Axioms of algorithmic logic - Historia wersji

AndrzejSalwicki: /* Axioms of algorithmic logic */

2015-11-19T17:08:24Z

‎Axioms of algorithmic logic

AndrzejSalwicki: /* Axioms of algorithmic logic */

2015-11-19T17:06:32Z

‎Axioms of algorithmic logic

AndrzejSalwicki: /* Axioms of algorithmic logic */

2015-11-19T17:04:52Z

‎Axioms of algorithmic logic

AndrzejSalwicki: /* Axioms of algorithmic logic */

2015-11-19T17:04:13Z

‎Axioms of algorithmic logic

AndrzejSalwicki: /* Axioms of algorithmic logic */

2015-11-19T17:03:30Z

‎Axioms of algorithmic logic

AndrzejSalwicki: /* Axioms of algorithmic logic */

2015-11-19T17:02:44Z

‎Axioms of algorithmic logic

AndrzejSalwicki: /* Axioms of algorithmic logic */

2015-11-19T16:58:02Z

‎Axioms of algorithmic logic

AndrzejSalwicki: /* Axioms of algorithmic logic */

2015-11-19T16:51:13Z

‎Axioms of algorithmic logic

AndrzejSalwicki: /* Axioms of algorithmic logic */

2015-11-19T16:44:10Z

‎Axioms of algorithmic logic

AndrzejSalwicki: /* Axioms of predicate calculus */

2015-11-19T16:42:52Z

‎Axioms of predicate calculus

@@ Linia 61: / Linia 61: @@
 <span style="color: Blue"><math>Ax_{18} \qquad ((x:=\tau)\gamma\equiv(\gamma(x/\tau)\wedge
-(x:=\tau)true))~\wedge((q:=\gamma\prime)\gamma\equiv\gamma(q/\gamma
+(x:=\tau)true))~\wedge((q:=\gamma^\prime)\gamma\equiv\gamma(q/\gamma^
 \prime))</math></span>

@@ Linia 64: / Linia 64: @@
 \prime))</math></span>
-<span style="color: Blue"><math>Ax_{19} \qquad \textbf{begin } K;M \textbf{ end} \alpha
+<span style="color: Blue"><math>Ax_{19} \qquad \textbf{begin } K;M \textbf{ end}\, \alpha
 \equiv K(M\alpha)</math></span>
 <span style="color: Blue"><math>Ax_{20} \qquad  \textbf{if}\ \gamma\ \textbf{then}\ K
-\ \textbf{else } M \textbf{ fi} \alpha\equiv((\lnot\gamma\wedge M\alpha
+\ \textbf{else } M \textbf{ fi}\, \alpha\equiv((\lnot\gamma\wedge M\alpha
 )\vee(\gamma\wedge K\alpha))</math></span>
-<span style="color: Blue"><math>Ax_{21} \qquad  \textbf{while }\gamma \textbf{ do }K\textbf{ od}\alpha\equiv((\lnot\gamma\wedge\alpha
+<span style="color: Blue"><math>Ax_{21} \qquad  \textbf{while }\gamma \textbf{ do }K\textbf{ od}\,\alpha\equiv((\lnot\gamma\wedge\alpha
 )\vee(\gamma\wedge K(\textbf{while }\gamma\textbf{ do }K\textbf{ od}
 (\lnot\gamma\wedge\alpha))))</math></span>

@@ Linia 52: / Linia 52: @@
 == Axioms of algorithmic logic ==
 <span style="color: Blue"><math>Ax_{14} \qquad K((\exists x)\alpha
-(x))\equiv(\exists y)(K\alpha(x/y)) </math></span>
+(x))\equiv(\exists y)(K\alpha(x/y)) </math></span> for <math> y\notin V(K) </math>
-−
 for <math> y\notin V(K) </math>
 <span style="color: Blue"><math>Ax_{15} \qquad K(\alpha\vee\beta)\equiv((K\alpha)\vee(K\beta))</math></span>

@@ Linia 52: / Linia 52: @@
 == Axioms of algorithmic logic ==
 <span style="color: Blue"><math>Ax_{14} \qquad K((\exists x)\alpha
-(x))\equiv(\exists y)(K\alpha(x/y))\ \ \ \ \ \ \ \ \ \ \ \ \  \</math></span>
+(x))\equiv(\exists y)(K\alpha(x/y)) </math></span>
 for <math> y\notin V(K) </math>

