View of On the Formal Ontology of Being and Time

$

5

7

<

.

8

à

<

  52&=1,.,),/2=2),&=1( 7RP/;9,QXPHU± '2,KWWSG[GRLRUJUI $1'5=(- %,à$7 _

2 )250$/1(- 2172/2*,, %<78 , &=$68



'RMHGQHMQDXNLQDOHĪ\EDGDQLH%\WXMDNRWDNLHJR LDWU\EXWyZNWyUHPXSU]\VáXJXMą>«@ MDNUyZQLHĪZ\UD]yZLSRMĊüWDNLFKMDN µZF]HĞQLHMV]\¶µSyĨQLHMV]\¶µURG]DM¶LµJDWXQHN¶ µFDáRĞü¶LµF]ĊĞü¶LLQQ\FKWHJRURG]DMX $5<6727(/(6 1DXNRZF\LILOR]RIRZLHSRV]XNXMą FDáRĞFLRZHJRV\VWHPXĞZLDWDLWRV\VWHPX NWyU\U]HWHOQLHMLSHáQLHMQDVWDZLRQ\MHVW QDUHIHUHQFMĊQLĪMĊ]\NSRWRF]Q\ :LOODUG9DQ2UPDQ48,1( :352:$'=(1,(



 -HĞOL S\WDQLD L WH]\ RQWRORJLF]QH PDMą VSHF\ILF]Q\ VHQV SR]QDZF]\ WR LVWQLHMą WHĪ PHWDRQWRORJLF]QH ]DVDG\ Z\MDĞQLDMąFH LFK VSHF\ILNĊ &R QDM PQLHMGZLHWDNLH]DVDG\PRĪQDRGQDOHĨüZSUDFDFK$U\VWRWHOHVD_2WRRQH 

3URI GU KDE $1'5=(-%,à$7 ² =DNáDG )LOR]RILL QD :\G]LDOH $GPLQLVWUDFML L 1DXN 6SR áHF]Q\FK3ROLWHFKQLNL:DUV]DZVNLHMDGUHVGRNRUHVSRQGHQFML3O3ROLWHFKQLNL:DUV]DZD HPDLODELODW#DQVSZHGXSO

_{$UW\NXá VWDQRZL UR]ZLQLĊFLH QLHNWyU\FK ZąWNyZ UHIHUDWX Ä/RJLF]QD WHRULD E\WX L F]DVX´}

Z\JáRV]RQHJRSRGF]DVNRQIHUHQFMLLogika a modalno. VIII Jesienna Konferencja Logiki.8/ OLVWRSDGDUDWDNĪHSHZQ\FKZąWNyZDUW\NXáyZ%,à$7LD3URMHNW]RVWDáVIL QDQVRZDQ\]HĞURGNyZ1DURGRZHJR&HQWUXP1DXNLSU]\]QDQ\FKQDSRGVWDZLHGHF\]MLQU'(& %+6

_{$5<6727(/(6Met.D $5<6727(/(6F} _{48,1(&\W]D6=8%.$}

_{=DLQWHUHVRZDQLH ILOR]RILą $U\VWRWHOHVD VWRSQLRZR URĞQLH Z RVWDWQLFK G]LHVLĊFLROHFLDFK ]RE}

$1'5=(- %,à$7 

 3RGVWDZRZH S\WDQLD RQWRORJLF]QH GRW\F]ą DWU\EXWyZ GRZROQHJR E\WX ZW\PVXEVWDQFMLQDWXUDOQ\FKLLQQ\FKSU]HGPLRWyZLVWQLHMąF\FKZF]DVLH

 7H]\RQWRORJLF]QH RSLVXMą DWU\EXW\ E\WX ]D SRPRFą HNVSOLNDWyZ RJyOQ\FK SRMĊüNWyUHVąNOXF]RZHZVWUXNWXU]HOXG]NLHJRP\ĞOHQLDRĞZLHFLHLXP\ĞOH_ 'R WHJR URG]DMX SRMĊü QDOHĪą PLĊG]\ LQQ\PL&2ĝ.72ĝ:&=(ĝ1,(-3Ïħ1,(- 52'=$-*$781(.RUD]&=ĉĝû&$à2ĝû

 =DVDGD  SU]\SRPLQD RĞZLHFHQLRZą LGHĊ ontologiae artificialis &KUL VWLDQD :ROIID ]RE VHNFMĊ  D WDNĪH ² GZXG]LHVWRZLHF]Qą NRQFHSFMĊ PHWDIL]\NL RSLVRZHM 3HWHUD 6WUDZVRQD 6XJHUXMH RQD QDVWĊSXMąFH REMDĞQLH QLHpojcie ontologiczneMHVWSRMĊFLHPSU]HGPLRWRZ\PWM]QDF]HQLHPSHZ QHJR WHUPLQX MĊ]\ND SU]HGPLRWRZHJR XĪ\ZDQ\P Z ZLHOX REV]DUDFK QDXNL MDNRNOXF]RZ\HOHPHQWVWUXNWXU\SHZQ\FKQLH]DZRGQ\FKVFKHPDWyZUR]XPR ZDĔ2EMDĞQLHQLHWRMHVWWHĪSU]\MPRZDQHMDNR]DáRĪHQLHGDOV]\FKUR]ZDĪDĔ

 -HĞOLGREU]HRNUHĞORQHS\WDQLDLWH]\RQWRORJLF]QHPDMąVHQVQDXNRZ\WR LFKIRUPXáRZDQLHDQDOL]DLV\VWHPDW\]DFMDSRGOHJDMąSHZQ\PRJyOQ\P]DVD GRP PHWRGRORJLL QDXN 5yZQLHĪ L WHJR URG]DMX ]DVDG\ PRĪQD Z\SURZDG]Lü ]UDFMRQDOQHMUHNRQVWUXNFMLQLHNWyU\FKWHNVWyZ6WDJLU\W\2WRGZLH]QLFK

 2QWRORJLDMHVWQDMRJyOQLHMV]ąQDXNąUHDOQą_{ZW\PVHQVLHMHVWRQDfilozofi}

pierwsz 

RNUHĞODQ\ PLDQHP ÄPHWDIL]\NL QHR$U\VWRWHOHVRZVNLHM´ 129271< L 129È.   'R WHJR QXUWXPRĪQD]DOLF]\üZLHOX]QDQ\FKDXWRUyZNWyU]\ZV]HURNLP]DNUHVLHVWRVXMąPHWRG\IRUPDOQH Z ILOR]RILL Z W\P 0 %XQJH 1LQR &RFFKLDUHOOD . )LQH 8 0HL[QHU 3 6LPRQV % 6PLWK 15HVFKHU

_{Ä'R >VXEVWDQFML@ X]QDZDQ\FK SRZV]HFKQLH QDOHĪą VXEVWDQFMH QDWXUDOQH QD SU]\NáDG RJLHĔ}

ZRGDSRZLHWU]HRUD]LQQHFLDáDSURVWHQDVWĊSQLHURĞOLQ\RUD]LFKF]ĊĞFL]ZLHU]ĊWDLF]ĊĞFL]ZLHU]ąW DZNRĔFXĞZLDWIL]\F]Q\LMHJRF]ĊĞFL1DWRPLDVWQLHNWyUHV]NRá\JáRV]ąSRJOąGĪHVXEVWDQFMDPLVą LGHH L SU]HGPLRW\ PDWHPDW\F]QH´ $5<6727(/(6 Met. D $5<6727(/(6 F  Ä6XE VWDQFMHQDWXUDOQH´QLHFRGDOHM6WDJLU\WD RNUHĞODMH PLDQHPÄVXEVWDQFML]P\VáRZ\FK´SU]HFLZ VWDZLDQH SU]HGPLRWRP DEVWUDNF\MQ\P LGHRP L SU]HGPLRWRP PDWHPDW\F]Q\P QDOHĪ\ EH] ZąW SLHQLD]DOLF]\üGRÄU]HF]\LVWQLHMąF\FKZF]DVLH´WHQRVWDWQL]ZURW]NROHLGRĞüF]ĊVWRSRMDZLD VLĊZUR]ZDĪDQLDFKQDWHPDWSRMĊFLD&=$68SU]HSURZDG]RQ\FKZ.VLĊG]H,9Fizyki

_{=ZURWeksplikat pojcia PR]QDF]DWXV\PEROOXEWHUPLQNWyUHJR]QDF]HQLHMHVWUH]XOWDWHP}

HNVSOLNDFML SRMĊFLD P QS V\PERO Ä+2´ MHVW HNVSOLNDWHP SRMĊFLD:2'$ D WHUPLQ ÄE\W´ MHVW

HNVSOLNDWHPSRMĊFLD&2ĝF]\WHĪ&2.2/:,(.

_{3RUSLHUZV]ąF]ĊĞüPRWWD36WUDZVRQZVND]XMH$U\VWRWHOHVDMDNRMHGQHJR]GZyFK±RERN}

, .DQWD ± S UHNXUVRUyZ metafizyki opisowej F]\OL PHWDIL]\NL RSLVXMąFHM WUHĞü L VLDWNĊ SRMĊü NOXF]RZ\FKZVWUXNWXU]HOXG]NLHJRP\ĞOHQLDRĞZLHFLH675$:621±

_{3U]H]nauki realneUR]XPLHP\WXQDXNLGRW\F]ąFH]MDZLVNLSURFHVyZ]DFKRG]ąF\FKZSU]\}

2 )250$/1(- 2172/2*,, %<78 , &=$68 

 :]RUFRZRXV\VWHPDW\]RZDQDZLHG]DRQWRORJLF]QDPDVWUXNWXUĊDNVMRPD W\F]QRGHGXNF\MQą

 =DVDGD  QDGDMH ILOR]RILL ÄSLHUZV]HM´ FKDUDNWHU RQWRORJLF]Q\  ² HNVSOLNDF\MQ\²UHDOQ\QDWRPLDVW]DVDGD²IRUPDOQ\3RMĊFLH2172 /2*,,MHVWWXUR]XPLDQH]JRGQLH]RJyOQ\PLZ\PRJDPLZVSyáF]HVQHMPHWRGR ORJLLQDXNL]DU\VWRWHOHVRZVNLPL]DVDGDPL±:W\PVHQVLHR Q W R O R J L D  M H V W  Q D M R J y O Q L H M V ] ą  Q D X N ą  U H D O Q ą  U R ] Z L M D Q ą  ] D  S R P R F ą  P H  W R G \  D N V M R P D W \ F ] Q H M  Z  M Ċ ] \ N X  S R M Ċ ü  R Q W R O R J L F ] Q \ F K  $U\VWRWHOHVRZVNLHWHUPLQ\ÄE\W´LÄE\WMDNRWDNL´F]\WHĪ²ZDOWHUQD W\ZQ\PSU]HNáDG]LH²ÄE\WMDNRE\W´QLHVąGRĞüMDVQH3U]\MPLMP\QDVWĊ SXMąFą UHNRQVWUXNFMĊ LFK ]QDF]HQLD byt MHVW WR EąGĨ MHGHQ ] HOHPHQWyZ PDNV\PDOQLH V]HURNLHM G]LHG]LQ\ SU]HGPLRWRZHM EąGĨ MHGQD ] NODV WDNLFK HOHPHQWyZ :SUDZG]LH $U\VWRWHOHV XĪ\áE\ WX SRMĊFLD52'=$-8 ]DPLDVW

SRMĊFLD./$6< DOH DNXUDW QLH PDP\ SRG UĊNą V]HURNR X]QDZDQHM SU]HG

PLRWRZHM QLHVHPDQW\F]QHM WHRULL URG]DMyZ ² Z SU]HFLZLHĔVWZLH GR WHRULL NODV : NRQWHNĞFLH ZVSyáF]HVQHM ILOR]RILL WUDNWRZDQHM MDNR F]ĊĞü V]HURNR SRMĊWHM QDXNL RJyOQ\ ORJLF]Q\ WHUPLQ ÄNODVD´ Z\GDMH VLĊ GRĞü GREU\P RGSRZLHGQLNLHP$U\VWRWHOHVRZVNLHJRSRMĊFLD52'=$-8.

 =JRGQLH]SRZ\ĪV]\PREMDĞQLHQLHPL]GXFKHPPHWDILOR]RILL$U\VWRWHOHVD SU]\MPXMHVLĊGDOHMQDVWĊSXMąFHGHILQLFMH3RSLHUZV]HprzedmiotGHILQLXMHP\ MDNR HOHPHQW SHZQHM NODV\ , SR GUXJLH ]DNáDGDP\ ĪH teoria ontologiczna MHVW DNVMRPDW\]RZDOQ\P ]ELRUHP ]GDĔ RJyOQ\FK R QLHRJUDQLF]RQ\P ]DNUHVLH NZDQ W\ILNDFML VIRUPXáRZDQ\FK ]D SRPRFą HNVSOLNDWyZ SRMĊü R Q W R O R J L F ] Q \ F K &HOHP RQWRORJLL MHVW UR]ZLą]\ZDQLH SHZQHM NODV\ SUREOHPyZ ILOR]RILF]Q\FK ]DSRPRFąQDMOHSV]\FKGRVWĊSQ\FKWHRULLRQWRORJLF]Q\FK3RGVWDZRZ\PZD UXQNLHP E\FLD GREUą WHRULą RQWRORJLF]Qą MHVW MHM ] J R G Q R Ğ ü  ]  Z L H G ] ą  G R E U ] H  X J U X Q W R Z D Q ą  Z  V ] F ] H J y á R Z \ F K  Q D X N D F K  U H D O Q \ F K  2VWDWQLHG]LHVLĊFLROHFLDVSU]\MDMąUR]ZRMRZLWDNSRMĊWHMRQWRORJLLL:W\P F]DVLH QDVWąSLáR RJURPQH RĪ\ZLHQLH SUDF ] ]DNUHVX DQDOLW\F]QHM PHWDIL]\NL Z W\P PHWDIL]\NL F]DVX ILOR]RILL IL]\NL RUD] metaontologii ² QRZHM VXEG\VF\SOLQ\ ILOR]RILF]QHM PDMąFHM QD FHOX Z\MDĞQLHQLH QDWXU\ L PHWRG DQDOLW\F]QHMRQWRORJLL_



_{Ä:V]\VWNLHQDXNLPDMąZVSyOQąSRGVWDZĊG]LĊNLZVSyOQ\PDNVMRPDWRPZVSyOQ\PLDNVMR}

PDWDPLQD]\ZDPWHNWyU\FKVLĊXĪ\ZDMDNRSU]HVáDQHNGRZRGXDQLHSU]HGPLRW\DQLDWU\EXW\ GRZRG]RQH´$5<6727(/(6An. wtóre D$5<6727(/(6D

_{7HUPLQ ÄPHWDRQWRORJLD´ MHVW WX UR]XPLDQ\ ]JRGQLH ] QDVWĊSXMąF\P REMDĞQLHQLHP Ä,I WKH}

$1'5=(- %,à$7 

 3RPLPRRZHJRRĪ\ZLHQLDZFLąĪEUDNXMHGREU]HRVDG]RQHMZWUDG\FMLILOR ]RILF]QHM NRQFHSFML GRVWDUF]DMąFHM RGSRZLHG]L QD pytanie o struktur

onto-logii-DNLHVąJáyZQHW\S\WHRULLRQWRORJLF]Q\FKLMDNLHSRGVWDZRZHUHODFMH

PLĊG]\QLPL]DFKRG]ą"&HOHPWHJRDUW\NXáXMHVWZVND]DQLHWDNLHMNRQFHSFML RUD]MHM ]DVWRVRZDQLHZ NRQVWUXNFMLSRGVWDZRZ\FKSU]\NáDGyZWHRULLRQWR ORJLF]Q\FK MHGQ\P ] QLFK MHVW SHZQD QRZD ZHUVMD WHRULL F]DVX Z\SHá QLRQHJR_

