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<div style='position:absolute;top:5.0%;left:5.05%;width:94.19%;height:4.75%'><span
style='font-family:黑体;mso-ascii-font-family:黑体;mso-fareast-font-family:黑体'>10.1.6<span
style="mso-spacerun: yes"> </span>情态演算的公理化 </span></div>
<div style='position:absolute;top:10.5%;left:5.05%;width:94.19%;height:4.75%'> </div>
<div style='position:absolute;top:15.75%;left:5.05%;width:94.19%;height:4.75%'>基本公理 </div>
<div style='position:absolute;top:21.0%;left:5.05%;width:94.19%;height:4.75%'> </div>
<div style='position:absolute;top:26.0%;left:5.05%;width:94.19%;height:5.25%'><span
style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman"'><i>(1)<span
style="mso-spacerun: yes"> </span>S0 </i></span><span
lang=EN-US style='mso-fareast-language:ZH-CN'><i>≠</i></span><span lang=EN-US
style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><i> do ( a, s )</i></span><span lang=EN-US
style='mso-fareast-language:ZH-CN;display:none'> </span></div>
<div style='position:absolute;top:30.75%;left:5.05%;width:94.19%;height:5.75%'><span
lang=EN-US style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><i>(2)<span style="mso-spacerun:
yes"> </span>do(a1, s1) = do( a2, s2) </i></span><span
lang=EN-US style='font-family:Symbol;mso-fareast-language:ZH-CN;mso-char-type:
symbol'><i>®</i></span><span lang=EN-US style='mso-fareast-language:ZH-CN'><i>(</i></span><span
lang=EN-US style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><i>a1 = a2</i></span><span lang=EN-US
style='mso-fareast-language:ZH-CN'><i>∧</i></span><span lang=EN-US
style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><i>s1 = s2</i></span><span lang=EN-US
style='mso-fareast-language:ZH-CN'><i>)</i></span><span lang=EN-US
style='mso-fareast-language:ZH-CN;display:none'> </span></div>
<div style='position:absolute;top:36.25%;left:5.05%;width:94.56%;height:5.75%'><span
lang=EN-US style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><i>(3)<span style="mso-spacerun: yes">
</span></i></span><span lang=EN-US style='font-family:Symbol;mso-fareast-language:
ZH-CN;mso-char-type:symbol'><i>"</i></span><span lang=EN-US
style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><i>P[P(S0) </i></span><span lang=EN-US
style='mso-fareast-language:ZH-CN'><i>∧</i></span><span lang=EN-US
style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><i>(</i></span><span lang=EN-US style='font-family:
Symbol;mso-fareast-language:ZH-CN;mso-char-type:symbol'><i>"</i></span><span
lang=EN-US style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><i>a, s)(P(s) </i></span><span lang=EN-US
style='font-family:Symbol;mso-fareast-language:ZH-CN;mso-char-type:symbol'><i>É</i></span><span
lang=EN-US style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><i> P(do(a, s))) </i></span><span lang=EN-US
style='font-family:Symbol;mso-fareast-language:ZH-CN;mso-char-type:symbol'><i>É</i></span><span
lang=EN-US style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><i> (</i></span><span lang=EN-US style='font-family:
Symbol;mso-fareast-language:ZH-CN;mso-char-type:symbol'><i>"</i></span><span
lang=EN-US style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><i>s )P( s )]</i></span><span lang=EN-US
style='mso-fareast-language:ZH-CN;display:none'> </span></div>
<div style='position:absolute;top:41.5%;left:5.05%;width:94.19%;height:5.75%'><span
lang=EN-US style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><i>(4)<span style="mso-spacerun:
yes"> </span></i></span><span lang=EN-US style='font-family:
Symbol;mso-fareast-language:ZH-CN;mso-char-type:symbol'><i>Ø</i></span><span
lang=EN-US style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><i> s < S0</i></span><span lang=EN-US
style='mso-fareast-language:ZH-CN;display:none'> </span></div>
<div style='position:absolute;top:47.25%;left:5.05%;width:94.19%;height:5.25%'><span
lang=EN-US style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><i>(5)<span style="mso-spacerun:
yes"> </span>s < do( a, s’ )</i></span><span lang=EN-US
style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'> </span><span lang=EN-US style='mso-fareast-language:
ZH-CN'>≡</span><span lang=EN-US style='font-family:"Times New Roman";
mso-ascii-font-family:"Times New Roman";mso-fareast-language:ZH-CN'><i>(Poss(a,
s</i></span><span lang=EN-US style='font-family:"Times New Roman";mso-hansi-font-family:
"Times New Roman";mso-fareast-language:ZH-CN'><i>’</i></span><span lang=EN-US
style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><i>) </i></span><span lang=EN-US style='mso-fareast-language:
ZH-CN'><i>∧</i></span><span lang=EN-US style='font-family:"Times New Roman";
mso-ascii-font-family:"Times New Roman";mso-fareast-language:ZH-CN'><i> s </i></span><span
lang=EN-US style='mso-fareast-language:ZH-CN'><i>≤</i></span><span lang=EN-US
style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><i> s’ )</i></span><span lang=EN-US
style='mso-fareast-language:ZH-CN;display:none'> </span></div>
<div style='position:absolute;top:53.0%;left:5.05%;width:94.19%;height:4.75%'><span
lang=EN-US style='mso-fareast-language:ZH-CN;display:none'> </span></div>
<div style='position:absolute;top:57.75%;left:5.05%;width:94.19%;height:5.25%'>直观解释<span
style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman"'>: </span></div>
<div style='position:absolute;top:63.75%;left:5.05%;width:108.05%;height:4.75%'>前两条公理是基于唯名假设,它们规定两个状态相等当且仅当 </div>
<div style='position:absolute;top:68.5%;left:5.05%;width:114.23%;height:5.25%'>它们有相同的动作序列和起始状态<span
style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman"'>.
</span>第三个公理是一个二阶归纳, </div>
<div style='position:absolute;top:73.75%;left:5.05%;width:109.17%;height:5.25%'>相当于域闭包公理,<span
style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman"'>
</span>即任意状态都是从初始状态经由重复执行 </div>
<div style='position:absolute;top:79.25%;left:5.05%;width:94.19%;height:5.25%'><span
lang=EN-US style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman";
mso-fareast-language:ZH-CN'><i>do</i></span>而来的<span style='font-family:"Times New Roman";
mso-ascii-font-family:"Times New Roman"'>. </span>后面两个公理则体现了<span
style='font-family:"Times New Roman";mso-ascii-font-family:"Times New Roman"'>
</span><span style='font-family:宋体;mso-ascii-font-family:宋体'>< 的含义. </span></div>
<div style='position:absolute;top:85.0%;left:5.05%;width:94.19%;height:4.75%'><span
style='mso-special-format:lastCR;display:none'> </span></div>
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