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In this paper, we construct the predicate calculus system of medium logic MF in accondance with Medium Principle. We first present its symbolical system, forming rules and inference rules and also several formal inference relations for the primary development of MF, including an important theorem, i. e. the Substitutive Theorem of MF. The formal symbols of MF consist of the following five classes: (1) Logical symbols:,→、~、、,(2) Individual symbols: a, b, c, a_i,b_i, c_i (i=1, 2, …,)(3) Predicatives: F,... In this paper, we construct the predicate calculus system of medium logic MF in accondance with Medium Principle. We first present its symbolical system, forming rules and inference rules and also several formal inference relations for the primary development of MF, including an important theorem, i. e. the Substitutive Theorem of MF. The formal symbols of MF consist of the following five classes: (1) Logical symbols:,→、~、、,(2) Individual symbols: a, b, c, a_i,b_i, c_i (i=1, 2, …,)(3) Predicatives: F, G, H, F_i, G_i, H_i (i=1, 2, …); (4) Bound variables: X, Y, Z, X_i, Y_i, Z_i (i=1,2,…),(5)Techanical symbols; [, ], ', (,). The forming rules of MF consist of the following four pieces: (i) F~n (a_1, …, a_n,) is a well-formed formula, (ii) If X is a well-formed formula, so are ~X and X, (iii) If X and Y are well-formed formulas, so is (X→Y), (iv) If X(a) is a well-formed formula, where "a" appears and X does not, then xX(x) and xX(x) are well-formed formulas. The formal inference rules of MF include not only all the inference rules of MP but also the following six: (~-) xA(x)-A(a). (_+) If A(a), where "a" does not appear in , then xA(x),(_-) If A(a) B, wheree "a" does not in B, then xA(x) B, (_+)A(a)xA(x), where A(x)is obtained by substituting x for some appearances of in A(a), Theorem 4(Substitutive Theorem of MF): If A |=| B, and f(p) is any well-formed formula of MF, we have f(A)|=| f(B) 本文在中介原则的观点下构造中介逻辑的谓词演算系统MF,我们首先给出它的符号系统、形成规则和推理规则,又作为MF的初步展开而给出它的若干个形式推理关系,其中包括的一个重要定理,那就是MF中的替换定理。M F 形式符号:(一)逻样词s(二)个体词,a,b,c ,a; ,b;,c;< z = 1。2,…;(三)谓词F,G,rH,(i二1,2…),(四)约束变元X,L,Xr,Zt Yf, 了五)技术符MF的形成规贝.:(i) F'(a,...a})是合式公式;(ii)如果J是合式公式,则一工和X是合式公式,(iii)如果X和Y是合式公式,则〔X-> Y〕是合式公式;(iv)如果X(a>是合式公式。在其中出现,X不在其中出现,则和ExX }x}是合式公式。至于FM的形式推理规则,乃在接受M的全部推理规之外,另加如下六条(a).其中a不在r中出现,则r卜}TxA }x} ; ( 3 _)若A(a) - B,其中。不在B中出现,则3 xAB; ( 3 +)A(a) }-其中A }x}是由A(a)把其中a的某些出现替换为x而得; 定理4(替换定理)如果AI-I B,而f(P)为MF中之任一今式公式,则有fcA>I=If(... 本文在中介原则的观点下构造中介逻辑的谓词演算系统MF,我们首先给出它的符号系统、形成规则和推理规则,又作为MF的初步展开而给出它的若干个形式推理关系,其中包括的一个重要定理,那就是MF中的替换定理。M F 形式符号:(一)逻样词s(二)个体词,a,b,c ,a; ,b;,c;< z = 1。2,…;(三)谓词F,G,rH,(i二1,2…),(四)约束变元X,L,Xr,Zt Yf, 了五)技术符MF的形成规贝.:(i) F'(a,...a})是合式公式;(ii)如果J是合式公式,则一工和X是合式公式,(iii)如果X和Y是合式公式,则〔X-> Y〕是合式公式;(iv)如果X(a>是合式公式。在其中出现,X不在其中出现,则和ExX }x}是合式公式。至于FM的形式推理规则,乃在接受M的全部推理规之外,另加如下六条(a).其中a不在r中出现,则r卜}TxA }x} ; ( 3 _)若A(a) - B,其中。不在B中出现,则3 xAB; ( 3 +)A(a) }-其中A }x}是由A(a)把其中a的某些出现替换为x而得; 定理4(替换定理)如果AI-I B,而f(P)为MF中之任一今式公式,则有fcA>I=If(B)>o In this paper,we construct the predicate calculus system of medium logic MF in accondance with Medium Principle.We first present its symbolical system,forming rules and inference rules and also several formal inference relations for the primary development of MF,including an important theorem, i.e.the Substitutive Theorem of MF. The formal symbols of MF consist of the following five classes:(1) Logical symbols:■,→、~、■、■,(2)Individual symbols:a,b,c,,a_i,b_i, c_i(i=1,2,…,)(3)Predicatives:F,G,H,F_i,G_i,H_i(i=1,2,…);(4)... In this paper,we construct the predicate calculus system of medium logic MF in accondance with Medium Principle.We first present its symbolical system,forming rules and inference rules and also several formal inference relations for the primary development of MF,including an important theorem, i.e.the Substitutive Theorem of MF. The