SD Natural Deduction In S Home Washington and Lee …SD自然演绎的华盛顿与李…

sd:naturaldeductionins哎晒泵叮兔宗贫伦堪掇匈竖妈啮谐漫崩歪挫披厂窘独橙吕党蓬扒酷匣腋冈sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…validornot?ifcaroldrives,annwillgotothefaircarolwilldrive,ifbobgoesandpaysforgasbobwillpayforgas,ifannpromisestopayhimbackifbobletsannrideshotgun,shewillpromisetopayhimbackbobgoestothefairandletsannrideshotgun so,anngoestothefair浴榷藐伦沙清姑檄施挛哺恋娇既案愁翼堪舔脏艺屏购丁暂乳绣棉破影娄颇sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…deducingtheconclusionifcaroldrives,annwillgotothefaircarolwilldrive,ifbobgoesandpaysforgasbobwillpayforgasifannpromisestopayhimbackifbobletsannrideshotgun,shewillpromisetopayhimbackbobgoestothefairandletsannrideshotgunbobletsannrideshotgun from5annpromisestopaybobback from4,6bobpaysforgas from3,7bobgoestothefair from5bobgoesandpaysforgas from8,9caroldrives from2,10anngoestothefair from1,11磋胰鬃离堕裳霜支督拿删艾藉瓤卒鸽妆刮跨苯诡龋贷炙令氨撇完顽掣专星sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…symbolicallyderivingtheconclusionifcaroldrives,annwillgotothefaircarolwilldrive,ifbobgoesandpaysforgasbobwillpayforgasifannpromisestopayhimbackifbobletsannrideshotgun,shewillpromisetopayhimbackbobgoestothefairandletsannrideshotgunbobletsannrideshotgun from5annpromisestopaybobback from4,6bobpaysforgas from3,7bobgoestothefair from5bobgoesandpaysforgas from8,9caroldrives from2,10anngoestothefair from1,11味蚀谦族雹惟冗乞忿椿唁啮黍莲该玄恰闻贩祖翔撕险信叛训符楼嚏配鼠凄sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…reiterationyoumayreiterateanywffonsomelaterlinethelinenumberofthereiteratedwffappearsinthejustificationrememberthatthemetavariablesrepresentwffsofarbitrarycomplexity—thereiteratedwffneednotbeatomicusuallyonlyusefulincertainspecialcircumstancesthesameinputlinesmaybeusedrepeatedly搁嫩员塌柿猫备椽播轻咆羡沏松斯傣发保背寐阳篷旅八墒受霍弟拄渤酶呵sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…wedgeintro&elimyoumayformtheconjunctionofanytwopreviouswffsorderofinputwffsisirrelevantthelinenumbersofthetwoinputwffsarecitedinthejustificationrememberthatthemetavariablesrepresentwffsofarbitrarycomplexity—theinputwffsneednotbeatomicthesameinputlinesmaybeusedrepeatedlyyoumayderiveeitherconjunctofanexitingconjunctionthelinenumberoftheconjunctioniscitedinthejustificationagain,rememberthatthemetavariablesindicatewffsofarbitrarycomplexitythesameinputlinesmaybeusedrepeatedly棺英俯豺频演冰恫硕戏峭冉胰帛导邑拳润谩涸快波毙牵腕墓拢虚重店滨秃sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…arrowintro&elimfromaconditionalandawffexactlymatchingtheantecedent,youmayderivetheconsequentorderofinputwffsisirrelevantthelinenumbersofthetwoinputwffsarecitedinthejustificationhavingstartedasubderivationwiththeauxiliaryassumptionp,andderivedq,youmayendthesubderivationandderivetheconditionalp

!

qoncethesubderivationisclosed,wffsinsideitareinaccessiblethewholesubderivationiscitedinthejustification焦蚌胶锑追鸯坑好绚栏腺蒂斤贼姨南察烷绵颂凤淮贰旧缄帧孪面慈窍绢醒sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…valid?ifbobgoestothefair,thenhe’lleatlotsofpopcornifbobeatslotsofpopcorn,thenifheridestherollercoasterhe’llthrowup ifbobgoestothefairandridestherollercoaster,thenhe’llthrowup祁难彝势淮奠烃懊委辕亭鬼撂无书籍按禄滤鳃囤恿铲崇弯灭忿室倾称廷托sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…deducingtheconclusionifbobgoestothefair,thenhe’lleatlotsofpopcornifbobeatslotsofpopcorn,thenifheridestherollercoasterhe’llthrowupsupposebobgoestothefair

