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1.
将修正的Gdel逻辑系统中的广义重言式理论进行推广,讨论了逻辑系统G中三类无限子代数上的广义重言式理论,并利用可达广义重言式的概念在■的三类子代数中分别给出F(S)关于同余的一个分划。  相似文献   

2.
G(o)del逻辑系统中的广义重言式理论   总被引:14,自引:0,他引:14  
本文将王国俊教授在逻辑系统,W,Wk中的广义重言式理论进行推广并应用到了Go(o)del逻辑系统(G-),G,Gn中.主要结果是 :在逻辑系统(G-),G中,重言式不可能由对非重言式进行有限次升级算法得到;在逻辑系统Gn中,对任一公式最多进行n次升级算法即可得到重言式;利用可达广义重言式概念和α-矛盾式概念分别在(G-),G,Gn中给出了F(S)的一个关于同余的分划.  相似文献   

3.
修正的G(o)del逻辑系统中三类无限子代数及其F(S)的分划   总被引:1,自引:0,他引:1  
将修正的G(o)del逻辑系统中的广义重言式理论进行推广,讨论了逻辑系统G-中三类无限子代数上的广义重言式理论,并利用可达广义重言式的概念在G-的三类子代数中分另q给出F(S)关于→同余的一个分划.  相似文献   

4.
Goedel逻辑系统中的广义重言式理论   总被引:8,自引:3,他引:5  
本文将王国俊教授在逻辑系统/W,W,Wk中的广义重言式理论进行推广并应用到了Gooedel逻辑系统/G,G,Gn中。主要结果是:在逻辑系统/G,G中,重言式不可能由对非重言式进行有限次升级算法得到;在逻辑系统Gn中,对任一公式最多进行n次升级算法即可得到重言式;利用可达广义重言式概念和α-矛盾式概念分别在/G,G,Gn中给出了F(S)的一个关于→同余的分划。  相似文献   

5.
本文将王国俊教授在逻辑系统 W,W,Wk中的广义重言式理论进行推广并应用到了Goo¨ del逻辑系统 G,G,Gn 中。主要结果是 :在逻辑系统 G,G中 ,重言式不可能由对非重言式进行有限次升级算法得到 ;在逻辑系统 Gn 中 ,对任一公式最多进行 n次升级算法即可得到重言式 ;利用可达广义重言式概念和 α-矛盾式概念分别在 G,G,Gn 中给出了 F( S)的一个关于 同余的分划。  相似文献   

6.
首先证明了在修正的Product逻辑系统中广义重言式有更加精细的区分;其次通过引入一类特殊的公式序列和特殊公式,进一步证明了对任意有理数a∈[0,1],可达α-重言式集是类类非空的,并同时给出了修正的Product逻辑系统中广义重言式的升级算法。  相似文献   

7.
系统RDP中的广义重言式理论   总被引:1,自引:0,他引:1  
研究带参数的模糊逻辑系统RDP中的广义重言式理论.结果表明系统RDP中只有三种不同的广义重言式,即(1/2),重言式,(1/2)+-重言式和重言式.将一些多值逻辑系统和模糊逻辑系统中行之有效的升级算法运用于系统RDP,证明在该系统中,升级算法可以将可迭0-重言式和可达(1/2)-重言式分别提升为可这(1/2)-重言式和可达(1/2)+-重言式,但是,对可达(1/2)+-重言式升级算法的结果仍然得到可达(1/2)+-重言式.这表明对非重言式有限次利用升级算法未必能得到重言式.  相似文献   

8.
将修正的Kleene逻辑系统中的语义MP规则和语义HS规则推广后应用于RDP逻辑系统,讨论了RDP逻辑系统中广义重言式的广义语义MP规则和广义语义HS规则,得出在逻辑系统D1/2中,广义语义(1/2)+-MP,(1/2)+-HS,1-MP,1-HS规则成立,而广义语义1/2-MP,1/2-HS规则不成立。  相似文献   

9.
扰动模糊命题逻辑系统中的广义重言式   总被引:1,自引:1,他引:0  
通过定义二维R0-蕴涵算子,将王国俊教授在逻辑系统形中的广义重言式理论推广并应用到二维赋值的扰动模糊命题逻辑系统西中,证明了这一系统中(μ,δ)-重言式就是某个(λ,1-λ)-重言式,最终获得与一维线性赋值格上完全相应的广义重言式分类。  相似文献   

10.
Lukasiewicz多值逻辑系统中的广义重言式理论   总被引:21,自引:3,他引:18  
引入一类特殊的公式序列Ak,k=1,2,…,证明了在Lukasiewicz多值逻辑系统,对任意真值a∈Ln而言,可达a-重言式类类不空,进一步证明了系统中广义重言式的类类互异定理,最后讨论了Lukasiewicz多值逻辑系统与经典二值逻辑系统中重言式之间的关系。  相似文献   