 7HUPLQÄIRUPDOQDRQWRORJLD´²XĪ\W\ZW\WXOHDUW\NXáX²R]QDF]DRQWR ORJLĊ UR]ZLMDQą ]D SRPRFą ZVSyáF]HVQ\FK PHWRG IRUPDOQ\FK ORJLF]Q\FK OXEQDMRJyOQLHMV]\FKPHWRGPDWHPDW\F]Q\FK8Z]JOĊGQLDMąF]DVDGĊGH V\JQDW WHJR WHUPLQX MHVW LGHQW\F]Q\ ] MHGQą ]H ZVSyáF]HVQ\FK ZHUVML RQWR ORJLLZVHQVLHZ\ZRG]ąF\PVLĊRG$U\VWRWHOHVD_  75=<.21&(3&-(2172/2*,,)250$/1(-



 =DUyZQRZ WUDG\F\MQHMMDNLZHZVSyáF]HVQHMILOR]RILLE\WXPRĪQDZ\ UyĪQLüW U ] \  N R Q F H S F M H  I R U P D O Q H M  R Q W R O R J L L   O R J L F ] Q H M H N V S O L  N D F \ M Q H M  L  H P S L U \ F ] Q H M .RQFHSFMHWH Z\VWĊSXMąZ]DOąĪNRZ\FKSR VWDFLDFKMXĪ ZG]LHáDFK$U\VWRWHOHVD2GJU\ZDMąWHĪLVWRWQą UROĊZH ZVSyá F]HVQHMILOR]RILL

 Ontologia logiczna ]ZDQD WX ]D - 3HU]DQRZVNLP ÄRQWRORJLNą´_{ MHVW}

RQWRORJLąNWyUHMUH]XOWDW\VąZ\UDĪDOQHZMĊ]\NXczystych formu logicznych



IRUPHWDRQWRORJ\LVµ:KDWGRZHPHDQZKHQZHDVN:+$7,67+(5(?¶DQGµ:KDWLVWKHFRUUHFW

PHWKRGRORJ\ RI RQWRORJ\"¶´ %(572 L 3/(%$1,   7HUPLQ WHQ XSRZV]HFKQLá VLĊ JáyZQLH G]LĊNLSXEOLNDFML9$1,1:$*(1

_{ 'ZLH ZHUVMH RZHM WHRULL ]RVWDá\ SU]HGVWDZLRQH Z SUDFDFK %,à$7  L D 5yĪQLFD}

PLĊG]\QLPLDWHRULąSU]HGVWDZLRQąZW\PDUW\NXOHMHVWREMDĞQLRQDZSU]\SLVLH

_{3RU QS GRĞü F]ĊVWR F\WRZDQH REMDĞQLHQLH Ä)RUPDO RQWRORJ\ >«@ LV D GLVFLSOLQH LQ}

ZKLFKWKHIRUPDOPHWKRGVRIPDWKHPDWLFDOORJLFDUHFRPELQHGZLWKWKHLQWXLWLYHSKLORVRSKLFDO DQDO\VHV DQG SULQFLSOHV RI RQWRORJ\ ZKHUH E\ RQWRORJ\ ZH PHDQ WKH VWXG\ DQG DQDO\VLV RI EHLQJ qua EHLQJ LQFOXGLQJ LQ SDUWLFXODU WKH GLIIHUHQW FDWHJRULHV RI EHLQJ DQG KRZ WKRVH FDWHJRULHVDUHFRQQHFWHGZLWKWKHQH[XVRISUHGLFDWLRQLQODQJXDJHWKRXJKWDQGUHDOLW\´&2& &+,$5(//$[LLL6DPWHUPLQÄRQWRORJLD´]RVWDáZSURZDG]RQ\GRHXURSHMVNLFKVáRZQLNyZ GRĞüSyĨQRERXVFK\áNXWUZDMąFHMSRQDGGZDW\VLąFHODWHSRNLZNWyUHMQLHPDOFDáDILOR]RILD E\áD UR]ZLMDQD MDNR QDXND R E\FLH LMHJR ZáDVQRĞFLDFK -DN ZLHP\ WHUPLQ yZ VWDá VLĊ SRSXODUQ\Z;9,,,ZLHNXJáyZQLHG]LĊNLSUDFRP&K:ROIID

_{1DWHPDW]QDF]HQLDWHUPLQXÄRQWRORJLDORJLF]QD´ L WHUPLQyZ EOLVNR]QDF]Q\FKZHZVSyá}

2 )250$/1(- 2172/2*,, %<78 , &=$68  WM IRUPXá ORJLF]Q\FK Z NWyU\FK QLH Z\VWĊSXMą ĪDGQH VWDáH SR]DORJLF]QH 3U]\NáDGDPL WUDG\F\MQ\FK WH] ] ]DNUHVX RQWRORJLL ORJLF]QHM Vą $U\VWRWHOH VRZVNLH SUDZD QLHVSU]HF]QRĞFL L Z\áąF]RQHJR ĞURGND F]\ WHĪ /HLEQL]MDĔVND ]DVDGD LGHQW\F]QRĞFL QLHRGUyĪQLDOQHJR 1DMSURVWV]H Q L H W D X W R O R J L F ] Q H  WZLHUG]HQLH RQWRORJLNL Z\UDĪD IRUPXáD Ä∃xyx≠y´ JáRV]ąFD ĪH LVWQLHMą FR QDMPQLHM GZD SU]HGPLRW\ %DUG]LHM ]áRĪRQ\FK SU]\NáDGyZ WDNLFK WZLHUG]HĔ ²]DUyZQRWDXWRORJLF]Q\FKMDNLQLHWDWXWRORJLF]Q\FK²GRVWDUF]DMąMĊ]\NL ZVSyáF]HVQ\FKV\VWHPyZORJLF]Q\FKZ\ĪV]\FKU]ĊGyZ

 Eksplikacyjna ontologia formalna MHVW RQWRORJLą UR]ZLMDQą ]D SRPRFą DNVMRPDW\F]QHM HNVSOLNDFML SRMĊü RQWRORJLF]Q\FK 2JyOQD LGHD HNVSOLND F\MQHM RQWRORJLL IRUPDOQHM ]RVWDáD MXĪ GRĞü Z\UDĨQLH RNUHĞORQD Z RVLHP QDVW\PZLHNXSU]H]:ROIIDZSRVWDFLMHJRNRQFHSFMLontologiae artificialis :HGáXJ:ROIIDSRMĊFLDRQWRORJLF]QH]ZDQHSU]H]HĔnotiones generalesVą SRZV]HFKQLH VWRVRZDQH Z UR]XPRZDQLDFK GRW\F]ąF\FK SU]\URG\ L XP\VáX RQWRORJLDHNVSOLNDF\MQDontologiae artificialisPDE\üQDXNąZNWyUHM]ELyU RZ\FK²QLHGRĞüMDVQ\FK²SRMĊüMHVWSU]HNV]WDáFDQ\ZGHGXNF\MQ\V\V WHPMDVQ\FKLZ\UDĨQ\FKLGHLRUD]]DVDG]QLPL]ZLą]DQ\FK_

 Empirycznaontologia formalna MHVWRQWRORJLąE\WyZLVWQLHMąF\FKZUHDO Q\PF]DVLH²DZLĊFSU]HGPLRWyZUHDOQHJRĞZLDWD²UR]ZLMDQą]DSRPRFą PHWRG\ DNVMRPDW\F]QHM ]JRGQLH ] QDV]ą QDMOHSV]ą ZLHG]ą XJUXQWRZDQą ZQDXNDFK V]F]HJyáRZ\FK 7D NRQFHSFMD MHVW NRQVHNZHQFMą ]DVDG  L  ]RE :SURZDG]HQLH 2ELH ]DVDG\ E\á\ VWRVRZDQH ]DUyZQR SU]H] $U\VWR WHOHVDMDNLSU]H]:ROIID3U]\NáDGHPGZXG]LHVWRZLHF]QHMZHUVMLHPSLU\F] QHMRQWRORJLLIRUPDOQHMMHVWRQWRORJLD0DULR%XQJHJR-HMRJyOQH]DVDG\Vą QDVWĊSXMąFH$.OXF]RZ\PHOHPHQWHPZV]HONLFKEDGDĔWHRUHW\F]Q\FK]D UyZQR Z QDXNDFK V]F]HJyáRZ\FK PDWHPDW\FH MDN L Z ILOR]RILL MHVW NRQ VWUXNFMDWHRULLĪDGQDLGHDRQWRORJLF]QDQLHMHVW ZSHáQLMDVQDSR]DNRQWHN VWHPWHRULL%7HRULHVą]HVREąZV\VWHPDW\F]Q\VSRVyESRZLą]DQHRQWR ORJLD MHVW V\VWHPHP WHRULL & 2QWRORJLD MHVW ]DVDGQLF]R wiedz cis WM Z\UDĪDOQą Z MĊ]\NX VIRUPDOL]RZDQ\P L naukow ]JRGQą ]H ZVSyáF]HV



_{:ROII SRGDZDá QDVWĊSXMąFH SU]\NáDG\ SRZV]HFKQLH VWRVRZDQ\FK SRMĊü RQWRORJLF]Q\FK} ,6727$ essentia,671,(1,( existentia$75<%87 attributio6326Ï% modus.21,(&=12ĝû necessitas35=<*2'12ĝûcontingentia0,(-6&( locus&=$6tempus'26.21$à2ĝû

per-fectio325=Ą'(. ordo3526727$ simplex=à2ĩ(1,( compositus :2/))  ± :HZVSyáF]HVQHMV]HURNRSRMĊWHMOLWHUDWXU]HPHWDILOR]RILF]QHMLVWQLHMąMHG\QLHSRMHG\QF]H Z]PLDQNLQDWHPDW:ROIILDĔVNLHMLGHLontologiae artificialis]REQS*,/621±  3$ħ  ± %85.+$5'7 L 60,7+ >@  *$5%$&= L 75<38=  ± %,à$7  ± ± 3HZQD ZHUVMD HNVSOLNDF\MQHM RQWRORJLL IRUPDOQHM MHVW UR]ZLMDQD ZPRQRJUDILL%,à$7RJyOQHREMDĞQLHQLDRZHMZHUVML]QDMGXMąVLĊZ%,à$7

$1'5=(- %,à$7 

Q\PL QDXNDPL UHDOQ\PL_{ =DVDG\ %XQJHJR $& Vą WHĪ DNFHSWRZDQH Z}

W\PPLHMVFX

 :VND]DQH NRQFHSFMH PRĪQD ]H VREą Z QDWXUDOQ\ VSRVyE SRáąF]\ü HNV SOLNDF\MQD RQWRORJLD IRUPDOQD ()2 PRĪH E\ü XMĊWD MDNR UH]XOWDW MĊ]\ NRZHJR Z]ERJDFHQLD L DNVMRPDW\F]QHJR UR]V]HU]HQLD RQWRORJLL ORJLF]QHM /2 D HPSLU\F]QD RQWRORJLD IRUPDOQD (0)2 ² MDNR UH]XOWDW DNVMRPD W\F]QHJRUR]V]HU]HQLD()2XZ]JOĊGQLDMąFHJRUH]XOWDW\V]F]HJyáRZ\FKQDXN HPSLU\F]Q\FK 3RWUDNWXMP\ ZSURZDG]RQH VNUyW\ MDNR V\PEROH RGSRZLHG QLFK]ELRUyZWZLHUG]HĔRQWRORJLF]Q\FKLR]QDF]P\OLWHUąÄ6´]ELyUZV]\VW NLFK WZLHUG]HĔ QDXNRZ\FK 3RVWXORZDQH ]ZLą]NL PRĪQD RSLVDü ]D SRPRFą LQNOX]ML /2 ()2 (0)2 6 ∅ ≠ w w w   2QWRORJLF]QLH]LQWHUSUHWRZDQHV\PEROHNZDQW\ILNDWRUDHJ]\VWHQFMDOQHJR ∃L]QDNXLGHQW\F]QRĞFL VąSU]\NáDGDPLHNVSOLNDWyZQDMEDUG]LHMSRGVWD ZRZ\FKSRMĊüORJLF]QRRQWRORJLF]Q\FKV\PEROÄ∃´MHVWHNVSOLNDWHPSRMĊFLD

,671,(1,$DV\PEROÄ ´²SRMĊFLD72ĩ6$02ĝ&,:NRQVHNZHQFMLGRZRO

QH SU]HGPLRWRZR ]LQWHUSUHWRZDQH WZLHUG]HQLH WHRULL LGHQW\F]QRĞFL SLHUZ V]HJR OXE Z\ĪV]\FK U]ĊGyZ VWDMH VLĊ SU]\NáDGHP ]GDQLD QDOHĪąFHJR GR ]ELRUX/2VWąGZQLRVHNRMHJRQLHSXVWRĞFL

 3RZ\ĪV]HREMDĞQLHQLDWZRU]ąRJyOQHUDP\GODMHGQROLWHMNRQFHSFMLRQWROR JLLIRUPDOQHM]DZLHUDMąFHM/2()2L(0)2*áyZQ\P]DGDQLHPSR]RVWDá\FK IUDJPHQWyZ DUW\NXáX MHVW UR]ZLQLĊFLH L REMDĞQLHQLH QLHNWyU\FK NOXF]RZ\FK V]F]HJyáyZRPDZLDQHMNRQFHSFMLZ]DNUHVLHGRW\F]ąF\P/2L()2ZGZyFK SR]RVWDá\FKVHNFMDFKF]ĊĞFL,_{DQDVWĊSQLHZVND]DQLHSRGVWDZRZ\FKSU]\} NáDGyZWHRULLRQWRORJLF]Q\FK]]DNUHVX/2()2L(0)2ZF]ĊĞFL,,2ZH SU]\NáDG\GRW\F]ąV\VWHPXPRQDG\F]QHMWHRULLLGHQW\F]QRĞFLGUXJLHJRU]ĊGX RUD]MHMGZyFKDNVMRPDW\F]Q\FKUR]V]HU]HĔVáDEHMHNVSOLNDF\MQHMLPRFQHM HPSLU\F]QHMZHUVMLWHRULLF]DVXZ\SHáQLRQHJR  _{%81*(Y±YL} _{2 QDWXUDOQRĞFL SRMĊü7+(5( ,6L7+( 6$0( ĞZLDGF]\ QLH W\ONR SRZV]HFKQRĞFL LFK XĪ\FLD}

ZMĊ]\NX QDXNL DOH WHĪ IDNW ĪH ]QDOD]á\ VLĊ RQH QD OLĞFLH $ :LHU]ELFNLHM LQWXLF\MQLH SURVW\FK MHGQRVWHNVHPDQW\F]Q\FKPDMąF\FKOHNV\NDOQHUHSUH]HQWDFMHZUHSUH]HQWDW\ZQ\P]ELRU]HMĊ]\ NyZĞZLDWD:,(5=%,&.$

