Introduccion A La Logica Moderna

540 Pages·6.212 MB·Spanish

by  Paez Andres

! " # $ % & ' ( ( ! ) "
* + , * + , ) - ! ( * + . % & / $ " *
!"#$%$&'(#) * *+,-.,-./0-+1*20('#'
!"#$%$&'(#) 3 *+,-.,-./0-+1*20('#'
! '(
"#$%& )*+
,
" - $ . # / 0 0 , 1 "
' ' '
! 2 ! 2 1 3 , 0 ! 4 . # * $ " !
!"#$%&’#()(*(%*+,’*)"(%’
-,.,/01*2334
!"#$%$&'(#) + *+,-.,-./0-+1*20('#'
!"#$%&’(()*"+,+-,+-*.)(,+/%&0$",+1+2"&$34+56078+9%.%#6:+;")<0$4)&,&+&0
-%4+2"&04=+>,(’-#,&+&0+?)0"(),4+@%(),-04=+A0B,$#,/0"#%+&0+>)-%4%CD,=
?E@F=+E&)()%"04+;"),"&04=+GHHI8
B8+JKHL+MINGK(/8
!@9O:++PIQRPJQRSPJRGIGRP
M8+T*.)(,+!8+;")<0$4)&,&+&0+-%4+2"&04+U?%-%/V),W8+>,(’-#,&+&0+?)0"(),4
@%(),-048+A0B,$#,/0"#%+&0+>)-%4%CD,+!!8+;")<0$4)&,&+&0+-%4+2"&04+U?%R
-%/V),W8+?E@F+!!!8+XD#8
?AA+MSH @9;2
!"#$%"&'%(#)#*+,'$&-.'(%'/001
!"
2+("34'!5%6
!
"'7+#8%"4#(&('(%'9.4'2+(%4:';&)<9=&('(%'>#%+)#&4'?.)#&9%4,
@%A&"=&$%+=.'(%';#9.4.BC&
D%93B.+.4E'FFGHGHG'I'FFGHGGG:'JK=:'/LF0I/L0M
J(#)#.+%4'7+#&+(%4
>&""%"&'M'NO'MGP/1:'J(#B#)#.'27'Q
2A&"=&(.'23"%.'HG1Q
R.S.=5,'@:>:,'>.9.$T#&
D%93B.+.4E'FFGHGHG'P'FFGHGGG:'JK=:'/MUMI'/01M'I'/0GG:';&KE'%K=:'/MLU
>.""%.'%9%)="*+#).E'#+B%(<+#V<+#&+(%4:%(<:).'I'9#T"%"#&V<+#&+(%4:%(<:).
W?RNE'G1UPGLUPQGLP/1/PG
@#&S"&$&)#*+'%9%)="*+#)&E'X(#=%"'J4="&=%S#&4'J(<)&=#8&4'Y=(&:
R.S.=5,'@:>:,')=.8&"9%.+V-&Z..:).$:$K
W$A"%4#*+E'>.")&4'J(#=."%4'Y=(&:
@#4%[.'(%')<T#%"=&E'\.43']#S<%9'^&"S&4
J+'9&').+="&A."=&(&E'@%'#6_<#%"(&'&'(%"%)Z&,'Y<(`#S'a#==S%+4=%#+,'>:'W:'Y%`#4,'29.+6.'>Z<")Z,
Y%.A.9('Yb`%+Z%#$,'>Z&"9%4'?&+(%"4'!%#")%,'c.==9.T';"%S%,'R%"="&+('d<44%99,
29B"%('N."=Z'aZ#=%Z%&(,'?&<9'e"#Af%,'e<"='cb(%9,'D."&9B'?f.9%$'-'@&8#('g#9T%"=:
W$A"%4.'%+'>.9.$T#&'I'!"#+=%('#+'>.9.$T#&
D.(.4'9.4'(%"%)Z.4'"%4%"8&(.4:'J4=&'A<T9#)&)#*+'+.'A<%(%'4%"'"%A".(<)#(&'+#'%+'4<'=.(.