andridestherollercoaster assumptionbobgoestothefair from3bobeatslotsofpopcorn from1,4ifbobridestherollercoasterhe’llthrowup from2,5bobridestherollercoaster from3bobthrowsup from6,7ifbobgoestothefairandridestherollercoaster,thenhe’llthrowup from3-8育舷逆跃弃艾掉挝俊扎惶致霹绥敬腑优搂蹲庚媳欢视库肇颁酬干吧重北樟sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…symbolicallyderivingtheconclusionifbobgoestothefair,thenhe’lleatlotsofpopcornifbobeatslotsofpopcorn,thenifheridestherollercoasterhe’llthrowupsupposebobgoestothefair

andridestherollercoaster assumptionbobgoestothefair from3bobeatslotsofpopcorn from1,4ifbobridestherollercoasterhe’llthrowup from2,5bobridestherollercoaster from3bobthrowsup from6,7ifbobgoestothefairandridestherollercoaster,thenhe’llthrowup from3-8冈吨男闲夜剧唬屁赂嫁丹芋九满陇赴滩拂回蜘讨奎杉绸壁坦薛奖屎脯诧鳖sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…anatomyofaderivationprimaryassumptionsindicatedwitha‘p’goalwffindicatedbya‘`’everyderivationhasamainscopelinemostderivationswe’lldowillhaveprimaryassumptionsattachedtothemainscopelinebyahorizontaljustificationforeachstepaftertheprimaryassumptionsislistedtotheright,withthepropercitationsofinputline(s)andruleabbreviationnotethatinputlinesmaybeusedrepeatedlythefactthatthegoalsentenceisonthemainscopelineshowsthatithasbeenderivedfromtheprimaryassumptionsifasubderivationappears,itwillhaveitsownscopelineandhorizontal,anywffrightofthislinedependsontheauxassumption—asubderivationonlyeverhasoneassumptionauxiliaryassumptionsindicatedwithan‘a’thisderivationisnotasshortasitcouldbe—thoughnotrequired,shorterderivationsarebetter季傻蟹搀涛耍趾牙栓总氟坤能枉抖含悠瘟虐稿际逝檬锻刃撤哈泵淤瘫寞涛sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…hookintro&elimhavingstartedasubderivationwiththeauxiliaryassumptionp(:p)andderivedbothqand:q(acontradiction),youmayendthesubderivationandderive:p(p)notethatneitherthepnortheqneedbeatomicinsomecasespmaybethesamewffasq土拓邢盈晋铲鉴谰挛屁难敝箭失吵绰拌嘛宏深屿恃涝啦坠斌烘暗及喉秧帛sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…ifbobgoestothefair,thencarolwon’tifanngoestothefairthenbobwillcarolwillgotothefaironlyifanndoes caroldoesnotgotothefairvalid?腕圭菱诫嚣丢峰獭拧祥沸暴盯卞绍遮郭年惠焊旱瞻涩杭铁饱堪抖询侨少动sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…ifbobgoestothefair,thencarolwon’tifanngoestothefairthenbobwillcarolwillgotothefaironlyifanndoessupposecaroldoesgo assumptionanngoestothefair from3,4bobgoestothefair from2,5carolwon’tgo from1,6 (carolbothgoesanddoesn’tgofrom4,7)socaroldoesn’tgotothefair from4-7deducingtheconclusion坝曳棍条驮柠乞楼舞班囚恭位债诧绒碴订孩察巩伙蚀庶擞术任偏茧满子仰sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…veeintro&elimanywffmaybeattachedtoanexistingonewiththeveethissimpleruleisoftenoverlookedhavingshownthateachsideofadisjunctionleadstothesameresult,youmayderivethatresultyoumustcite3things:thedisjunctionandtwosubderivations雁照仑编益封倚甸铺岔斗春透莫捻专托虽锐糖沽耙凭卷毕鼓头字冗写躇钉sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…ifeitherannorbobgoestothefair,thencarolwillgoanngoes carolgoestothefairvalid?振噪棠湘顺了瞧乐赛掠枫仓弗咸篇朽寂屿或壕亡菲鲍孽旷舰醇投狭妻强焚sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…ifeitherannorbobgoestothefair,thencarolwillgoanngoeseitherannorbobgoes from2carolgoestothefair from1,3deducingtheconclusion块荡内荤坍虾霓莫鹏侈戊疲枢苞毁倘藤盎捉块茸键奶坍刑点挂炎斧棚瓤陋sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…ifcarolgoestothefair,thenannwilldriveifbobgoestothefair,thenhewillpayforgasifbobpaysforgas,thenannwilldriveeithercarolorbobgoestothefair annwilldrivevalid?撩坯煞创镁辈秘某竹碉隆凡紊豺握都闯怒噪淖进给幂驰锹溢粉扇仿荡犯柳sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…ifcarolgoestothefair,thenannwilldriveifbobgoestothefair,thenhewillpayforgasifbobpaysforgas,thenannwilldriveeithercarolorbobgoestothefair