_{=HZ]JOĊGXQDRJUDQLF]HQLDGRW\F]ąFHREMĊWRĞFLSXEOLNDFMLSRPLMDQHVąWXV]F]HJyá\GRW\}

F]ąFH(0)22JUDQLF]DP\VLĊWXMHG\QLHGRZVND]DQLDZ VHNFMLW\SRZHJRSU]\NáDGXMHM ]DVWRVRZDĔ

2 )250$/1(- 2172/2*,, %<78 , &=$68  22172/2*,,/2*,&=1(-

 1DWXUDOQ\PRGSRZLHGQLNLHPILOR]RILF]QHJRSRMĊFLD%<78MHVWSRMĊFLH&=( *2ĝF]\WHĪ&=(*2.2/:,(.3URVW\QDP\VáQDGNZHVWLąÄ-DNLHWZLHUG]HQLD GREU]H XJUXQWRZDQH ZH ZVSyáF]HVQHM QDXFH GRW\F]ą F ] H J R N R O Z L H N"´ SURZDG]L GR ZQLRVNX ĪH QDMRJyOQLHMV]\PL WZLHUG]HQLDPL RQWRORJLF]Q\PL OHĪąF\PLXSRGVWDZZLHG]\QDXNRZHMVąSU]HGPLRWRZR]LQWHUSUHWRZDQHSUD ZD NODV\F]QHM ORJLNL NZDQW\ILNDWRUyZ ] LGHQW\F]QRĞFLą QLHNRQLHF]QLH SLHUZV]HJR U]ĊGX 1DOHĪą GR QLFK SUDZD RGSRZLDGDMąFH WUDG\F\MQ\P ]DVDGRPÄE\WXLP\ĞOL´²QLHVSU]HF]QRĞFLZ\áąF]RQHJRĞURGNDLWRĪVDPR ĞFL²DWDNĪH]DVDG\FKDUDNWHU\VW\F]QHGODORJLNLNODV\F]QHMMDNSUDZRQLH RGUyĪQLDOQRĞFLLGHQW\F]QHJRLSUDZRHJ]\VWHQFMDOQHMJHQHUDOL]DFML  5yZQLHĪDQDOL]DRJyOQHMWUHĞFLSRGVWDZRZ\FKSRMĊüORJLF]QRRQWRORJLF] Q\FK²WDNLFKMDN,671,(1,(,'(17<&=12ĝû1$/(ĩ(1,(35=('0,27L./$6$ ² SURZDG]L GR ZQLRVNX ĪH SRGVWDZRZH ]DVDG\ ] QLPL ]ZLą]DQH Vą Z\ UDĪDOQHZSRVWDFLF]\VW\FKIRUPXáNODV\F]QHMORJLNL

 8MĊFLD GZX OXE ZLHORW\SLNDOQH WHM ORJLNL PRJą RND]Dü VLĊ V]F]HJyOQLH XĪ\WHF]Q\PQDU]ĊG]LHPDQDOL]\WHJRURG]DMXWZLHUG]HĔ=DáyĪP\QDXĪ\WHN UR]XPRZDQLDĪHL MHVWWUyMW\SLNDOQ\PV\VWHPHPZNWyU\P]PLHQQHSLHUZ V]HJR W\SX ORJLF]QHJR x y « SU]HELHJDMą SU]HGPLRW\ ]PLHQQH GUXJLHJR W\SXXY«²NODV\D]PLHQQHWU]HFLHJRW\SXpq«²]GDU]HĔ-HĞOLL MHVW GREU]H RNUHĞORQ\ SRG Z]JOĊGHP IRUPDOQ\P L HNVSOLNDF\MQ\P D ZLĊF MHJR WH]\ WUDIQLH L Z SHáQL HNVSOLNXMą RJyOQH SRMĊFLD35=('0,278 ./$6< ,='$5=(ē L MHĞOL SU]\MPXMHP\ VWDQRZLVNR ĪH NDĪG\ E\W MHVW SU]HGPLR

WHPNODVąOXE]GDU]HQLHPWR W U y M W \ S L N D O Q D  W H R U L D  L G H Q W \ F ] Q R Ğ F L 

LI M H V W  Z V ] \ V W N L P   F ] H J R  S R W U ] H E X M H P \  G R  Z \ U D Ī H Q L D  R Z H 

J R  V W D Q R Z L V N D_{  =JRGQLH ]H ]QDQą PHWD]DVDGą NODV\F]QHM PHWDIL]\NL}

SRMĊFLH%<78PRĪH E\ü REMDĞQLRQH Z MĊ]\NX WHM WHRULL MDNR SRMĊFLH V\VWH

PDW\F]QLHZLHOR]QDF]QHÄDQDORJLF]QH´ZQDVWĊSXMąF\VSRVyE

xMHVWE\WHP_⇔∃yy x XMHVWE\WHP_⇔∃YY X

pMHVWE\WHP_⇔∃qq p

 )RUPXáD Ä∃yy  x´ ]QDF]\ ERZLHP ĪH LVWQLHMH SU]HGPLRW WRĪVDP\ ]SU]HGPLRWHPx6NRURÄE\W´]QDF]\W\OHFRÄFRĞFRLVWQLHMH´WRIRUPXáD



_{-HĞOLLMHVWV\VWHPHPORJLNLNZDQW\ILNDWRUyZ]LGHQW\F]QRĞFLąWRV\PEROÄL}I_{´R]QDF]DWX}

WHRULĊ LGHQW\F]QRĞFL SRZVWDáą Z Z\QLNX UHGXNFML MĊ]\ND L GR ]ELRUX IRUPXá QLH]DZLHUDMąF\FK VWDá\FKSR]DORJLF]Q\FK=DFKRG]LRF]\ZLĞFLH]ZLą]HNL̍LŸLI̍LI

$1'5=(- %,à$7  WDPRĪHE\üRGF]\W\ZDQDSU]HGPLRWxMHVWE\WHP:NRQVHNZHQFMLSRSU]H] XQLZHUVDOQHGRPNQLĊFLH ZVND]DQHMIRUPXá\X]\VNXMHP\RQWRORJLF]QLH]LQ WHUSUHWRZDQąWH]ĊORJLNLJáRV]ąFąLĪNDĪG\SU]HGPLRWMHVWE\WHPZSLHUZ V]\P]QDF]HQLX ∀x∃yy x  3RGREQDDQDOL]DGZyFKSR]RVWDá\FKSU]\SDGNyZSURZDG]LGRDQDORJLF] Q\FKZQLRVNyZNDĪGDNODVDMHVWE\WHPZGUXJLP ]QDF]HQLXLNDĪGH]GD U]HQLHMHVWE\WHPZWU]HFLP]QDF]HQLX

 Silna ontologiczna interpretacja V\VWHPX ORJLF]QHJRL SROHJDQDX]QDQLX

LI MDNR ÄNDQRQLF]QHM´ WHRULL E\WX RNUHĞODMąFHM ZáDĞFLZą L QLHUHGXNRZDOQą

VWUXNWXUĊ U]HF]\ZLVWRĞFL -HĞOL Z MĊ]\NX L QLH PD LQQ\FK W\SyZ ]PLHQQ\FK SR]D]PLHQQ\PLUHSUH]HQWXMąF\PLSU]HGPLRW\NODV\L]GDU]HQLDX ] \ V N X  M H P \  Z  R E U Ċ E L H  W D N L H M  L Q W H U S U H W D F M L  R J y O Q ą  L  Ğ F L V á ą  FKRü W\ONR ÄDQDORJLF]Qą´ W H ] Ċ  J á R V ] ą F ą   L Ī  N D Ī G \  E \ W  M H V W  S U ] H G  P L R W H P   N O D V ą  O X E  ] G D U ] H Q L H P1DJUXQFLHVLOQHMLQWHUSUHWDFMLRQWR ORJLF]QHML RZąWH]ĊSRĞUHGQLRZ\UDĪDIRUPXáD ∀x∃yy x∧∀X∃YY X∧∀p∃qp q  = QLHFR RGPLHQQą V\WXDFMą PDP\ GR F]\QLHQLD ZyZF]DV JG\ GRSX V]F]DP\ PRĪOLZRĞü Z]ERJDFHQLD L L W\P VDP\P LI_{ R LQQH W\S\ E\WyZ} 7DND saba interpretacja ontologiczna ORJLNL QLH GRVWDUF]D RGSRZLHG]L QD S\WDQLH ÄR QDWXUĊ E\WX´ FKRü PRĪH VWDQRZLü ZDĪQ\ ZNáDG GR NRQVWUXNFML V\VWHPXGRVWDUF]DMąFHJRWDNLHMRGSRZLHG]L6SURZDG]DVLĊRQDGRXVWDOHQLD PDNV\PDOQLHV]HURNLHMG]LHG]LQ\SU]HGPLRWRZHMGODLI_{SU]HGPLRWRZHMLQWHU} SUHWDFMLNZDQW\ILNDWRUyZSLHUZV]HJRU]ĊGXHJ]\VWHQFMDOQHMLQWHUSUHWDFMLNZDQ W\ILNDWRUD V]F]HJyáRZHJR GRZROQHJR U]ĊGX RUD] RNUHĞOHQLD LQWXLF\MQHJR RQWRORJLF]QHJRVSRVREXF]\WDQLDIRUPXá

 2ND]XMH VLĊ ĪH ZDUXQNLHP X]\VNDQLD GREU\FK RGSRZLHG]L QD SRGVWD ZRZH S\WDQLD RQWRORJLF]QH Vą ZF]HĞQLHMV]H UR]ZLą]DQLD NZHVWLL ] SRJUDQL F]D PHWDRQWRORJLL L ILOR]RILL ORJLNL  -DNL V\VWHP ORJLNL NZDQW\ILNDWRUyZ ]LGHQW\F]QRĞFLąMHVWZáDĞFLZąNDQRQLF]QąSRGVWDZąRQWRORJLL"-DNLHVą SLHUZRWQH ORJLF]QH W\S\ E\WyZ JHQHURZDQH SU]H] yZ V\VWHP F]\ Vą QLPL QS W\S\ SU]HGPLRWyZ NODV ]GDU]HĔ LWG"  -DNLH RNUHĞOD RQ UHODFMH ORJLF]QH PLĊG]\ E\WDPL F]\ Vą QLPL QS UHODFMH LGHQW\F]QRĞFL QDOHĪHQLD E\FLDÄXF]HVWQLNLHP´]GDU]HQLDLWG"-DNLHVąIRUPDOQHZáDVQRĞFLRZ\FK

2 )250$/1(- 2172/2*,, %<78 , &=$68  UHODFML" 1DMRJyOQLHMV]D F]ĊĞü RQWRORJLL REHMPXMąFD DQDOL]Ċ S\WDĔ ± ]RVWDMHZWHQVSRVyEXWRĪVDPLRQD]/2

 :QLQLHMV]\PDUW\NXOHQLHUR]ZDĪDVLĊNZHVWLL±_{:MHJRGDOV]\FK}

F]ĊĞFLDFK VWRVRZDQH MHVW PLQLPDOQH ]DFKRZXMąFH VWDQGDUGRZH SRMĊFLH

,17(535(7$&-, : 02'(/8 UR]V]HU]HQLH VWDQGDUGRZHM ORJLNL ] LGHQW\F]QR

ĞFLą R NZDQW\ILNDFMĊ Z\ĪV]HJR U]ĊGX F]\OL PRQDG\F]QD ORJLND GUXJLHJR U]ĊGX 062 Monadic Second Order Logic =DNáDGD VLĊ WHĪ VáDEą LQWHU SUHWDFMĊRQWRORJLF]QąWHJRV\VWHPXQLHZ\NOXF]DVLĊZLĊFPRĪOLZRĞFLZ]ER JDFHQLD 062,_{ WM PRQDG\F]QHM WHRULL LGHQW\F]QRĞFL R GRGDWNRZH W\S\}

]PLHQQ\FKQSR]PLHQQHIXQNF\MQHGUXJLHJRU]ĊGX]PLHQQHZ\ĪV]HJRU]Ċ GXF]\WHĪVSHF\ILF]QH]PLHQQHUHSUH]HQWXMąFH]GDU]HQLD_

 8Z]JOĊGQLDMąF IDNW ĪH 062 MHVW V\VWHPHP HNVWHQVMRQDOQ\P FDáNRZLFLH

QDWXUDOQD MHVW MHJR LQWHUSUHWDFMD MDNR V\VWHPX ] SRGZyMQą NZDQW\ILNDFMą ÄSR SU]HGPLRWDFK´ ∃x«x L ÄSR NODVDFK´ ∃X«X 7HRULD LGHQW\F]QRĞFL

062,_{ VWDMH VLĊ Z REUĊELH WHM LQWHUSUHWDFML ORJLF]Qą WHRULą SU]HGPLRWyZ NODV}

RUD]GZyFKUHODFMLLGHQW\F]QRĞFLLQDOHĪHQLD-DNZLHP\MHVWWRWHRULD]QDF]QLH VáDEV]DRGVWDQGDUGRZHMWHRULLPQRJRĞFL7DRVWDWQLDLSRGREQLHV\VWHP\QLH VWDQGDUGRZH R ]EOLĪRQHM VLOH HNVSUHVML MHVW EDUG]R VLOQ\P QDU]ĊG]LHP DQDOL]\ SRGVWDZPDWHPDW\NL2NROLF]QRĞüWDPRĪHE\üSR]\W\ZQLHRFHQLDQD]SHUVSHN W\Z\ ILOR]RILL PDWHPDW\NL L VHPDQW\NL ILOR]RILF]QHM EXG]L QDWRPLDVW LVWRWQH ZąWSOLZRĞFLPHWDRQWRORJLF]QH6WRVRZDQLHZRJyOQHMRQWRORJLLWDNVLOQ\FKWHR ULLMHVWQDUDĪRQH]MHGQHMVWURQ\QD]DU]XWQLHUR]VWU]\JDOQRĞFLQLHNWyU\FKZDĪ Q\FKS\WDĔZ\UDĪDOQ\FKZLFKMĊ]\NDFKQSS\WDQLDRORJLF]QąZDUWRĞüKLSR WH]\ FRQWLQXXP D ] GUXJLHM VWURQ\ ² QD ]DU]XW ZSURZDG]DQLD RQWRORJLF]QLH ZąWSOLZ\FKE\WyZR]QDPLRQDFKPDWHPDW\F]Q\FKDUWHIDNWyZ]ELRUyZRPRF\ Z\ĪV]HMQLĪFRQWLQXXP]ELRUyZNWyU\FKQLHSRWUDILP\VNRQVWUXRZDüLWG

/RJLND PRQDG\F]QD GUXJLHJR U]ĊGX JHQHUXMH ÄHJ]\VWHQFMDOQLH OHNNą´ WHRULĊ NODV Z SRVWDFL 062,_{ ]ELyU MHM VSHF\ILF]Q\FK WZLHUG]HĔ HJ]\VWHQ}