formal symbols of MF consist of the following five classes:(1) Logical symbols:■,→、~、■、■,(2)Individual symbols:a,b,c,,a_i,b_i, c_i(i=1,2,…,)(3)Predicatives:F,G,H,F_i,G_i,H_i(i=1,2,…);(4) Bound variables:X,Y,Z,X_i,Y_i,Z_i(i=1,2,…),(5)Techanical symbols; [,],’,(,). The forming rules of MF consist of the following four pieces:(i)F~n(a_1, …,a_n)is a well-formed formula,(ii)If X is a well-formed formula,so are ~X and ■X,(iii)If X and Y are well-formed formulas,so is(X→Y),(iv) If X(a)is a well-formed formula,where“a”appears and X does not,then ■xX(x) and ■xX(x) are well-formed formulas. The formal inference rules of MF include not only all the inference rules of MP but also the following six:(■)■xA(x)-A(a).(■) If ■A(a), where“a”does not appear in■,then■xA(x),(■)If A(a)■B, wheree“a” does not in B,then■xA(x)■B,(■)A(a)■xA(x),where A(x)is obtained by substituting x for some appearances of in A(a),(■) ■A(x)■x■A(x),(■)■xA(x)■x■A(x). Theorem 4(Substitutive Theorem of MF):If A|=|B,and f(p) is any well-formed formula of MF,we have f(A)|=|f(B) 本文在中介原则的观点下构造中介逻辑的谓词演算系统 MF,我们首先给出它的符号系统、形成规则和推理规则,又作为 MF的初步展开而给出它的苦干个形式推理关系,其中包括的一个重要定理,那就是 MF 中的替换定理。MF 的形式符号:(一)逻辑词■,→,~,■;(二)个体词,a,b,c,a_i,b_i,c_i(i=1,2,…);(三)谓词 F,G,H,F_i,G_iH_i,(i=1,2,…);(四)约束变元 X,Y,Z,X_i,Z_iY_i,(i=1,2,…):(五)技术符[,],’,(,)·MF 的形成规则:(i)F~n(a_1,…,a_n)是合式公式;(ii)如果 X 是合式公式,则~X 和■X 是合式公式;(iii)如果 X 和 Y是合式公式,则[X→Y]是合式公式;(iv)如果 X(a)是合式公式,a 在其中出现,X 不在其中出现,则■xX(x)和 ExX(x)是合式公式。至于 FM 的形式推理规则,乃在接受 MP 的全部推理规之外,另加如下六条:(■_-)■xA(x)■A(a);(■_+)若■A(a),其中 a 不在■中出现,则■xA(x);(■_-)若 A(a)■B,其中 a 不在 B 中出现,则■xA(x... 本文在中介原则的观点下构造中介逻辑的谓词演算系统 MF,我们首先给出它的符号系统、形成规则和推理规则,又作为 MF的初步展开而给出它的苦干个形式推理关系,其中包括的一个重要定理,那就是 MF 中的替换定理。MF 的形式符号:(一)逻辑词■,→,~,■;(二)个体词,a,b,c,a_i,b_i,c_i(i=1,2,…);(三)谓词 F,G,H,F_i,G_iH_i,(i=1,2,…);(四)约束变元 X,Y,Z,X_i,Z_iY_i,(i=1,2,…):(五)技术符[,],’,(,)·MF 的形成规则:(i)F~n(a_1,…,a_n)是合式公式;(ii)如果 X 是合式公式,则~X 和■X 是合式公式;(iii)如果 X 和 Y是合式公式,则[X→Y]是合式公式;(iv)如果 X(a)是合式公式,a 在其中出现,X 不在其中出现,则■xX(x)和 ExX(x)是合式公式。至于 FM 的形式推理规则,乃在接受 MP 的全部推理规之外,另加如下六条:(■_-)■xA(x)■A(a);(■_+)若■A(a),其中 a 不在■中出现,则■xA(x);(■_-)若 A(a)■B,其中 a 不在 B 中出现,则■xA(x)■B;(■_+)A(a)■xA(x),其中 A(x)是由 A(a)把其中 a 的某些出现替换为 x 而得;■xA(x)■x■A(x);■xA(x)■■x■A(x).定理4(替换定理)如果 A■B,而 f(P)为 MF 中之任一合式公式,则有 f(A)■f(B)。 The phenomenon of evolutionary compatibility refers to the depth and scope of the mosaic characteristics and the uncertainty produced at different evolutionary levels, which are reflected in the aspects of co—existenee of distinct features and traits of living things, of advanced and primary development and of extinction and establishment during the evolutionary processes. Generally, the hereditary wealth that has been gained by living things would never be lost easily. The compatibility of evolution manifests... The phenomenon of evolutionary compatibility refers to the depth and scope of the mosaic characteristics and the uncertainty produced at different evolutionary levels, which are reflected in the aspects of co—existenee of distinct features and traits of living things, of advanced and primary development and of extinction and establishment during the evolutionary processes. Generally, the hereditary wealth that has been gained by living things would never be lost easily. The compatibility of evolution manifests itself in a melodious way. This kind of melody is the one with genetic information. The nature of evolutionary compatibility is that living things remain essentially the same despite all apparent changes. Therefore, evolutionary compatibility holds genetic information of different sources. The so—called uncertainty is a description of the process of compatibility. 进化的兼容性现象是指在进化历程中生物不同性质与特点共存,先进与原始共存,绝灭和新生共存等事实所反映的在深度和广度上的镶嵌性以及在各种水平上产生的不确定性。所以从整体上看,生物在进化过程中获得的遗传财富决不轻易丢失。进化的兼容是以旋律的形式表现的,这种旋律就是遗传信息的旋律。进化兼容的本质是生物万变不离其宗的道理,因此进化的兼容是指不同来源遗传信息的兼容,不同生物信息的兼容,所谓不确定性就是对这种兼容过程的描述。
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