+#'%+'4<4'A&"=%4,'+#'"%S#4="&(&'%+'.'="&4$#=#(&'A."'<+'4#4=%$&'(%'"%)<A%"&)#*+'(%'#+B."$&)#*+,
%+'+#+S<+&'B."$&'.'A."'+#+Sh+'.=".'$%(#.,'4%&'$%)5+#).,'B.=._<C$#).,'%9%)="*+#).,
$&S+3=#).,'%9%)=".*A=#).,'A."'B.=.).A#&'.'A."')<&9_<#%"'.=".,
4#+'%9'A%"$#4.'A"%8#.'A."'%4)"#=.'(%'9.4'%(#=."%4:
!"#$%$&'(#) 4 *+,-.,-/01-*23+1('#'
!"#$%&'&$%(&
!"#$%$&'(#) 4 *+,-.,-./0-+1*20('#'
!"#$%$&'(#) 4 *+,-.,-./0-+1230('#'
0567869:5
0$/1*(!% !"""
23 (%"(/0#%4+564!(%4+&/+,*+,)-!(* 2
232 78'9+/4+,*+,)-!(*: 2
23; /"'"(!*&%4+<+0$%0%4!(!%"/4 =
23= *$-'./"#%4 >
23? *$-'./"#%4+!"&'(#!@%4 2A
23B 4!,%-!4.%4+(*#/-)$!(%4 2=
23> 4%$!#/4 2C
23C 4!,%-!4.%4+D!0%#9#!(%4+<+&!4<'"#!@%4 2E
23F 0$/.!4*4+"%+*1!$.*#!@*4 ;=
23E /"#!./.*4 ;=
232A (%"4!4#/"(!*+,)-!(*+&/+'"+(%"G'"#% ;>
2322 @/$&*&H+1*,4/&*&+<+/8'!@*,/"(!*+,)-!(* ;C
0$!./$*+0*$#/
,*+,)-!(*+0$%0%4!(!%"*,
;3 !"#$%&'((!)"+*+,*+,)-!(*+0$%0%4!(!%"*, =2
;32 ,/#$*4+0$%0%4!(!%"*,/4+&/+#$ =2
;3; (%"G'"(!)" ==
;3= &!4<'"(!)" =B
;3? 0'"#'*(!)" =>
;3B "/-*(!)" =C
;3> (%.5!"*(!)"+&/+(%"/(#%$/4+,)-!(%4 =F
;3C (%"&!(!%"*,+.*#/$!*, ?2
;3F 5!(%"&!(!%"*,+.*#/$!*, ?C
!"#$%$&'(#) . *+,-.,-./0-+1*20('#'
(0%$"/#1/*"(!!&%%
;3E /"'"(!*&%4+('*"#!1!(*&%4 BA
;32A ,*+4!"#*I!4+&/+#$ B=
=3 4/.6"#!(*+&/,+,/"-'*G/+#$ BC
=32 (%"&!(!%"/4+&/+@/$&*& BC
=3; #*5,*4+&/+@/$&*& BE
=3= #*'#%,%-J*4H+(%"#$*&!((!%"/4+<+1)$.',*4+(%"#!"-/"#/4 >;
=3? /8'!@*,/"(!*+4/.6"#!(* >>
=3B (%"4!4#/"(!*+4/.6"#!(* >F
=3> @*,!&/K+/+!.0,!(*(!)"+4/.6"#!(* CA
=3CL ,*+5*$$*+&/+4D/11/$+<+,*+&*-*+&/+"!(%& CE
?3 6$5%,/4+&/+@/$&*&+&/+#$ F=
?32 0$%0!/&*&/4+4/.6"#!(*4+<+(%"4!4#/"(!*+4/.6"#!(* F=
?3; ,*+/4#$'(#'$*+&/+'"+6$5%,+&/+@/$&*& FC
?3= $/-,*4+0*$*+,*+(%"G'"(!)"H+,*+&!4<'"(!)"+<+,*+"/-*(!)" E;
?3? $/-,*4+0*$*+/,+(%"&!(!%"*,+<+/,+5!(%"&!(!%"*, E?