FMDOQ\FK VSURZDG]D VLĊ GR WH]\ ĪH LVWQLHMą FR QDMPQLHM GZLH NODV\ SXVWD LXQLZHUVDOQD:V]F]HJyOQRĞFLZ062,_{QLH]DNáDGDVLĊLVWQLHQLDNODVZLHOR} HOHPHQWRZ\FKNODVSRWĊJRZ\FKDQLSDUXSRU]ąGNRZDQ\FK_  _{:SURZDG]HQLHGRWHMSUREOHPDW\NL]DZLHUDPRQRJUDILD%,à$7} _{1DMZDĪQLHMV]HDVSHNW\ILOR]RILF]QH]ZLą]DQH]W\PV\VWHPHP]RVWDá\ZVND]DQHZQDVWĊS} QHMVHNFML3HZQąZHUVMĊDNVMRPDW\NLGODÄF]\VWHM´062IRUPXáXMHVLĊZVHNFML3RGVWDZRZH ZLDGRPRĞFLGRW\F]ąFHPHWDORJLF]Q\FKZáDVQRĞFLV\VWHPX062SRGDMH6+$3,52± '\VNXVMDILOR]RILF]Q\FKDVSHNWyZORJLNLGUXJLHJRU]ĊGX]DZLHUDZVSRPQLDQDSUDFD%,à$7 _{*%RRORVVáXV]QLHZ]ZLą]NX]W\P]ZUDFDáXZDJĊ%22/26ĪHMHVWWRWHRULD} ]E\WVáDEDDE\PRĪQDMąE\áRWUDNWRZDü±MDNWRXF]\QLá4XLQHZVZRMHM]QDQHMNU\W\FHZSUDF\ 4XLQH±MDNRÄWHRULĊPQRJRĞFLZRZF]HMVNyU]H´

$1'5=(- %,à$7 

1DMF]ĊĞFLHM Z\VXZDQ\ DUJXPHQW SU]HFLZNR WUDNWRZDQLX ORJLNL PRQD G\F]QHM MDNR ZáDĞFLZHJR QDU]ĊG]LD DQDOL]\ GRW\F]\ MHM semantycznej

nie-penociR]QDF]DWRĪHQLHZV]\VWNLHMHMWDXWRORJLHPRĪQDZQLHMXGRZRG

QLü:LVWRFLHMHVWWRVáDERĞüRGNWyUHMZROQDMHVWORJLNDVWDQGDUGRZD1LH MHVWWRMHGQDNIXQGDPHQWDOQDVáDERĞü062VNRURWDRVWDWQLDMHVWMHMF]ĊĞFLą

&RZLĊFHMDQDORJLF]Q\]DU]XWPRĪQDVIRUPXáRZDüSU]HFLZNRORJLFHVWDQ GDUGRZHMMHVWRQDZSU]HFLZLHĔVWZLHGR062V\VWHPHPniekategorycznym W]Q QLH LVWQLHMH WHRULD SLHUZV]HJR U]ĊGX SRVLDGDMąFD PRGHO QLHVNRĔF]RQ\ NWyUHM ZV]\VWNLH PRGHOH Vą L]RPRUILF]QH_{ -HGQRF]HĞQLH QLH ZLGDü ĪDGQHJR}

PHWRGRORJLF]QHJR NU\WHULXP XVWDODQLD KLHUDUFKLL ZáDVQRĞFL V\VWHPyZ GHGXNF\MQ\FKNWyUHX]DVDGQLDáRE\SU]HNRQDQLHLĪSHáQRĞüMHVWZáDVQRĞFLąZ MDNLPĞVHQVLHÄZDĪQLHMV]ą´RGNDWHJRU\F]QRĞFLDWDNĪH²QDRGZUyW_

1LHZLGDüZLĊF]DVDGQLF]\FKP H W R G R O R J L F ] Q \ F K WUXGQRĞFL]ZLą]D Q\FK ] DNFHSWDFMą ORJLNL PRQDG\F]QHM MDNR QDU]ĊG]LD DQDOL]\ ILOR]RILF]QHM LIRUPDOL]DFML WHRULL NWyUH ² Z WHQ F]\ LQQ\ VSRVyE ² L WDN Vą MXĪ ]D DQJDĪRZDQH Z RQWRORJLĊ NODV ,VWQLHMH QDWRPLDVW V]HUHJ DUJXPHQWyZ I L O R  ] R I L F ] Q \ F K  ]D MHM X]QDQLHP MDNR XĪ\WHF]QHJR QDU]ĊG]LD IRUPDOQHM ILOR ]RILLE\WX0RĪQDZVND]DüFRQDMPQLHMWU]\WDNLHDUJXPHQW\

3R SLHUZV]H 062 GREU]H N R U H V S R Q G X M H  ]  $ U \ V W R W H O H V R Z V N ą  L G H ą  t y p i k a l n e g o d u a l i z m u ]JRGQLH ] NWyUą LVWQLHMą GZD W\S\ NDWH JRUHPDWyZ Z W\P MHGHQ SRGVWDZRZ\ ] NDĪG\P ] QLFK ]ZLą]DQH Vą SR GREQH GR VLHELH ÄDQDORJLF]QH´ SRMĊFLD,671,(1,$ 2GSRZLHGQLNLHP W\FK

SRMĊüVą]QDF]HQLDGZyFKW\SyZHJ]\VWHQFMDOQHMNZDQW\ILNDFMLZ\UDĪDOQ\FK ZMĊ]\NXORJLNLPRQDG\F]QHMÄSRSU]HGPLRWDFK´LÄSRNODVDFK´

3R GUXJLH 062 ]DZLHUD NRPSOHWQH D ZLĊF QLH Z SRVWDFL VFKHPDWyZ OHF] ]DPNQLĊW\FK WH] RGSRZLHGQLNL $U\VWRWHOHVRZVNLFK ]DVDG QLHVSU]HF] QRĞFLLZ\áąF]RQHJRĞURGNDRUD]/HLEQL]MDĔVNLHMORJLNLLGHQW\F]QRĞFLRGSR ZLHGQLNLWHVąW\SRZHGODFDáHMWUDG\F\MQHMILOR]RILLE\WX



_{-HVWWRNRQVHNZHQFMDWZLHUG]HQLD6NROHPD/|ZHQKHLPD7DUVNLHJR}

_{ 3RU %22/26  = RQWRORJLF]QHJR SXQNWX ZLG]HQLD NDWHJRU\F]QRĞü PRJáDE\ E\ü}

X]QDQDQDZHWMDNRÄZDĪQLHMV]D´RGSHáQRĞFLXZ]JOĊGQLDMąFQLHNWyUHNRQVHNZHQFMHW]ZSDUDGRNVX 6NROHPDNWyU\QLHGRW\F]\WHRULLNDWHJRU\F]Q\FK1LHNWyU]\DXWRU]\QS+3XWQDPXZDĪDMąĪH NRQVHNZHQFMH WH SURZDG]ą GR SHZQHM ZHUVML DQW\UHDOL]PX :DUWR GRGDü ĪH 062 VWDáD VLĊ Z RVWDWQLFKODWDFKSRSXODUQDZWHRULLDXWRPDWyZFRPD]ZLą]HN]IDNWHPUR]VWU]\JDOQRĞFLIUDJPHQWX 062EH]SUHG\NDWyZZLHORDUJXPHQWRZ\FK]REQS*5b'(/et al. ±

_{Ä6SRĞUyGU]HF]\MHGQHVąRJyOQHLQQHMHGQRVWNRZHRJyOQ\PLQD]\ZDPWHNWyUH]QDWXU\}

VZHM PRJą E\ü RU]HNDQH R ZLHOX U]HF]DFK D MHGQRVWNRZH WH NWyUH QLH PRJą E\ü RU]HNDQH >RZLHOX U]HF]DFK@ QS ©F]áRZLHNª PRĪH E\ü RU]HNDQ\ RZLHOX RVREDFK ©.DOOLDVª R MHGQHM´ $5<6727(/(6Herm.DE$5<6727(/(6

2 )250$/1(- 2172/2*,, %<78 , &=$68  , SR WU]HFLH 062 JHQHUXMH SHZQą ZDĪQą GOD ZVSyáF]HVQHM QDXNL HNV WHQVMRQDOQąZHUVMĊWHRULLSRZV]HFKQLNyZRNROLF]QRĞüWDF]\QLMąV\VWHPHP  I L O R ] R I L F ] Q L H  Q L H W U \ Z L D O Q \ P L]DUD]HPQ D X N R Z R  X Ī \ W H F ] Q \ P  3RZ\ĪV]H DUJXPHQW\ VNáDQLDMą GR X ] Q D Q L D  062 MDNR SRGVWDZRZHJR QDU]ĊG]LDORJLF]QHMHNVSOLNDFMLRJyOQ\FKSRMĊü,671,(1,$35=('0,278./$6< ,'(17<&=12ĝ&,L1$/(ĩ(1,$ RUD] ² XZ]JOĊGQLDMąF IDNW ]DDQJDĪRZDQLD

ZVSyáF]HVQHM PDWHPDW\NL L QDXNL Z RQWRORJLĊ NODV ² MDNR S R G V W D  Z R Z H J R  Q D U ] Ċ G ] L D  I R U P D O Q H M  R Q W R O R J LL_

2(.63/,.$&<-1(-2172/2*,,)250$/1(-



 -HĞOL P MHVW SRMĊFLHP RQWRORJLF]Q\P WR MHVW WHĪ SRMĊFLHP UHSUH]HQWRZD Q\P SU]H] VWDáą SHZQHJR QLH]DZRGQHJR VFKHPDWX ZQLRVNRZDQLD QLHNR QLHF]QLHVFKHPDWXF]\VWRORJLF]QHJRVWRVRZDOQHJRZZLHOXREV]DUDFKUDFMR QDOQHJR P\ĞOHQLD R ĞZLHFLH ,QWXLF\MQLH ]DFKRG]L WHĪ LPSOLNDFMD RGZURWQD .RQLXQNFMDREXLPSOLNDFMLGRVWDUF]DQDVWĊSXMąFHJRREMDĞQLHQLDP MHVWSRMĊ FLHPRQWRORJLF]Q\P]DZV]HLW\ONRZWHG\JG\PMHVWSRMĊFLHPUHSUH]HQWR ZDQ\P SU]H] VWDáą SHZQHJR QLH]DZRGQHJR VFKHPDWX ZQLRVNRZDQLD VWRVR ZDOQHJRZZLHOXREV]DUDFKUDFMRQDOQHJRP\ĞOHQLDRĞZLHFLH ,'(17<&=12ĝû ,671,(1,( , 1$/(ĩ(1,('2 ./$6< Vą SRGVWDZRZ\PL SU]\NáDGDPLSRMĊüRQWRORJLF]Q\FKVąRQHUHSUH]HQWRZDQHSU]H]VWDáHZLHOX QLH]DZRGQ\FK L SRZV]HFKQLH VWRVRZDQ\FK VFKHPDWyZ UHJXá ORJLF]Q\FK 2WRSU]\NáDG\WDNLFKVFKHPDWyZ_ Regua Leibniza

(

 

)

a b a b α α = 

_{:QLRVHN WHQ QLH ]DZLHUD VXJHVWLL R ]EĊGQRĞFL SRV]XNLZDĔ XĪ\WHF]Q\FK Z RQWRORJLL IRU}

PDOQHMV\VWHPyZORJLF]Q\FKEĊGąF\FKUR]V]HU]HQLDPL062QSV\VWHPyZORJLNLSU]HGPLRWyZ NODV L ZáDVQRĞFL :UĊF] SU]HFLZQLH QD JUXQFLH SU]\MĊWHJR WX ]DáRĪHQLD R VáDEHM RQWRORJLF]QHM LQWHUSUHWDFML062SRV]XNLZDQLDWDNLFKUR]V]HU]HĔVąZSHáQLX]DVDGQLRQH

_{:VFKHPDWDFKSRQLĪHMV\PEROHaba}

«anUHSUH]HQWXMąGRZROQHQD]Z\LQG\ZLGXRZH

RUD]αUHSUH]HQWXMH]GDQLHZNWyU\PĪDGQDWDNDQD]ZDQLHZ\VWĊSXMHZ]DVLĊJXIXQNWRUDLQWHQ VMRQDOQHJR6\PEROÄαab´R]QDF]DIRUPXáĊNWyUDSRZVWDMH]IRUPXá\]GDQLRZHMαZZ\QLNX ]DVWąSLHQLD QD]Z\ b ]D a Z MHGQ\P OXE Z ZLHOX PLHMVFDFK Z\VWąSLHQLD a = NROHL V\PERO Äαxa´R]QDF]DIRUPXáĊNWyUDSRZVWDMH]IRUPXá\]GDQLRZHMαZZ\QLNXSRGVWDZLHQLDQD]Z\

$1'5=(- %,à$7 

 3U]\NáDGHP]DVWRVRZDĔWHMUHJXá\MHVWUR]XPRZDQLHZNWyU\PX]QDMHP\ ZQLRVHN Ä$U\VWRWHOHV XURG]Lá VLĊ Z 6WDJLU]H´ QD SRGVWDZLH GZyFK SU]H VáDQHN Ä6WDJLU\WD MHVW W\P VDP\P FR $U\VWRWHOHV´ RUD] Ä6WDJLU\WD XURG]Lá VLĊZ6WDJLU]H´ Regua Kartezjusza

(

)

   x a x x a α α ∃ = ∧   =JRGQLH ] UHJXáą .DUWH]MXV]D X]QDMHP\ ZQLRVHN Ä,VWQLHMH WRĪVDP\ ]H PQąSU]HGPLRWP\ĞOąF\´QDSRGVWDZLHSU]HVáDQNLÄ-D P\ĞOĊ´_-DNZLHP\ UHJXáDWDMHVWZWyUQąUHJXáąVWDQGDUGRZHMORJLNL Regua komprehensji

(



)

 RLOH]PLHQQD QLHMHVWZROQDZ     x a X X x x X X α α α ∃ ≠ ∅ ∧ ∀ ∈ ⇔

=JRGQLH ] UHJXáą NRPSUHKHQVML X]QDMHP\ ZQLRVHN Ä,VWQLHMH QLHSXVWD NODVD ZV]\VWNLFK L W\ONR SU]HGPLRWyZ U]HF]\ZLVW\FK´ QD SRGVWDZLH SU]HVáDQNL Ä-HVWHP SU]HGPLRWHP U]HF]\ZLVW\P´ 3U]HGVWDZLRQ\ VFKHPDW MHVW MHGQą ]UHJXáZWyUQ\FK062SRGVWDZąMHMGRZRGXMHVWGHILQLFMDNODV\SXVWHMSUD ZRHJ]\VWHQFMDOQHMJHQHUDOL]DFMLLDNVMRPDWNRPSUHKHQVML²]REVHNFMĊ

5HJXá\.DUWH]MXV]DLNRPSUHKHQVMLVąVFKHPDWDPLZNWyU\FKLVWRWQąUROĊ RGJU\ZDMą RJyOQH SRMĊFLD,'(17<&=12ĝ&,L,671,(1,$ WR RVWDWQLH MHVW Z\ UDĪRQHZWUHĞFLNZDQW\ILNDWRUDHJ]\VWHQFMDOQHJRGRGDWNRZRZUHJXOHNRP SUHKHQVML LVWRWQą UROĊ RGJU\ZD RJyOQH SRMĊFLH1$/(ĩ(1,$ :VND]DQH VFKH PDW\ QLHMDNR O H J L W \ P L ] X M ą  L F K  QDWXUDOQH RGSRZLHGQLNL MDNR SRMĊFLD RQWRORJLF]QH7ĊPHWRGĊlogicznej legitymizacji pojcia P²SROHJDMąFąQD ZVND]DQLX V]HURNR VWRVRZDQHJR L QLH]DZRGQHJR VFKHPDWX ZQLRVNRZDQLD ZNWyU\PP MHVWUHSUH]HQWRZDQHSU]H]SHZQąVWDáąVFKHPDWX²PRĪQD]SR ZRG]HQLHP]DVWRVRZDüGRVHOHNFMLZLHOXLQQ\FKSRMĊü /RJLF]QD OHJLW\PL]DFMD GDQHJR SRMĊFLD SRSU]HG]D MHJR SHáQą DNVMRPD W\F]QąHNVSOLNDFMĊ1LHPDOJRWRZHMFKDUDNWHU\VW\NLSRV]F]HJyOQ\FKHWDSyZ WHMSURFHGXU\GRVWDUF]DQDVWĊSXMąF\RSLVPHWRG\DNVMRPDW\F]QHM  _{=DSURSRQRZDQHWXRNUHĞOHQLHÄUHJXáD.DUWH]MXV]D´QDZLą]XMHGR]ZURWXÄXRJyOQLRQHSRG}