@@ Linia 52: / Linia 52: @@
 == Axioms of algorithmic logic ==
 <span style="color: Blue"><math>Ax_{14} \qquad K((\exists x)\alpha
-(x))\equiv(\exists y)(K\alpha(x/y))\ \ \ \ \ \ \ \ \ \ \ \ \  \</math></span> for <math> y\notin V(K) </math>
+(x))\equiv(\exists y)(K\alpha(x/y))\ \ \ \ \ \ \ \ \ \ \ \ \  \</math></span>
 <span style="color: Blue"><math>Ax_{15} \qquad K(\alpha\vee\beta)\equiv((K\alpha)\vee(K\beta))</math></span>

@@ Linia 64: / Linia 64: @@
 \prime))</math></span>
-<span style="color: Blue"><math>Ax_{19} \qquad '''begin'''} $K;M$ \textbf{end} $\alpha
+<span style="color: Blue"><math>Ax_{19} \qquad \textbf{begin} K;M \textbf{end} \alpha
-\equiv K(M\alpha)$
+\equiv K(M\alpha)</math></span>
-<span style="color: Blue"><math>Ax_{20} \qquad  \textbf{if} $\gamma$ \textbf{then} $K
+<span style="color: Blue"><math>Ax_{20} \qquad  \textbf{if}\ \gamma\ \textbf{then}\ K
-$ \textbf{else} $M$ \textbf{fi} $\alpha\equiv((\lnot\gamma\wedge M\alpha
+\ \textbf{else } M \textbf{ fi} \alpha\equiv((\lnot\gamma\wedge M\alpha
-)\vee(\gamma\wedge K\alpha))$
+)\vee(\gamma\wedge K\alpha))</math></span>
-<span style="color: Blue"><math>Ax_{21} \qquad  \textbf{while}~
+<span style="color: Blue"><math>Ax_{21} \qquad  \textbf{while }\gamma \textbf{ do }K\textbf{ od}\alpha\equiv((\lnot\gamma\wedge\alpha
-$\gamma$~\textbf{do}~$K$~\textbf{od}~$\alpha\equiv((\lnot\gamma\wedge\alpha
+)\vee(\gamma\wedge K(\textbf{while }\gamma\textbf{ do }K\textbf{ od}
-)\vee(\gamma\wedge K($\textbf{while}~$\gamma$~\textbf{do}~$K$~\textbf{od}$%
+(\lnot\gamma\wedge\alpha))))</math></span>
-(\lnot\gamma\wedge\alpha))))$
-<span style="color: Blue"><math>Ax_{22} \qquad \displaystyle{\bigcap K\alpha\equiv
+<span style="color: Blue"><math>Ax_{22} \qquad \bigcap K\alpha\equiv
-(\alpha\wedge(K\bigcap K\alpha))}$
+(\alpha\wedge(K\bigcap K\alpha))</math></span>
 <span style="color: Blue"><math>Ax_{23} \qquad \bigcup K\alpha
-\equiv(\alpha\vee(K\bigcup K\alpha))$ </span>
+\equiv(\alpha\vee(K\bigcup K\alpha))</math> </span>

@@ Linia 50: / Linia 50: @@
 (x))\equiv(\exists y)(K\alpha(x/y))\ \ \ \ \ \ \ \ \ \ \ \ \  \ for\ y\notin V(K) </math></span>
 == Axioms of algorithmic logic ==
 \item[$Ax_{15}$] $K(\alpha\vee\beta)\equiv((K\alpha)\vee(K\beta))$
 \item[$Ax_{16}$] $K(\alpha\wedge\beta)\equiv((K\alpha)\wedge(K\beta))$%

@@ Linia 46: / Linia 46: @@
 <span style="color: Blue"><math>Ax_{13} \qquad (\forall x)\alpha(x)\equiv\lnot
 (\exists x)\lnot\alpha(x)</math>
 <span style="color: Blue"><math>Ax_{14} \qquad K((\exists x)\alpha
 (x))\equiv(\exists y)(K\alpha(x/y))\ \ \ \ \ \ \ \ \ \ \ \ \  \ for\ y\notin V(K) </math></span>