11.
This paper focuses on hierarchical structures of formulas in fuzzy logical systems. Basic concepts and hierarchical structures of generalized tautologies based on a class of fuzzy logical systems are discussed. The class of fuzzy logical systems contains the monoidal t-norm based system and its several important schematic extensions: the ?ukasiewicz logical system, the Gödel logical system, the product logical system and the nilpotent minimum logical system. Furthermore, hierarchical structures of generalized tautologies are applied to discuss the transformation situation of tautological degrees during the procedure of fuzzy reasoning.  相似文献   

12.
R_0-代数[0,1]的子代数与广义重言式   总被引:12,自引:1,他引:11  
王龙春  王国俊 《数学学报》2004,47(3):521-526
本文是对修正的Kleene系统中广义重言式理论的推广,讨论了R_0-代数[0,1]的各类无限子R_0-代数中的广义重言式,证明了在子R_0-代数E_2中,中存在着可数多个不同的广义重言式。  相似文献   

13.
Most of the normal forms for fuzzy logics are versions of conjunctive and disjunctive classical normal forms. Unfortunately, they do not always preserve tautologies and contradictions which is important, for example, for automated theorem provers based on refutation methods.De Morgan implicative systems are triples like the De Morgan systems, which consider fuzzy implications instead of t-conorms. These systems can be used to evaluate the formulas of a propositional language based on the logical connectives of negation, conjunction and implication. Therefore, they determine different fuzzy logics, called implicative De Morgan fuzzy logics.In this paper, we will introduce a normal form for implicative De Morgan systems and we will show that for implicative De Morgan fuzzy logics whose t-norms are strict, this normal form preserves contradictions as well as tautologies.  相似文献   

14.
We study implicational formulas in the context of proof complexity of intuitionistic propositional logic (IPC). On the one hand, we give an efficient transformation of tautologies to implicational tautologies that preserves the lengths of intuitionistic extended Frege (EF) or substitution Frege (SF) proofs up to a polynomial. On the other hand, EF proofs in the implicational fragment of IPC polynomially simulate full intuitionistic logic for implicational tautologies. The results also apply to other fragments of other superintuitionistic logics under certain conditions.In particular, the exponential lower bounds on the length of intuitionistic EF proofs by Hrube? (2007), generalized to exponential separation between EF and SF systems in superintuitionistic logics of unbounded branching by Je?ábek (2009), can be realized by implicational tautologies.  相似文献   

15.
Vector logic is a mathematical model of the propositional calculus in which the logical variables are represented by vectors and the logical operations by matrices. In this framework, many tautologies of classical logic are intrinsic identities between operators and, consequently, they are valid beyond the bivalued domain. The operators can be expressed as Kronecker polynomials. These polynomials allow us to show that many important tautologies of classical logic are generated from basic operators via the operations called Type I and Type II products. Finally, it is described a matrix version of the Fredkin gate that extends its properties to the many-valued domain, and it is proved that the filtered Fredkin operators are second degree Kronecker polynomials that cannot be generated by Type I or Type II products. Mathematics Subject Classification: 03B05, 03B50.  相似文献   

16.
扰动模糊命题逻辑的代数结构及其广义重言式性质   总被引:5,自引:1,他引:4  
着眼于扰动模糊命题逻辑的代数结构,为研究二维扰动模糊命题逻辑最大子代数I2R及其广义重言式提供了一些代数理论基础,最后研究了子代数间广义重言式的关系.  相似文献   

17.
We consider logical expressions built on the single binary connector of implication and a finite number of literals (Boolean variables and their negations). We prove that asymptotically, when the number of variables becomes large, all tautologies have the following simple structure: either a premise equal to the goal, or two premises which are opposite literals (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

18.
First the expansion of the ?ukasiewicz (propositional and predicate) logic by the unary connectives of dividing by any natural number (Rational ?ukasiewicz logic) is studied; it is shown that in the predicate case the expansion is conservative w.r.t. witnessed standard 1‐tautologies. This result is used to prove that the set of witnessed standard 1‐tautologies of the predicate product logic is Π2‐hard. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

19.
We prove that for sufficiently large , there are tautologies of size that require proofs containing lines in axiomatic systems of propositional logic based on the rules of substitution and detachment. Received October 19, 1995  相似文献   

20.
区间值模糊命题逻辑系统的广义恒真式   总被引:5,自引:1,他引:4  
建立区间值模糊命题逻辑系统F(∨,∧,σ┴,c),其中,α^-θ┴b=(α^-)^c┴b^-,┴是I[0,1]中的t-余范;讨论系统F(∨,∧,σ┴,c)与对应的模糊命题逻辑系统F(∨,∧,σ┴,c)在广义恒真式方面的相互关系,得到定理:T^-[0,α](F^-∨,∧,σ┴,c)=Tα(F(∨,∧,σ┴,c))。  相似文献   

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