VWDZRZH WZLHUG]HQLH 'HVFDUWHVD´ XĪ\ZDQHJR SU]H] + 6FKRO]D QD R]QDF]HQLH WH]\ >@ VIRU PXáRZDQHMZVHNFMLSRU6à83(&.,L%25.2:6.,-HGQD]LPSOLNDF\MQ\FKZHUVMLWHM WH]\MHVWZáDĞQLHSRGVWDZąUHJXá\.DUWH]MXV]D

2 )250$/1(- 2172/2*,, %<78 , &=$68   SRGDQLHPRĪOLZLHNUyWNLHMOLVW\LQWXLF\MQLH]UR]XPLDá\FKstaych

ter-minówpierwotnychQLH]GHILQLRZDQ\FKZMĊ]\NXWHRULLT

 ZSURZDG]HQLH GR MĊ]\ND WHRULL T terminów wtórnych Z\áąF]QLH QD SRGVWDZLHGHILQLFMLVIRUPXáRZDQ\FK]DSRPRFąWHUPLQyZSLHUZRWQ\FK OXEXSU]HGQLR]GHILQLRZDQ\FK

 VIRUPXáRZDQLH ]D SRPRFą WHUPLQyZ WHRULL T OLVW\ aksjomatów WH] SLHUZRWQ\FK F]\OL ]GDĔ NWyUH Vą EH] GRZRGX X]QDQH Z T MHGQR F]HĞQLH]GDQLDWHZ\GDMąVLĊRF]\ZLVWHLX]QDQHVą]DSUDZG]LZHEH] ĪDGQHJRGDOV]HJRX]DVDGQLHQLD

 X]QDQLH MDNR tez wtórnych WHRULL T Z\áąF]QLH WDNLFK ]GDĔ NWyUH PRJą E\üXGRZRGQLRQHQDSRGVWDZLHDNVMRPDWyZGHILQLFMLRUD]]GDĔXSU]HG QLRXGRZRGQLRQ\FK_

 =JRGQLH ] Wą FKDUDNWHU\VW\Ną ]DáRĪHQLHP GRZROQHM SURFHGXU\ DNVMRPDW\ ]DFML GDQHJR ]ELRUX ]GDĔ MHVW PRĪOLZRĞü LQWXLF\MQHJR REMDĞQLHQLD VHQVX LFK WHUPLQyZ SLHUZRWQ\FK : SUDNW\FH PRĪOLZRĞü WD F]ĊVWR ZLąĪH VLĊ ]H ZVND ]DQLHPQDWXUDOQHJRVSRVREXF]\WDQLDW\SRZ\FKIRUPXáZNWyU\FKZ\VWĊSXMą WHWHUPLQ\DWDNĪH]SRGDQLHPW\SRZ\FKSU]\NáDGyZLFKGHV\JQDWyZHZHQ WXDOQLH WHĪ ² LFK W\SRZ\FK NRQWUSU]\NáDGyZ 7DN REMDĞQLRQH UR]XPLHQLH WHUPLQyZMHVWIRUPDOQLHZ\UDĪRQHZMĊ]\NXSU]HGPLRWRZ\PWHRULLTZSRVWD FLMHMSRGVWDZRZ\FKDNVMRPDWyZSRVWXODWyZ]QDF]HQLRZ\FKLGHILQLFML_  'RGDWNRZ\PHWDSHPZLHĔF]ąF\PREMDĞQLHQLHWUHĞFLHNVSOLNRZDQ\FKWHU PLQyZQDJUXQFLH]DNVMRPDW\]RZDQHMWHRULLMHVWZ\SURZDG]HQLHQDMEDUG]LHM FKDUDNWHU\VW\F]Q\FKWH]ZWyUQ\FKZUD]]LFKLQWXLF\MQąLQWHUSUHWDFMąRUD] ZVND]DQLH QDMEDUG]LHM FKDUDNWHU\VW\F]Q\FK KLSRWH] VWDQRZLVN ]DJDGQLHĔ Z\UDĪDOQ\FKZMĊ]\NXRZHMWHRULL_

 3RáąF]HQLH ZVND]DQHM SRZ\ĪHM SURFHGXU\ ] SURFHGXUą ORJLF]QHM OHJLW\ PL]DFMLSRMĊüSURZDG]LGRRNUHĞOHQLDQDVWĊSXMąFHMSURFHGXU\aksjomatycznej

eksplikacji poj ontologicznych

 _{7$56.,} _{2GSRMĊFLD7(25,, =$.6-20$7<=2:$1(-QDOHĪ\RGUyĪQLüZĊĪV]H]DNUHVRZRSRMĊFLHteorii} sformalizowanejÄ7HRULĊDNVMRPDW\F]QąNWyUHMMĊ]\N]RVWDáVIRUPDOL]RZDQ\LNWyUDZ\SRVDĪRQD ]RVWDáDZSRMĊFLHGRZRGXIRUPDOQHJRQD]\ZDVLĊWHRULąVIRUPDOL]RZDQą´7$56., _{2GU]XFDVLĊWXSU]\MPRZDQąQLHNLHG\WH]ĊmetodologicznegoformalizmuDQDORJLF]QąGR} WH]\ IRUPDOL]PX'+LOEHUWD ZILOR]RILLPDWHPDW\NL]JRGQLH]NWyUąMHGQ\P]HWDSyZIRUPD OL]DFML WHRULL MHVW Q D G D Z D Q L H  VHQVX MHM WHUPLQRP VSHF\ILF]Q\P ]D SRPRFą VWRVRZQ\FK DNVMRPDWyZWHMWHRULL3U]HFLZQLHSU]\MPXMHVLĊ±]JRGQLH]ÄLQWXLF\MQ\P´SRGHMĞFLHP*)UH JHJR L $7DUVNLHJR ± ĪH LVWRWą WDNLHM IRUPDOL]DFML MHVW H N V SO L N D F M D  LQWXLF\MQLH GDQHJR XSU]HGQLRVHQVXRZ\FKWHUPLQyZ

$1'5=(- %,à$7 

L Z\EyULLQWXLF\MQHREMDĞQLHQLH]ELRUXSRMĊüSUHWHQGXMąF\FKGRPLDQD SRMĊüRQWRORJLF]Q\FK

LL ORJLF]QDOHJLW\PL]DFMDSRMĊüZVND]DQ\FKZL

LLLF]ĊĞFLRZD IRUPDOL]DFMD UH]XOWDWyZ L L LL Z SRVWDFL SURMHNWyZ DNVMRPDWyZLGHILQLFML

LY SHáQD IRUPDOL]DFMD DNVMRPDWyZ L GHILQLFML ZVND]DQ\FK Z LLL QD JUXQFLHGDQHJRV\VWHPXORJLNL Y GRZRG\QDMEDUG]LHMFKDUDNWHU\VW\F]Q\FKWH]ZWyUQ\FKZREUĊELHWHR ULLX]\VNDQHMZLYRUD] YL ZVND]DQLHQDMEDUG]LHMFKDUDNWHU\VW\F]Q\FKKLSRWH]Z\UDĪDOQ\FKZMĊ ]\NXVNRQVWUXRZDQHMWHRULLQLHEĊGąF\FKMHMWH]DPL  021$'<&=1$7(25,$,'(17<&=12ĝ&,,1$/(ĩ(1,$



 3U]\NáDGHPXĪ\FLDSRZ\ĪV]HMPHWRG\ZRQWRORJLFH/2MHVWHNVSOLNDFMD RJyOQ\FKSRMĊü,'(17<&=12ĝ&,,671,(1,$L1$/(ĩ(1,$WM%<&,$(/(0(1 7(0 ./$6< Z REUĊELH PRQDG\F]QHM WHRULL LGHQW\F]QRĞFL GUXJLHJR U]ĊGX

062,_{ 3RPLMDP\ WX ]H Z]JOĊGX QD RJUDQLF]DQLD ÄREMĊWRĞFLRZH´ DUW\NXáX}

QLHNWyUH V]F]HJyá\ ZVWĊSQ\FK HWDSyZ L±LLL =JRGQLH ] XZDJDPL SRF]\ QLRQ\PL Z SRSU]HGQLHM VHNFML UHJXá\ /HLEQL]D .DUWH]MXV]D L NRPSUHKHQVML VąSU]\NáDGDPLRF]\ZLVW\FKLXQLZHUVDOQ\FKVFKHPDWyZNWyUHOHJLW\PL]XMą SRMĊFLD ,671,(1,$ L 72ĩ6$02ĝ&, MDNR SRMĊFLD RQWRORJLF]QH GRGDWNRZR

RVWDWQLD]Z\PLHQLRQ\FKUHJXáOHJLW\PL]XMHSRMĊFLH1$/(ĩ(1,$

 6áRZQLN 062,_{ VNáDGD VLĊ ] GZyFK W\SyZ ]PLHQQ\FK SU]HGPLRWRZ\FK}

x x«xyz«LNODVRZ\FKX X«XYZ«)RUPXá\SURVWH

062,_{ PDMą SRVWDFL Äx  y´ ÄX  Y´ L Äx ∈Y´ )RUPXá\ ]áRĪRQH Vą ]EX}

GRZDQHSRGREQLHMDNZORJLFHVWDQGDUGRZHMGRVSHF\ILNLWHJRMĊ]\NDQDOHĪ\ PRĪOLZRĞüZLą]DQLD]PLHQQ\FKN O D V R Z \ F K SU]H]NZDQW\ILNDWRU\_  $NVMRPDW\062,_{VąQDVWĊSXMąFH}   

_{ 3RQLĪV]D DNVMRPDW\]DFMD 062},_{ MHVW UyZQRZDĪQD ] ORJLF]Qą WHRULą NODV S U]HGVWDZLRQą}

2 )250$/1(- 2172/2*,, %<78 , &=$68 

062 α R LOH α MHVW 062,_{SRGVWDZLHQLHP WDXWRORJLL NODV\F]QHJR UDFKXQNX} ]GDĔ 062 ∀tαŸαts_ 062  α tsŸ∃tα 062 t sŸαŸα ts 062 ∀xx∈X⇔x∈YŸX Y 062 ∀Xx∈X⇔y∈XŸx y 062 ∃X∀yy ∈X⇔αRLOH]PLHQQDXQLHMHVWZROQDZα  3RGREQLHMDNZSU]\SDGNXVWDQGDUGRZHMORJLNLUHJXáDPLGHGXNFMLWZLHU G]HĔ ZWyUQ\FK GOD 062,_{ Vą modus ponens UHJXáD GRSLV\ZDQLD NZDQW\}

ILNDWRUDHJ]\VWHQFMDOQHJR∃xRGSRZLHGQLR∃XGRSRSU]HGQLNDLPSOLNDFML NWyUHMQDVWĊSQLNQLH]DZLHUD]PLHQQHMZROQHMxRGSRZLHGQLRXRUD]UHJXáD GRSLV\ZDQLD NZDQW\ILNDWRUD RJyOQHJR ∀x ∀X GR QDVWĊSQLND LPSOLNDFML NWyUHMSRSU]HGQLNQLH]DZLHUD]PLHQQHMZROQHMxX

 1DVWĊSXMąFH IRUPXá\ 062,_{ Vą MHM WH]DPL Z QDZLDVDFK SRGDQH Vą}

VSRVRE\ F]\WDQLD IRUPXá ZVND]XMąFH QD SU]\MĊWą WX RQWRORJLF]Qą LQWHUSUH WDFMĊ062,_ >@ ∀tt t  NDĪG\E\WMHVWWRĪVDP\]VREąZVW\OL]DFMLPHWDORJLF]QHMLGHQW\F]QRĞüMHVWUHODFMą ]ZURWQą >@ ∀tst s Ÿs t    LGHQW\F]QRĞüMHVWUHODFMąV\PHWU\F]Qą >@ ∀tst’t s∧s t’Ÿt t’    LGHQW\F]QRĞüMHVWUHODFMąSU]HFKRGQLą >@ ∃tst s    LGHQW\F]QRĞüMHVWUHODFMąQLHSXVWą >@ αt∧∼αsŸ∼t s    MHĞOLt PDZáDVQRĞüαRUD]sQLHPDZáDVQRĞFLαWRtLsQLHVąWRĪVDPH >@ αs/t⇔∃ss t∧α t PDGDQąZáDVQRĞüZWZLVWQLHMHE\WWRĪVDP\]tNWyU\PDWĊZáDVQRĞü 

_{ 0HWD]PLHQQH t s UHSUH]HQWXMą WX GRZROQH ]PLHQQH SLHUZV]HJR OXE GUXJLHJR U]ĊGX}

3RGVWDZLHQLHαt/sMHVWSRSUDZQHJG\VSHáQLDMąVWDQGDUGRZHZDUXQNLSRSUDZQRĞFLDSRQDGWR± JG\ ]PLHQQH t L s Vą WHJR VDPHJR W\SX WM DOER SLHUZV]HJR DOER GUXJLHJR U]ĊGX 3RGREQLH ]DVWąSLHQLHαt//sMHVWSRSUDZQHJG\VSHáQLDVWDQGDUGRZHZDUXQNLSRSUDZQRĞFLRUD]]PLHQQHtL

sVąWHJRVDPHJRW\SX

_{ 0HWDV\PERO µαt¶ R]QDF]D WX GRZROQą IRUPXáĊ 062I Z NWyUHM ]PLHQQD µt¶ Z\VWĊSXMH}

$1'5=(- %,à$7 

 $NVMRPDW\ 062062 JHQHUXMą NRPSOHWQH UHDOLVW\F]QH Z VHQVLH UHD OL]PX SRMĊFLRZHJR L HNVWHQVMRQDOQH ZHUVMH DU\VWRWHOHVRZVNLFK ]DVDG QLH VSU]HF]QRĞFLL Z\áąF]RQHJRĞURGNDDWDNĪH/HLEQL]MDĔVNLHM ]DVDG\LGHQW\F] QRĞFLSU]HGPLRWyZQLHRGUyĪQLDOQ\FKLNU\WHULXPLGHQW\F]QRĞFLNODV_ >@ ∼∃x∃Yx∈Y∧∼x∈Y  QLHLVWQLHMHSU]HGPLRWNWyU\QDOHĪ\GRGDQHMNODV\L]DUD]HPGRQLHMQLHQDOHĪ\ >@ ∀x∀Yx∈Y∨∼x∈Y  NDĪG\SU]HGPLRWQDOHĪ\GRGDQHMNODV\OXEGRQLHMQLHQDOHĪ\ >@ x y⇔∀Zx∈Z⇔y∈Z  SU]HGPLRW\VąLGHQW\F]QHZWZQDOHĪąGRW\FKVDP\FKNODV >@ X Y⇔∀xx∈X⇔x∈Y  NODV\VąLGHQW\F]QHZWZQDOHĪąGRQLFKWHVDPHSU]HGPLRW\