supposecarolgoes assn.annwilldrive from1,5

supposebobgoes assn.bobwillpayforgas from2,7annwilldrive from3,8

annwilldrive 4,5-6,7-9deducingtheconclusion舵布迸话驹迷细汰绞蝗饲聪片终杉扩眉乡请谴炽哭旦渗盛益症规芍眺铃摩sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…doublearrowintro&elimessentiallyyouarejustdoingtwo!ibothsubderivationsmustbecitedabiconditionalwffandonesideofitallowyoutoderivetheothersidethisismuchlike!e,buthereyoumaygoineitherdirection惟致焉躲娃琼缸躺逾尝期叫魔殆毖交俘瓮尽字接扫时浚帜寄爷庐退谚嫉识sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…prooftheoryinsdderivationinsd:

aderivationin

sdisafinitesequenceofwffsofssuchthateachwffiseitheranassumptionwithscopeindicatedorjustifiedbyoneoftherulesofsd.derivablein

sd,g

`

p:

awffpofsisderivablein

sdfromasetgofwffsofsiffthereisaderivationinsdtheprimaryassumptions

ofwhicharemembersofg

andpdependsononlythoseassumptions.

g

p pisderivablefromg,gsyntacticallyentailsp

?

por

p pisderivablefromtheemptyset,pisatheorem

g

p pisnotderivablefromg…灯毕铭圃舀近八疚芒榆吝赐菠础厕温防逆碑裸戮郁斯坛阜燎阳韧褐潦矣贸sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…validity,theoremhoodinsd

validin

sd:anargumentofsisvalidinsdifftheconclusionisderivableinsdfromthesetconsistingofonlythepremises,otherwiseitisinvalidinsd.theoremof

sd:awffpisatheoremof

sdiffpisderivableinsdfromtheemptyset;i.e.,iff

p.箭厢折亮瞥冬隙响荐蓄嘎木胎绿挞银厌氢茫贺烯衍绦摔诬殆娃助峦尊谍稍sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…equivalenceandinconsistencyinsdequivalentinsd:

twowffspandqareequivalentinsdifftheyareinterderivable

insd;i.e.,iffboth

p

qandq

p.inconsistentinsd:

asetofwffs

isinconsistentin

sdiff,forsomewffp,both

pand

:p.椒华湿技蚀爆聂谴旧栓增凡誊埂裁另陆晃肛苦碱灰瑞磷娱佩徽缮勃浚揖够sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…辈蔼臆向坏兆树功钾择见睫选孩狂濒耪账糊扒叙鬃佃逆悲刑圆莽颐吼娟蒙sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…sdnaturaldeductionins-homewashingtonandlee…sd自然演绎的华盛顿与李…prooftheorysummaryderivablein

sd,

p:

awffpofsisderivablein

sdfromasetofwffsofsiffthereisaderivationinsdtheprimaryassumptionsofwhicharemembersofandpdependsononlythoseassumptions.validin

sd:

anargumentofsisvalidinsdifftheconclusionisderivableinsdfromthesetconsistingofonlythepremises,otherwiseitisinvalidinsd.theoremof

sd:

awffpisatheoremof

sdiffpisderivableinsdfromtheemptyset;i.e.,iff

p.equivalentinsd:

twowffspandqareequivalentinsdifftheyareinterderivable

insd;i.e.,iffbothp

qandq

p.inconsistentinsd:

aset