shaanxi Normal University Xi’an China

The present paper introduces the notion of the probabilistic truth degree of a formula by means of Borel probability measures on the set of all valuations,endowed with the usual product topology,in classical two-valued propositional *** approach not only overcomes the limitations of quantitative logic,which require the probability measures on the set of all valuations to be the countably infinite product of uniform probability measures,but also remedies the drawback that probability logic behaves only *** is proved that the notions of truth degree,random truth degree in quantitative logic and the probability of formulas in probability logic can all be brought as special cases into the unified framework of the probabilistic truth *** quantitative logic and probability logic are *** also proves a one-to-one correspondence between deductively closed theories and topologically closed subsets of the space of all valuations,and a one-to-one correspondence between probabilistic truth degree functions and Borel probability measures on the space of all *** second part of the present paper proposes an axiomatic definition of the probabilistic truth degree,and it is finally proved that each probabilistic truth degree function is represented by a unique Borel probability measure on the space of all valuations in the way given in the first *** a theory which we call probabilistic and quantitative logic in the framework of classical propositional logic is established.

关键词： probabilistic truth degree finite separation property probability logic quantitative logic probabilistic and quantitative logic

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quantitative Method Based on Cotangent Similarity Degree in Three-Valued ?ukasiewicz logic

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Chinese Journal of Electronics 2021年第1期30卷 134-144页

作者： YU Peng School of Arts and Sciences Shaanxi University of Science and Technology

The main purpose of this paper is to establish a type of quantitative model by using the contangent similarity function in the three-valued?ukasiewicz propositional logic system ?;. We introduce the concepts of the cotangent similarity degree, cotangent pseudo-distance and cotangent truth degree of the propositions, together with their basic properties in ?;.We investigate the relationship between the cotangent truth degree and contangent pseudo-distance, and prove the continuity of the logical connectives ?, ∨ and → in the ?;logical metric space. We propose a graded reduction method and three types of graded reasoning frameworks on the propositions set F（S）, and provide several examples and basic properties of it.

关键词： Cotangent similarity degree Approximate reasoning quantitative logic Three-valued logic

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