Schemat komprehensji aksjomat definicyjny 062 JHQHUXMH WH]Ċ R LVW

QLHQLX NODV\ SXVWHM SRSU]H] SRGVWDZLHQLH ]D  IRUPXá\ Äy  y´ L NODV\ XQLZHUVDOQHMSRSU]H]SRGVWDZLHQLH]DIRUPXá\Äy y´ >@ ∃X∼∃yy∈X >@ ∃X∀yy∈X  =DVWRVRZDQLHzasady ekstensjonalnoci062GRIRUPXáGHILQLXMąF\FK NODVĊSXVWąLNODVĊXQLZHUVDOQąXPRĪOLZLDZ\SURZDG]HQLHWH]JáRV]ąF\FKĪH LVWQLHMHFRQDMZ\ĪHMMHGQDNODVDSXVWDLFRQDMZ\ĪHMMHGQDNODVDXQLZHUVDOQD >@ ∼∃yy∈X∧∼∃yy∈YŸX Y >@ ∀yy∈X∧∀yy∈YŸX Y  7H]\WHXPRĪOLZLDMą]GHILQLRZDQLHVWDá\FKPRQDG\F]Q\FK >@ 9 X⇔∀xx∈X    NODVDXQLZHUVDOQDMHVWNODVąZV]\VWNLFKSU]HGPLRWyZ >@ ∅ X⇔a∃xx∈X    NODVDSXVWDMHVWNODVąGRNWyUHMQLHQDOHĪ\ĪDGHQSU]HGPLRW  3RQLHZDĪ9MHVWNODVąQLHSXVWąFRZ\QLND]>@RERZLą]XMHWH]D >@ 9≠∅  _{Ä.RPSOHWQRĞü´ W\FK ZHUVML R]QDF]D ĪH Vą RQH ]DPNQLĊW\PL ]GDQLDPL D QLH VFKHPDWDPL}

]GDĔ MDN Z ORJLFH VWDQGDUGRZHM = NROHL LFK UHDOLVW\F]Q\ FKDUDNWHU Z\QLND ] IDNWX ĪH NZDQ W\ILNRZDQHVąZQLFKNODV\DZLĊFSHZQHJRW\SXSRZV]HFKQLNL

2 )250$/1(- 2172/2*,, %<78 , &=$68   1DSRGVWDZLHGHILQLFMLNODV\SXVWHM>@SUDZDHJ]\VWHQFMDOQHMJHQHUD OL]DFML 062 RUD] DNVMRPDWX NRPSUHKHQVML 062 PRĪQD Z\SURZDG]Lü IRUPXáĊEĊGąFąSRGVWDZąUHJXá\NRPSUHKHQVML >@ α x/yŸ ∃XX ≠∅∧ ∀xx ∈X⇔αRLOH]PLHQQDXQLHMHVWZROQDZα  :062,_{GDVLĊ]GHILQLRZDüZLHOHRJyOQ\FKRGSRZLHGQLNyZ]QDQ\FKSR} MĊüWHRULRPQRJRĞFLRZ\FKRWRSU]\NáDG\WDNLFKGHILQLFML y∈^x_«xn`⇔y x∨«∨y xn X⊂Y⇔∀x x ∈ XŸx ∈ Y

x∈ {y`⇔ y/xRLOH]PLHQQDx QLHMHVWZROQDZ X∩Y ^xx∈X∧x∈Y`

X ∪Y ^xx∈X∨x∈Y` X−Y ^xx∈X∧¬x∈Y`

(.63/,.$&<-1$7(25,$&=$68:<3(à1,21(*2



 :]ERJDFHQLHVáRZQLNDWHRULL062,_{RSR]DORJLF]QHHNVSOLNDW\SRMĊüRQWR}

ORJLF]Q\FK SURZDG]L RG RQWRORJLNL /2 GR IRUPDOQHM RQWRORJLL HNVSOLND F\MQHM ()2 3U]\NáDGDPL WDNLFK HNVSOLNDWyZ Vą V\PEROH Ä70´ ÄNODVD FKZLO´ÄNODVDPRPHQWyZ´LÄ´ÄSRSU]HG]D´ÄMHVWFKZLOąZF]HĞQLHMV]ąRG´ 7HUPLQ\WHVąSRĞUHGQLROHJLW\PL]RZDQHSU]H]SRGVWDZRZHVFKHPDW\ORJLNL WHPSRUDOQHM_  =DZV]HE\áRWDNĪH MHVW EĊG]LH a B B a =DZV]HEĊG]LHWDNĪH   E\áR V MH W a a B B  ,FKEH]SRĞUHGQLHMOHJLW\PL]DFMLGRVWDUF]DMą]HVWDQGDU\]RZDQHRGSRZLHG QLNLSRZ\ĪV]\FKVFKHPDWyZ   MHVW ZFKZLOLREHFQHM

'ODNDĪGHMFKZLOL ZF]HĞQLHMV]HMRG LVWQLHMHFKZLODSyĨQLHMV]DRG ZNWyUHM MHVW

a B t

t t t a B

 

MHVW ZFKZLOLREHFQHM

'ODNDĪGHMFKZLOL SyĨQLHMV]HMRG LVWQLHMHFKZLODZF]HĞQLHMV]DRG ZNWyUHM MHVW

a B t t t t a B  _{3RGVWDZąW\FKVFKHPDWyZVąDNVMRPDW\PLQLPDOQHJRV\VWHPXORJLNLWHPSRUDOQHM.} t]RE *25$1.2L*$/721

$1'5=(- %,à$7  6WDMHVLĊWHUD]ZLGRF]QHĪHREDUR]ZDĪDQHSUHG\NDW\ÄFKZLOL´ L ÄE\FLD ZF]HĞQLHMV]\P´VąSRĞUHGQLRimplicite UHSUH]HQWRZDQHZSRGDQ\FKVFKH PDWDFKORJLNLWHPSRUDOQHMSUHG\NDWÄE\FLDSyĨQLHMV]\P´WUDNWXMHP\WXMDNR GHILQLF\MQLHZWyUQ\xMHVWFKZLOąpóniejszRGy]DZV]HLW\ONRZWHG\JG\ x≠yLxQLHMHVWFKZLOąZF]HĞQLHMV]ąRGy  .DĪGDWHRULDF]DVXMHĞOLMHVWSR]EDZLRQDHNVSOLNDFMLSRMĊFLD&=$68 :< 3(à1,21(*2 35=('0,27$0, MHVW HNVSOLNDF\MQLH QLHNRPSOHWQD Z]JOĊGHP

WHJRQDWXUDOQHJRSRMĊFLDRQWRORJLF]QHJRSRGVWDZRZHJRUDFMRQDOQ\PP\ĞOH QLXRUHDOQ\PĞZLHFLH8Z]JOĊGQLHQLHWHJRIDNWXSURZDG]LGRQDVWĊSXMąFHJR REMDĞQLHQLDczasMHVWNODVąFKZLOZ\SHáQLRQ\FKSU]HGPLRWDPLLXSRU]ąGNR ZDQ\FKUHODFMąSRSU]HG]DQLD_

 :ORJLF]QHMHNVSOLNDFMLSRMĊFLD&=$68:<3(à1,21(*2SRWU]HEXMHP\RG

SRZLHGQLHJR SUHG\NDWX temporalnego istnienia F]\OL LVWQLHQLD SU]HGPLRWX ZGDQHMFKZLOL:\GDMHVLĊĪHSUHG\NDWWDNLMHVWGRĞüF]ĊVWR²FRQDMPQLHM

implicite — VWRVRZDQ\ZMĊ]\NXQDWXUDOQ\PLZMĊ]\NXQDXNL8Ī\ZDP\JR

ZV]F]HJyOQRĞFLJG\PyZLP\ĪHRVREDNWyUHMGRW\F]\GDQDKLVWRULDIDN W\F]QLH LVWQLDáD Z WDNLP D WDNLP F]DVLH FKRü MXĪ QLH LVWQLHMHQLH Ī\MH OXE JG\PyZLP\ĪHSHZLHQJDWXQHN]ZLHU]ąWLVWQLDáZGDQHMHSRFHDOHMXĪQLH LVWQLHMH Z\PDUá ĪH SHZQH PLDVWR LVWQLDáR DOH MXĪ QLH LVWQLHMH L WDN GDOHM =WHJR W\SX VIRUPXáRZDQLDPL ZLąĪH VLĊ RF]\ZLVW\ VFKHPDW ZQLRVNRZDQLD tUHSUH]HQWXMHZQLPWHUDĨQLHMV]RĞü ( )      LVWQLHMH Z\áąF]QLH ZF]DVLHRG GR QLHLVWQLHMHZFKZ O  L L a t t t t a t < _  6FKHPDW WHQ PRĪH E\ü ]DSLVDQ\ Z SRVWDFL Z SHáQL VIRUPDOL]RZDQHM ]HVWDQGDU\]RZDQHM R LOH G\VSRQXMHP\ DNVMRPDW\Ną GOD SUHG\NDWX WHPSRUDOQHJRLVWQLHQLD-HĞOLZWDNLHMDNVMRPDW\FH]ZURWÄxLVWQLHMHZFKZLOL

y´ MHVW UHSUH]HQWRZDQ\ SU]H] IRUPXáĊ Äx(y´ WR Z SHáQL ]HVWDQGDU\]RZDQD

ZHUVMDSRZ\ĪV]HJRVFKHPDWXPDSRVWDü       ( a  ( x a x t x t t t a t ∀ Ÿ < < < _ 

_{'HILQLFMD WD MHVW LQWXLF\MQą SRGVWDZą NRQVWUXNFML GZyFK ZHUVML WHRULL 70( S U]HGVWDZLR}

Q\FK Z SUDFDFK %,à$7  D 1LHFR LQQD ZHUVMD WHM WHRULL ]RVWDQLH SU]HGVWDZLRQD ZQD VWĊSQHMVHNFML

2 )250$/1(- 2172/2*,, %<78 , &=$68   5RG]LVLĊS\WDQLHMDNZ\JOąGDRJyOQDWHRULDHNVSOLNDF\MQD²]EXGRZDQD QDED]LH062,_{²EĊGąFDPLQLPDOQ\PV\VWHPHPSRVWXODWyZREMDĞQLDMąF\FK}

SRMĊFLD&+:,/,3235=('=$1,$ L,671,(1,$ : &+:,/, 3U]\NáDGHP WDNLHM

WHRULLMHVWV\VWHP0(−_{SU]HGVWDZLRQ\SRQLĪHM}

 : NRQVWUXNFML WHRULL 0(−_{ Z\FKRG]LP\ RG Z]ERJDFHQLD VáRZQLND WHRULL}

062,_{RSUHG\NDW\Ä70´Ä´LÄ(´3U]\MPXMHP\VNUyW\GHILQLF\MQH}

3x ^y ∃zz x∧y(z` )x ^y ∃zxz ∧y(z`

1x ^yy(x`

 (OHPHQWDPLNODV\3xVąZV]\VWNLHLW\ONRSU]HGPLRW\LVWQLHMąFHZF]D

VLH ZF]HĞQLHMV]\P RG FKZLOL x HOHPHQWDPL NODV\ )x ² SU]HGPLRW\ LVW

QLHMąFH Z F]DVLHSyĨQLHMV]\PRG xDHOHPHQWDPL1x²SU]HGPLRW\LVW

QLHMąFHZFKZLOLx.ODVĊ3xQD]\ZDüEĊG]LHP\przeszociFKZLOLx

NODVĊ)x²przyszocixDNODVĊ1x²teraniejszocix

 1DVWĊSXMąFH DNVMRPDW\ FKDUDNWHU\]XMą RJyOQą VWUXNWXUĊ F]DVX Z\SHá QLRQHJR

062062ZZHUVMLZ]ERJDFRQHMRIRUPXá\]DZLHUDMąFHVWDáHÄ70´Ä´LÄ(´ 070 x  y Ÿx∈70∧y ∈70

070 xyŸ∼y x 070 xy∧yzŸxz

070 x∈70∧y ∈70Ÿx < y∨y < x∨x y 0(  x(yŸy ∈70

0( y ∈70Ÿ∃xax ∈70∧x(y 0( xy ∈70 ∧3x 3yŸx y

 $NVMRPDW\070070VWZLHUG]DMąĪHSRSU]HG]DQLHMHVWUHODFMąRNUHĞ ORQąZNODVLHFKZLO070SU]HFLZ]ZURWQą070SU]HFKRGQLą070 L OLQLRZą 070 $NVMRPDW\ WH QLH Vą FDáNRZLFLH QHXWUDOQH ] ILOR]RILF] QHJR SXQNWX ZLG]HQLD HOLPLQXMą RQH VNUDMQLH KLSRWHW\F]QH ÄPRGHOH WRSR ORJLF]QH´ F]DVX PLDQRZLFLH MHJR ]DPNQLĊWRĞü F]DVRNUąJ RUD] UR]JDáĊ ]LRQRĞüF]DVZLGá\_{'RNáDGQLHMNRQFHSFMDF]DVXRNUĊJXMHVWZ\NOXF]RQD}

SU]H] 070 PRĪQD ZLĊF yZ SRVWXODW RNUHĞOLü PLDQHP aksjomatu

otwar-tociF]DVXDNRQFHSFMDF]DVXZLGHá²SU]H]070aksjomatliniowoci

F]DVX2ELHNRQFHSFMHVąWHĪZ\NOXF]RQHZMĊ]\NXQDWXUDOQ\PLZMĊ]\NX



_{5HJXá\GHGXNFMLGOD0(}−_{SR]RVWDMąEH]]PLDQ} _{3RU$8*867<1(.}

$1'5=(- %,à$7 

QDXNL 8Ī\WNRZQLF\ W\FK MĊ]\NyZ QD RJyá RGU]XFDMą PRĪOLZRĞü ĪH FKZLOD SyĨQLHMV]DSRSU]HG]DZÄNROHF]DVX´FKZLOĊZF]HĞQLHMV]ą3RGREQLHQDRJyá RGU]XFDMąPRĪOLZRĞüF]DVXZLGHáLVWQLHQLDGZyFKUyĪQ\FKFKZLO]NWyU\FK ĪDGQDQLHMHVWZF]HĞQLHMV]DRGGUXJLHM_

 8Z]JOĊGQLDMąF SRZ\ĪV]H VSRVWU]HĪHQLH RUD] RF]\ZLVWRĞü DNVMRPDWyZ 070DNVMRPDWÄFKZLORZRĞFL´L070DNVMRPDWSU]HFKRGQLRĞFLSRGD Qą DNVMRPDW\NĊ ZROQR X]QDü ]D ZáDĞFLZą HNVSOLNDFMĊ QDWXUDOQ\FK SRMĊü

&+:,/,L&+:,/,:&=(ĝ1,(-6=(-

 0( VWZLHUG]D ĪH SU]HFLZG]LHG]LQą UHODFML WHPSRUDOQHJR LVWQLHQLD MHVW NODVD FKZLO : ĞZLHWOH UR]ZDĪDQ\FK ZF]HĞQLHM SU]\NáDGyZ GRW\F]ąF\FK SU]HV]áHJROXESU]\V]áHJRLVWQLHQLDRVyEJDWXQNyZ]ZLHU]ąWPLDVWJDODNW\N LWG ]JRGQRĞü DNVMRPDWX 0( ] SRZV]HFKQLH VWRVRZDQ\PL VFKHPDWDPL UR]XPRZDĔMHVWGRĞüRF]\ZLVWD

