Nonmonotonic Logic

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K^]=EC6=>XY`fJhmr;XY=>`s?Rt;XY=@=&CnKY9;:u=$XY:uKYGIHJ^Ko?BPWMit,=$GFP
KvlwGZJdJY?&GIMNKY=k\,:E?kH*=>P,JS:&T@U;:VPWH*:=BCxc
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Mi:ut7:uP,MiGFPb<R=$PˆKL9;:QH*=$PbP;:&H*KLGFj@:&Jnt;XY:&J^:VP
Kd?BPWM„KY9b:‰tbXY=$t,:VXLKYG[:&Jd?BKLKYXYG[\;U;KL:&MNKY=kKY9;:V`ŠeiHh:VXYK‹?BGFP
?&\,JSKLXo?$HhKŒC6:&?&KYU;XL:&J=BCKY9;:QH*=>P,JS:&T@U;:VPWH*:XY:uAI?BKLGF=>Pˆ?&XY:XY:u`f?BXLq$?&\;AFp}JSK‹?B\;A[:Q?$H*XL=@JYJdAF=><$GZHVJ*m
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H*=>P,JS:~T‚U;:uP,H*:=BCcR˜N™@šR›
mœ9,?BKKY9;GZJ`N:&?&P,JGIJDKL9,?BK?&Pip}H*=>P,H*AFUWJSGF=>PfMiX‹?~]dPNC6XL=$`s?QJS:VKd=&C
t;XL:V`NGZJS:&J]dGFA[A\,:EtbXY:&J^:VXYj@:&M}?$J?RH*=$P,HhAFU,J^GF=$Pf:Vj@:uPNGC|KY9;:t;XL:V`NGZJS:vJS:VKdGZJdJSU;t;tbAF:V`N:uPiKL:&M
]dG[KY9_?$M;M
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t;XL:V`NGZJS:vJS:VKd<>XY=&]J*m
89;:`N=>P;=$KL=$P;GZH*GFK^pkt;XY=>t7:uXYK^pa ,=&]JC6XY=$`¡?$JYJ^U;`Nt;KLGF=>P,JKY9,?&K?&XY:QMi:V:ut;AFpkXY=@=>KY:&MfGFP
\,=$KL9ˆKL9;:t;XY=@=&CnKY9;:u=$XYp_?&P,MNKY9;:QJS:u`f?BP
KYGZHVJ*e@P;=>K{=>P;AFpN=&CH*AZ?$JYJ^GIHV?&AA[=$<$GZH$ei\bU;K{=&C`}=@JSK
t;9bGFAF=gJS=>t;9;GIHu?BA0AF=><$GZHVJd?$Jd]:VA[A…m|rWXL=$`zKL9;:t;XY=@=&CnKY9b:V=$XL:VKYGZHJSK‹?BP,Mit,=>GFP
KVe,`N=$P;=>KY=>P;GIH*G[K^p
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pfMi:VXLGFj>?BKLGF=>P„=&CnKY9b:¢C6=>XY`kU;AI?Ql£C6XY=>`sKY9;:t;XL:V`NGIJ^:J^:VKc
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:VXYG[j$?&KYG[=$P0e,J^GFP,H*:¢JSKo?&P,M;?&XoM
G[PiC6:VXY:uP,H*:XYU;A[:&JdMi:Vt,:VP,Mf=$P;A[pN=$PfKL9;:t;XY:&J^:VP,H*:=&CG[PiC6=$XL`f?BKLGF=$P¥eiP;=>K{G[KoJd?B\WJS:VP,Hh:@mn89;:
j@:VXLGO€Hu?BKYG[=$PN=&C`}=$P;=>KY=$PbGIH*G[KSpkGIJheiG—Cn?&Pip
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GFKYG[=$Pf=BC|C6U;XYKL9;:VXdt;XL:V`NGIJ^:&JnHV?BPfA[:&?$MNKY=kKY9b:
XL:VKYX‹?$H*KLGF=$Pf=&Cn?kH*=$PWH*AFU,J^GF=>Pˆ?&AFXL:&?$Mip‡MiXo?V]dP0e,J^=aKL9,?BKKY9;:QH*=>P,H*A[U,JSG[=$P_JS:VKdPb:V:&MNP;=$K
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J^:V:V`¸KY=k<$U;GZMi:`aU,Ho9k=BCn=>U;XdGFP
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piKL9;GFPb<aA[GFq@:v?ªC6=>XY`f?&A0Mi:*OWP;GFKLGF=$P¥ei]:QHV?&PfKY9;G[P;qN=BCDMi:*C’?BUbAFK
XL:&?$J^=$P;G[P;<;e;j@:VXLpNXY=>U;<$9bAFp@eb?$JdXY:&?>JS=$PbGFP;<kKY9,?&K{XL:VAFG[:&JD=>PˆKL9;:Q?B\,J^:VP,H*:=BC|GFP
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º U;PbAF:&JLJKY9;:VXL:GIJGFP
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KL9,?BKvÀ„GZJd?E\;GFX‹Me,H*=$PWH*AFU,M
:KY9,?&KÀN ,GF:~JU;P;AF:~JYJKY9b:VXY:GIJG[PiC6=$XL`f?BKLGF=>PNKY=RKL9;:QH*=$P
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H*=>PiKLXo?&XYp@mn½U;KdPb=B]e;G[`f?B<>GFP;:KY9W?BKKY9;GZJt;XY:V`}GIJS:vJS:uK{GZJdJSU;t;tbAF:V`N:uPiKL:&ME]dGFKL9„KL9;:
?>M;MiGFKLGF=>P,?BA0G[PiC6=$XL`f?BKLGF=$P}KY9,?&K8]:V:VK^pNM
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89;:O,:VAZMN=BC|P;=$P;`}=$P;=>KY=$PbGIH‰A[=$<>GIH{\,:V<g?BPƒGFPfKL9;:AI?BKL:RÄVÅ@Æ&Ç
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GIMi:¢?«\,?&AI?&P,H*:&MfJSUbXYj@:Vpk=BCnKL9;:O,:VAZMaGFP
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p}H*=$P,J^GIMi:uXYGFPb<kJS=$`}:‰=&CKL9;:t;XY=>\;AF:u`fJDKL9,?BKAF:&MkKY=
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