 0(MHVWIRUPDOQ\PZ\UD]HPSRGVWDZRZHMLQWXLFML]ZLą]DQHM]SRMĊFLHP F]DVX Z\SHáQLRQHJR Z NDĪGHM FKZLOL G]LHMH VLĊ ]GDU]D OXE WUZD FRĞ FR FKZLOą QLH MHVW -HVW WR Z LVWRFLH SHZQD ZHUVMD tezy o niesubstancjalnoci QLHDEVROXWQRĞFL czasu NDĪGD FKZLOD MHVW Z\SHáQLRQD SU]H] SHZLHQ SU]HG PLRWQLHEĊGąF\FKZLOą

 0( GRVWDUF]D GRGDWNRZHJR NU\WHULXP LGHQW\F]QRĞFL GOD FKZLO SRGVWD ZRZH NU\WHULXP SU]\SRPQLMP\ MHVW LPSOLNRZDQH SU]H] DNVMRPDW 070 FKZLOH Vą LGHQW\F]QH JG\ ĪDGQD ] QLFK QLH SRSU]HG]D GUXJLHM 0( MHVW UyZQRZDĪQ\SRSU]H]SUDZDWUDQVSR]\FMLLGH0RUJDQD]IRUPXáą

0(¶ x ∈70 ∧y ∈70∧xyŸ3x≠3y

 0(¶VWZLHUG]DĪHUyĪQHFKZLOHPDMąUyĪQHSU]HV]áRĞFL3U]\SRPQLMP\ ĪH SRVáXJXMHP\ VLĊ WX RQWRORJLF]Q\P D ZLĊF PRĪOLZLH V]HURNLP SRMĊFLHP

35=('0,278REHMPXMąF\PQLHW\ONRSRGVWDZRZHLQG\ZLGXDDOHWHĪZV]HO NLHLFKNRPELQDFMHRGG]LDá\ZDQLDLWUDQVIRUPDFMH:W\PNRQWHNĞFLHNU\WH ULXP0(¶Z\GDMHVLĊFDáNRZLFLHRF]\ZLVWHLVWQLHQLHGZyFKUyĪQ\FKFKZLO F]DVXRWZDUWHJRPDMąF\FKGRNáDGQLHWHVDPHÄKLVWRULH´QLHMHVWPRĪOLZH  _{3R]RVWDZLDP\ZW\PPLHMVFXRWZDUWąNZHVWLĊPRĪOLZRĞFLUR]V]HU]HQLD0(}−_{RDSDUDWXUĊ}

SRMĊFLRZąOHĪąFąXSRGVWDZVHPDQW\NLF]DVXUR]JDáĊ]LRQHJRbranching time semantics:WDNLP HZHQWXDOQ\PUR]V]HU]HQLXNODVD70FKZLOVWDQRZLáDE\Z\UyĪQLRQą]DNWXDOL]RZDQąXU]HF]\ ZLVWQLRQąJDáąĨF]DVX

_{$NVMRPDW\ 070070 RGSRZLDGDMą VWDQGDUGRZHM VHPDQW\FH GOD ORJLNL WHPSRUDOQHM}

:DUWR SRGNUHĞOLü ĪH Z WHJR URG]DMX WHRULDFK ]DNáDGDQH MHVW SRMĊFLH czasu obiektywnego F]\OL F]DVXNWyUHJRPRPHQW\LRNUHV\PRJąE\üZRELHNW\ZQ\VSRVyELGHQW\ILNRZDQHLPLHU]RQH]D SRPRFą VWRVRZQ\FK QDU]ĊG]L NDOHQGDU]D L ]HJDUD 3RUXV]DP\ VLĊ WX ZLĊF Z REUĊELH SUREOH PDW\NLW]Z%WHRULLZVHQVLHSRFKRG]ąF\PRG-0(0F7DJJDUWD

2 )250$/1(- 2172/2*,, %<78 , &=$68   0RĪQD Z\ND]Dü ĪH SRMĊFLD&+:,/, L &+:,/, :<3(à1,21(- Vą RQWR ORJLF]QLHUyZQRZDĪQH >@ x ∈70⇔∃yy ∉70∧y(x    >]0(0(062@  7H]D>@X]DVDGQLDXĪ\ZDQLH]ZURWXÄRQWRORJLDF]DVXZ\SHáQLRQHJR´QD R]QDF]HQLHWHRULL0(−_  .RQVHNZHQFMą0(LGHILQLFML>@MHVWZDUXQNRZDWH]DPHWDIL]\F]QHJR UHDOL]PX >@ 70≠∅Ÿ∃x¬x ∈70

 =JRGQLH ] >@ MHĞOL F]DV istnieje realnie W]Q MHVW QLHSXVW\ WR LVWQLHMH FRQDMPQLHMMHGHQSU]HGPLRWQLHEĊGąF\FKZLOą

 2F]\ZLVWRĞüNRQVHNZHQFML>@L>@SRWZLHUG]DWUDIQRĞüGRNRQDQ\FKZ REUĊELH 0(−_{ HNVSOLNDFML SRMĊü&=$68 L&=$68 :<3(à1,21(*2 3RMĊFLH} &=$68MDNR]ELRUXFKZLOOLQLRZRXSRU]ąGNRZDQHJRSU]H]UHODFMĊSRSU]HG]D

QLDE\ZDRNUHĞODQH PLDQHP ÄVWDQGDUGRZHJR´_{-HVWRQRQDW\OHRJyOQHĪH}

QLH NROLGXMH DQL ] SRWRF]Q\PL ]Z\F]DMDPL MĊ]\NRZ\PL ]ZLą]DQ\PL ] XĪ\ FLHPZ\UD]yZÄZF]HĞQLHM´OXEUyZQRZDĪQ\FKÄSU]HG´ÄLSRWHP«´RUD] ÄFKZLOD´_{DQL]IL]\NDOQ\PSRMĊFLHPF]DVX}_

 -Ċ]\N0(−_{XPRĪOLZLDÄPRGHORZDQLH´QLHNWyU\FKRJyOQ\FKNRQFHSFMLF]DVX}

2WRSU]\NáDG\IRUPXáUHSUH]HQWXMąF\FKWU]\Z\EUDQHNRQFHSFMH

+ ∀xyx ∈70∧y ∈70 Ÿ∃zxz∧zy

 F]DVMHVWJĊVW\ + ∀xx∈70 Ÿ∃yyx  F]DVQLHPDSRF]ąWNX + ∀xx∈70 Ÿ∃yxy  F]DVQLHPDNRĔFD :67521ĉ(03,5<&=1(-7(25,,ĝ:,$7$5($/1(*2



 (PSLU\F]QąPRFQąZHUVMĊPRQDG\F]QHMWHRULLF]DVXZ\SHáQLRQHJRR]QD F]RQą WX V\PEROHP Ä0(´ RWU]\PXMHP\ Z Z\QLNX UR]V]HU]HQLD DNVMRPDW\NL

0(−_{RGZDGRGDWNRZHDNVMRPDW\0(L0(JáRV]ąFHLĪLVWQLHMHFRQDMPQLHM} 

_{=REQS$8*867<1(./(32,'(9,1à$*26=Ä:SURZDG]HQLH´} _{2ZH Z\UD]\ OXE LFK V\QRQLP\ Vą SRZV]HFKQLH VWRVRZDQH Z MĊ]\NX QDWXUDOQ\P ]RE}

:,(5=%,&.$

$1'5=(- %,à$7  MHGHQSU]HGPLRWLVWQLHMąF\ZGZyFKUyĪQ\FKFKZLODFKRUD]LVWQLHMHFRQDMPQLHM MHGHQSU]HGPLRWQLHLVWQLHMąF\ZĪDGQHMFKZLOLWMSU]HGPLRWSR]DF]DVRZ\ 0( ∃xyzx(y∧x(z∧yz 0( ∃x∀yax(y_

 $NVMRPDW 0( MHVW ILOR]RILF]Qą NRQVHNZHQFMą GRZROQHJR UH]XOWDWX REVHU ZDFML NDĪG\ REVHUZRZDQ\ SU]HGPLRW LVWQLHMH FR QDMPQLHM Z GZyFK UyĪQ\FK FKZLODFK = NROHL 0( MHVW ILOR]RILF]Qą NRQVHNZHQFMą GRZROQHM WHRULL HPSL U\F]QHMNWyUHMLVWRWQąF]ĊĞFLąMHVWDU\WPHW\NDOLF]EQDWXUDOQ\FKOXELQQDWHRULD PDWHPDW\F]QD'RGDWNRZąSU]HVáDQNąILOR]RILF]QąQLH]EĊGQąGRZ\SURZDG]H QLD0(]WDNLHMWHRULLMHVW]GDQLHJáRV]ąFHLĪĪDGHQSU]HGPLRWPDWHPDW\F]Q\ QLHLVWQLHMHZF]DVLHGRNáDGQLHMQLHLVWQLHMHZMDNLHMNROZLHNFKZLOL_

 7U]HEDSRQRZQLHSRGNUHĞOLüĪHSRVáXJXMHP\VLĊWXRQWRORJLF]Q\PDZLĊF PRĪOLZLHV]HURNLPSRMĊFLHP35=('0,278 ,671,(-Ą&(*2 : &=$6,(3RMĊFLH

WR REHMPXMH PLĊG]\ LQQ\PL SXQNW\ F]DVRSU]HVWU]HQL : W\P VHQVLH NDĪGD FKZLOD t MHVW Z\SHáQLRQD SU]H] FR QDMPQLHM MHGHQ SU]HGPLRW SHZLHQ SXQNW

ptxyzF]WHURZ\PLDURZHMF]DVRSU]HVWU]HQLÏZSXQNW]]DáRĪHQLDUyĪQL

VLĊRGFKZLOLtW\PVDP\PSRVWXODW0(MHVWVSHáQLRQ\

 :SRGREQ\VSRVyEPRĪQDZ\ND]Dü]JRGQRĞü0(]RJyOQąWHRULąZ]JOĊG QRĞFLGODGRZROQHMSDU\FKZLOttMHĞOLt≠tWR^ptxyztt`≠

^ptxyztt`MHĞOLFKZLOHtLtVąUyĪQHWR]ELRU\ZF]HĞQLHMV]\FKRG

QLFKSXQNWyZF]DVRSU]HVWU]HQLVąUyĪQH  3URVW\PLNRQVHNZHQFMDPL0(VąWH]\RQLHSXVWRĞFLNODV\FKZLOUHODFML E\FLDZF]HĞQLHMV]\PLWHPSRUDOQHMUHODFMLLVWQLHQLD >@ 70≠∅ >@ ∃xyxy >@ ∃xyx(y  8Z]JOĊGQLDMąF>@L0(X]QDMHP\ >@ ∃x∃yx(y∧¬x ∈70    FRQDMPQLHMMHGHQSU]HGPLRWQLHEĊGąF\FKZLOąLVWQLHMHZF]DVLH  _{5HJXá\GHGXNFMLGOD0(SR]RVWDMąEH]]PLDQ} _{0(UyĪQLVLĊRGREXZHUVML70(WHRULLF]DVXZ\SHáQLRQHJRSU]HGVWDZLRQ\FKZSUDFDFK}

%,à$7  L D : V]F]HJyOQRĞFL Z MHGQHM ] W\FK ZHUVML RERZLą]XMH GRGDWNRZ\ DNVMRPDW VWZLHUG]DMąF\FLąJáRĞüLVWQLHQLDSU]HGPLRWyZZF]DVLH5yZQLHĪDNVMRPDW0(UyĪQLVLĊRGVZR MHJRRGSRZLHGQLNDZ70(VWZLHUG]DMąFHJRĪHFKZLOHVąLGHQW\F]QHJG\VąZ\SHáQLRQHSU]H] WĊ VDPą WHUDĨQLHMV]RĞü D 0( MHVW VLOQLHMV]\ RG VZRMHJR RGSRZLHGQLND Z 70( VWZLHUG]D MąFHJRĪHNDĪGDFKZLODMHVWZ\SHáQLRQDSU]H]SHZLHQSU]HGPLRW²QLHNRQLHF]QLHUyĪQLąF\VLĊRG GRZROQHMFKZLOL,ZUHV]FLHZ70(QLHRERZLą]XMH0(

2 )250$/1(- 2172/2*,, %<78 , &=$68   1DVXZD VLĊ S\WDQLH R PRĪOLZRĞü ZSURZDG]HQLD SRMĊFLDĝ:,$7$ 5($/ 1(*2 Z MĊ]\NX 0( = ILOR]RILF]QHJR SXQNWX ZLG]HQLD Z\GDMH VLĊ FDáNR

ZLFLH X]DVDGQLRQD MHJR GHILQLFMD MDNR NODV\ 5 SU]HGPLRWyZ LVWQLHMąF\FK ZF]DVLHLQLHEĊGąF\FKFKZLODPL

5 ^x¬x ∈70∧∃yx(y`

 :GHILQLFMLWHMGRNRQXMHVLĊZLVWRFLHXWRĪVDPLHQLDGZyFKSRMĊüĝ:,$7$ 5($/1(*2L'=,('=,1< 35=('0,27Ï: ,671,(-Ą&<&+ : &=$6,( QLHEĊGą

F\FK FKZLODPL ,QVSLUDFMĊ GR WHJR XWRĪVDPLHQLD PRĪH VWDQRZLü XPLDUNR ZDQ\ UHDOL]P $U\VWRWHOHVD_{ -HGQDNĪH QDMEDUG]LHM Z\UDĨQH VIRUPXáRZDQLD}

WHMOXESRNUHZQ\FKLGHL]QDMGXMHP\ZILOR]RILLZVSyáF]HVQHM2WRSU]\NáDG WDNLHJRVIRUPXáRZDQLD

ĝZLDW UHDOQ\ WDN Z]LĊW\ MDN JR XMPXMHP\ Z FRG]LHQQ\P SU]HGILOR]RILF]Q\P GRĞZLDGF]HQLX Z\GDMH VLĊ WDN V]F]HJyOQLH XRUJDQL]RZDQ\ ĪH ZV]\VWNR FRNRO ZLHN Z\VWĊSXMH Z MHJR REUĊELH MHVW Z MDNLĞ VSRVyE F]DVRZH OXEMDNRĞ ]ZLą]DQH ]F]DVHP_

 1D SLHUZV]\ U]XW RND PRJáRE\ VLĊ Z\GDZDü ĪH SRMĊFLHĝ:,$7$ 5($/ 1(*2SRZLQQRE\üDQDOL]RZDQHQLHMDNRNODVDZVHQVLHG\VWU\EXW\ZQ\P

OHF] MDNR SHZQD PHUHRORJLF]QD FDáRĞü ,VWQLHMą GZLH UDFMH SU]HPDZLDMąFH SU]HFLZNR WDNLHM DQDOL]LH 3R SLHUZV]H JG\E\ ĞZLDW UHDOQ\ E\á PHUHR ORJLF]QąFDáRĞFLąWRMHJRF]ĊĞFLDPLE\á\E\SU]HGPLRW\WDNUyĪQRURGQHMDN Z\EXFK\VXSHUQRZ\FKVWDFMHEHQ]\QRZHVNRNLQDUFLDUVNLHLSURFHV\P\Ğ ORZH 7D NRQVHNZHQFMD QLH Z\GDMH VLĊ GRĞü LQWXLF\MQD , SR GUXJLH Z QLH NWyU\FKXV]F]HJyáRZLHQLDFKRJyOQHMRQWRORJLLQSZILOR]RILLSU]\URG\SR WU]HEXMHP\ ² QLH]DOHĪQLH RG SRZ\ĪV]\FK UR]ZDĪDĔ ² SRMĊFLD.260268

MDNRSHZQHMIL]\F]QLHÄ]ZDUWHM´F]DVRSU]HVWU]HQQHMFDáRĞFLĞZLDWDSU]\URG\ ']LHG]LQD NRVPRVX Z\GDMH VLĊ ]DVDGQLF]R NDWHJRULDOQLH ZĊĪV]D RG QLH MHGQRURGQHMG]LHG]LQ\ĞZLDWDUHDOQHJRQS]PLDQ\NXOWXURZHFKRüVąUHDO QH QLH PXV]ą E\ü ² L UDF]HM QLH SRZLQQ\ E\ü ² UR]ZDĪDQH MDNR SURFHV\ SU]\URGQLF]H8WRĪVDPLDMąFRELHG]LHG]LQ\SRSDGOLE\ĞP\ZVNUDMQąZHUVMĊ IL]\NDOL]PX = NROHL RGUyĪQLDQLH GZyFK PHUHRORJLF]Q\FK FDáRĞFLĞZLDWyZ QDUD]LáRE\QDVQD]DU]XWPQRĪHQLDE\WyZSRQDGSRWU]HEĊ

 2GU]XFLü WHĪ WU]HED LGHĊ HNVSOLNDFML SRMĊFLD ĝ:,$7$ 5($/1(*2 MDNR

V\VWHPXUHODF\MQHJR=W\PURG]DMHPDQDOL]\ZLąĪHVLĊ]NROHLWUXGQRĞüQLH

 _{3RUSU]\SLV}

$1'5=(- %,à$7  DUELWUDOQHJRZ\ERUXWDNLHMOXELQQHMXQLNDOQHMVWUXNWXU\WRĪVDPHM]HĞZLDWHP UHDOQ\P7UXGQRĞüWĊZSURVW\VSRVyERPLMDP\SU]\MPXMąFSURVWHRNUHĞOHQLH ÄĞZLDWDUHDOQHJR´MDNRG]LHG]LQ\SU]HGPLRWyZF]DVRZ\FK7RUR]VWU]\JQLĊFLH SURZDG]LGRRF]HNLZDQHJRRGUyĪQLHQLDXQLNDOQHJRĞZLDWDUHDOQHJRRGWDNLHM OXELQQHMMHJRVWUXNWXU\F]DVRSU]HVWU]HQQHMNDX]DOQHMLWG  =GHILQLFML5L>@PRĪQDEH]SRĞUHGQLRZ\SURZDG]LüNRQVHNZHQFMĊ >@ 5≠∅    ĞZLDWUHDOQ\ÄLVWQLHMH´GRNáDGQLHMMHVWQLHSXVWąNODVą  0RĪQDZ\ND]DüĪHIRUPXá\+L+ZVND]DQHZ]DNRĔF]HQLXSRSU]HG QLHMVHNFMLQLHVąWH]DPL0(FR]DW\PLG]LH0(MHVWWHRULąQLHVSU]HF]Qą :\QLNWHQIRUPXáXMHP\ZSRVWDFLPHWDWZLHUG]HQLD 0(7$7:,(5'=(1,(0(MHVWWHRULąQLHVSU]HF]Qą '2:Ï'V]NLFRZ\0(MĊ]\NLQWHUSUHWXMP\ZQDVWĊSXMąF\VSRVyE]PLHQ QHSU]HGPLRWRZHSU]HELHJDMą]ELyUOLF]EQDWXUDOQ\FK1DZLĊF]PLHQQH NODVRZH ² ZV]\VWNLH SRG]ELRU\ WHJR ]ELRUX VSHF\ILF]QH VWDáH SU]\M PXMąQDVWĊSXMąFH]QDF]HQLDV\PEROÄ13´SRQLĪHMR]QDF]D]ELyUOLF]ESD

U]\VW\FK

a bZWZab∈1₃RUD]ab a( bZWZb∈1₃RUD]a!b

70  13

 3U]\ WHM LQWHUSUHWDFML ZV]\VWNLH DNVMRPDW\ 0( SU]HFKRG]ą Z SUDZG]LZH ]GDQLD PRQDG\F]QHM DU\WPHW\NL OLF]E QDWXUDOQ\FK GUXJLHJR U]ĊGX QDWR PLDVW IRUPXá\ + L + ² Z ]GDQLD IDáV]\ZH 7\P VDP\P 0( MHVW WHRULą QLHVSU]HF]QąRLOHV\VWHPPRQDG\F]QHMDU\WPHW\NLGUXJLHJRU]ĊGXMHVWQLH VSU]HF]Q\FRQDOHĪDáRGRZLHĞü

=$.2ē&=(1,(



 ']LHG]LQDSU]HGPLRWRZDWHRULL0(MHVWPDNV\PDOQLHV]HURNąNODVą-HGQR F]HĞQLHNDĪG\WHUPLQSLHUZRWQ\0(MHVWHNVSOLNDWHPSHZQHJRSRMĊFLDRQWR ORJLF]QHJR72ĩ6$02ĝ&,1$/(ĩ(1,$&+:,/,%<&,$&+:,/Ą:&=(ĝ1,(-6=Ą ,671,(1,$:&+:,/,0(MHVW]DWHP W H R U L ą  R Q W R O R J L F ] Q ą

 0(MHVWWHRULąVNRQVWUXRZDQąQDJUXQFLHV\VWHPXORJLF]QHJR062 NWyU\ MHVW G R E U ] H  X J U X Q W R Z D Q \  Z H  Z V S y á F ] H V Q \ F K  Q D X N D F K  I R U P D O Q \ F K-HVWWRWHRULDQ L H V SU ] H F ] Q D QDJUXQFLHWHJRV\VWHPX

2 )250$/1(- 2172/2*,, %<78 , &=$68 

0( JHQHUXMH ILOR]RILF]QLH IXQGDPHQWDOQ\ SRG]LDá SU]HGPLRWyZ QD SU]HG

PLRW\UHDOQHF]DVRZHLLGHDOQHSR]DF]DVRZHZ\NOXF]DSHZQHVWDQRZLVNR ZNODV\F]Q\PVSRU]HILOR]RILF]Q\PQRPLQDOL]PRUD]]DZLHUDQDMRJyOQLHMV]H WH]\ GRW\F]ąFH ĞZLDWD UHDOQHJR =DWHP 0( MHVW W H R U L ą  I L O R ] R I L F ] Q L H  Q L H W U \ Z L D O Q ą 

6WUXNWXUD ORJLF]QD 0( RG]ZLHUFLHGOD ZVND]DQą Z DUW\NXOH VWUXNWXUĊ IRUPDOQHM RQWRORJLL E\WX Z NWyUHM ZDUVWZD HPSLU\F]QD MHVW QDGEXGRZDQD QDGZDUVWZąHNVSOLNDF\MQąDWD]NROHL²QDGZDUVWZąORJLF]Qą:V]F]H JyOQRĞFLZWHRULL0(RERZLą]XMąRQWRORJLF]QLH]LQWHUSUHWRZDQHSUDZDNOD V\F]QHM ORJLNL QLHVSU]HF]QRĞFL Z\áąF]RQHJR ĞURGND HJ]\VWHQFMDOQHM JHQH UDOL]DFMLQLHRGUyĪQLDOQRĞFLLGHQW\F]QHJRRUD]NU\WHULDLGHQW\F]QRĞFLGODSU]HG PLRWyZ L NODV 0( MHVW ZLĊF WHRULą UR]ZLMDQą QD JUXQFLH SHZQHJR V\VWHPX R Q W R O R J L N L  062,_{ 0( ]DZLHUD VWDáH SR]DORJLF]QH ²&+:,/, %<&,$}

:&=(ĝ1,(-6=<0 L ,671,(1,$ : &=$6,(² UHSUH]HQWXMąFH SHZQH SRMĊFLD

RQWRORJLF]QHRUD]DNVMRPDW\HNVSOLNXMąFHLFKRJyOQ\VHQV0(MHVWZLĊFWHĪ WHRULąUR]ZLMDQąQDJUXQFLHSHZQHJRV\VWHPXR Q W R O R J L L  H N V S O L N D F \ M  Q H M  0(−_{ , ZUHV]FLH DNVMRPDW\ 0( Vą ]JRGQH ] ILOR]RILF]Q\PL NRQVHN}

ZHQFMDPLZLHG]\GREU]HXJUXQWRZDQHMZQDXNDFKHPSLU\F]Q\FK:V]F]H JyOQRĞFL0(L0(Vą]JRGQH]SRGVWDZRZ\PL]DáRĪHQLDPLRJyOQHMWHRULL Z]JOĊGQRĞFL D VSHF\ILF]QH DNVMRPDW\ HJ]\VWHQFMDOQH 0( L 0( ² ]GRZROQąWHRULąHPSLU\F]Qą]DZLHUDMąFąWUHĞüPDWHPDW\F]Qą:W\PVHQVLH 0(MHVWV\VWHPHPH P S L U \ F ] Q H M  R Q W R O R J L L  I R U P D O Q H M









5()(5(1&-( 

$5<6727(/(6DAnalityki wtóre.:$5<6727(/(6Dziea wszystkie7Kategorie,

Her-meneutyka, Analityki pierwsze, Analityki wtóre, Topiki, O dowodach sofistycznych. 3U]Há

.D]LPLHU]/HĞQLDN±:DUV]DZD3DĔVWZRZH:\GDZQLFWZR1DXNRZH

$5<6727(/(6EHermeneutyka:$5<6727(/(6Dziea wszystkie7Kategorie,

Her-meneutyka, Analityki pierwsze, Analityki wtóre, Topiki, O dowodach sofistycznych. 3U]Há

.D]LPLHU]/HĞQLDN±:DUV]DZD3DĔVWZRZH:\GDZQLFWZR1DXNRZH

$5<6727(/(6 F Metafizyka : $5<6727(/(6 Dziea wszystkie 7 Fizyka, O niebie,

O powstawaniu i niszczeniu, Meteorologika, O wiecie, Metafizyka. 3U]Há.D]LPLHU]/HĞQLDN

±:DUV]DZD3DĔVWZRZH:\GDZQLFWZR1DXNRZH

$8*867<1(.=G]LVáDZNatura czasu:DUV]DZD3DĔVWZRZH:\GDZQLFWZR1DXNRZH %(572)UDQFHVFRL0DWWHR3/(%$1,Ontology and Metaontology: A Contemporary Guide

/RQGRQ1HZ'HOKL1HZ<RUN6\GQH\%ORRPEVEXU\

%,à$7$QGU]HMOntologiczna interpretacja logiki. U podstaw ontologii logicznej/XEOLQ :\GDZQLFWZR80&6

$1'5=(- %,à$7 

%,à$7$QGU]HMOntologia formalna jako teoria eksplikacyjna/XEOLQ:\GDZQLFWZR1DX NRZH*DYDJDL

%,à$7$QGU]HMÄ&]\PMHVWRQWRORJLF]QDILOR]RILDIRUPDOQD"´Przegld Filozoficzny QU±

%,à$7$QGU]HMDÄ&]\ĞZLDWUHDOQ\QDSHZQRLVWQLHMH"2SHZQ\PXĪ\FLXPHWRGIRUPDO Q\FKZILOR]RILLF]DVX´:Myli o jzyku, nauce i wartociach. Seria druga. Profesorowi

Jackowi Jadackiemu w siedemdziesit rocznic urodzin5HG$QQD%URĪHN$OLFMD&K\ELĔ

VND 0DULXV] *U\JLDQLHF L 0DUFLQ 7NDF]\N ± :DUV]DZD :\GDZQLFWZR 1DXNRZH

Semper.

%22/26*HRUJHÄ2ORJLFHGUXJLHJRU]ĊGX´:Filozofia logiki5HG-DQ:ROHĔVNL 3U]Há&H]DU\&LHĞOLĔVNLL$QQD6LHUV]XOVND±:DUV]DZD:\GDZQLFWZR6SDFMD)XQ GDFMD$OHWKHLD

%81*( 0DULR  Treatise on Basic Philosophy 9RO  Ontology I: The Furniture of the

World'RUGUHFKW%RVWRQ'5HLGHO

%85.+$5'7 +DQV L %DUU\ 60,7+  Handbook of Metaphysics and Ontology 0XQLFK 3KLORVRSKLD

&2&&+,$5(//$ 1LQR  Formal Ontology and Conceptual Realism 1HZ <RUN 6SULQJHU 9HUODJ

)(6(5(GZDUGÄ,QWURGXFWLRQDQ$ULVWRWHOLDQ5HYLYDO"´:Aristotle on Method and

Meta-physics 5HG (GZDUG )HVHU ± 3KLORVRSKHUV LQ 'HSWK +RXQGPLOOV %DVLQJVWRNH 1HZ

<RUN3DOOJUDYH0DFPLOODQ

*$5%$&= 3DZHá L 5REHUW 75<38=  Ontologia poza ontologi. Studium metateoretyczne

u podstaw informatyki/XEOLQ:\GDZQLFWZR.8/

*,/621eWLHQQHByt i istota3U]Há'RQDWD(VNDL-HU]\1RZDN:DUV]DZD,QVW\WXW :\GDZQLF]\3$;

*25$1.2 9DOHQWLQ L $QWKRQ\ *$/721  Ä7HPSRUDO /RJLF´ : The Stanford

Encyclo-pedia of Philosophy 5HG (GZDUG 1 =DOWD 'RVWĊS KWWSVSODWRVWDQIRUGHGX

DUFKLYHVZLQHQWULHVORJLFWHPSRUDO

*5b'(/(ULFK:ROIJDQJ7+20$6L7KRPDV:,/.(UHGAutomata, logics, and infnite

games. A guide to current research/HFWXUH1RWHVLQ&RPSXWHU6FLHQFH%HUOLQ6SULQ

JHU9HUODJ

,1*$5'(15RPDQSpór o istnienie wiata7, Ontologia egzystencjalna:DUV]D ZD3DĔVWZRZH:\GDZQLFWZR1DXNRZH

/(32,'(9,15RELQÄ5HODWLRQLVPDQG7HPSRUDO7RSRORJ\3K\VLFVRU0HWDSK\VLFV"´:

The Philosophy of Time5HG5RELQ/H3RLGHYLQL0XUUD\0DF%HDWK2[IRUG2[

IRUG8QLYHUVLW\3UHVV

à$*26=0DUHNRealno czasu:URFáDZ:\GDZQLFWZR8QLZHUV\WHWX:URFáDZVNLHJR 129271<'DQLHO'L/XNiã129È.Neo-Aristotelian perspectives in metaphysics1HZ

<RUN5RXWOHGJH

3$ħ %RJXVáDZ  Epistemologiczne zao enia ontologii Christiana Wolffa :URFáDZ :\ GDZQLFWZR8QLZHUV\WHWX:URFáDZVNLHJR

48,1( :LOODUG 9DQ 2UPDQ  Filozofia logiki 3U]Há +DOLQD 0RUWLPHU :DUV]DZD 3DĔVWZRZH:\GDZQLFWZR1DXNRZH

48,1(:LOODUG9DQ2UPDQÄ7KH9DULDEOHDQGLWV3ODFH,Q5HIHUHQFH´:Philosophical

Subjects: Essays Presented to P.F. Strawson. 5HG=DN9DQ6WUDDWHQUHG±2[IRUG

&ODUHQGRQ3UHVV

6+$3,52 6WHZDUW  Foundations without foundationalism. A case for second-order logic 1HZ<RUN2[IRUG2[IRUG8QLYHUVLW\3UHVV