?3B #*'#%,%-J*4H+(%"#$*&!((!%"/4+<+1)$.',*4+!"&/#/$.!"*&*4 2AA
?3> /8'!@*,/"(!*+4/.6"#!(* 2A=
?3C !.0,!(*(!)"+<+@*,!&/K+4/.6"#!(* 2AB
B3 &/&'((!)"+"*#'$*,+/"+#$ 2AE
B32 ,*4+$/-,*4+&/+&/$!@*(!)"+&/,+4!4#/.*+&/+&/&'((!)"+"*#'$*, 22A
B3232 (%"G'"(!)" 22A
B323; (%"&!(!%"*, 22;
B323= "/-*(!)" 22>
B323? &!4<'"(!)" 22E
B323B 5!(%"&!(!%"*, 2;;
B3; /4#$*#/-!*4+0*$*+(%"4#$'!$+&/$!@*(!%"/4 2;?
B3= (%"(/0#%4+564!(%4+&/,+4!4#/.*+&/+&/&'((!)"+"*#'$*, 2=A
B3=32 &/$!@*5!,!&*&+/"+&'( 2=A
B3=3; @*,!&/K 2=2
B3=3= #/%$/.*4 2==
B3=3? /8'!@*,/"(!* 2=?
B3=3B !"(%"4!4#/"(!* 2=B
B3?L &'() 2=E
%"""
!"#$%$&'(#) 5 *+,-.,-./0-+1*40('#'
CPORNETFEANCIIDOO
S
EGUNDAPARTE
L
ALÓGICADEPRIMERORDEN
6. INTRODUCCIÓN A LA LÓGICA DE PREDICADOS 147
6.1 I LC 148
NTRODUCCIÓN INFORMAL A
6.1.1 T 148
ÉRMINOS SINGULARES
6.1.2 T 149
ÉRMINOS GENERALES
6.1.3 E 150
NUNCIADOS SINGULARES
6.1.4 E 152
NUNCIADOS GENERALES
6.2 I LC 153
NTRODUCCIÓN FORMAL AL LENGUAJE
6.3 S LC 162
INTAXIS FORMAL DE
6.4 E 168
NUNCIADOS CATEGÓRICOS
6.5 E 177
NUNCIADOS CATEGÓRICOS COMPLEJOS
6.6 E 185
NUNCIADOS CON CUANTIFICACIÓN MÚLTIPLE
6.7* L LC 193
AFORMANORMALPRENEXADEUNAFÓRMULADE
6.8 L 200
ÓGICA CUANTIFICADA CONIDENTIDAD
6.9 D 206
ESCRIPCIONES DEFINIDAS
7. SEMÁNTICA DEL LENGUAJE LC 212
7.1 L LC 213
A VALUACIÓN E INTERPRETACIÓN DE LAS FÓRMULAS DE
7.1.1 E UD 213
L
7.1.2 L 214
A INTERPRETACIÓN DE LOS PREDICADOS
7.1.3 L 217
A INTERPRETACIÓN DE LAS CONSTANTES
7.1.4 V 218
ALUACIONES NO INTERPRETADAS
7.1.5 D 220
EFINICIÓN FORMAL DE UNA VALUACIÓN
7.2 R LC 221
EGLAS DEVALUACIÓN DE
7.2.1 R 221
EGLAS PARA FÓRMULAS ATÓMICAS
7.2.2 R 223
EGLAS PARA FÓRMULAS MOLECULARES
7.2.3 R 225
EGLAS PARA FÓRMULAS CUANTIFICADAS
7.3 M 233
ODELOS
7.4 P LC 239
ROPIEDADES SEMÁNTICAS DE LAS FÓRMULAS DE
7.5 E 244
QUIVALENCIA SEMÁNTICA
7.6 C 247
ONSISTENCIA SEMÁNTICA
7.7 V 249
ALIDEZ E IMPLICACIÓN SEMÁNTICA
7.8 S LCI 253
EMÁNTICA PARA
7.9* E LC 255
L FRAGMENTO MONÁDICO DE
ix
!"#$%$&'(#) 3 **+,-+*,,./0-1*2
! " # $ % & ' (
)* +",(-#./0#/1#"0%0/0#/"# 234
)*5 "#6-%./0#/0#.&(7!(.'&'89/0#/-(./&:%9;'$'&%0("#. 234
)*2 1%-:%&'(9#./#9/:9/+",(-/0#/1#"0%0 23<
)*4 #-/("0#9/0#/0#.&(7!(.'&'89/0#/:9/+",(-/0#/1#"0%0 2=5
)*> !"(!'#0%0#./.#7+9;'&%./?/&(9.'.;#9&'%/#9/"# 2=>
)*@ #-/!"(,-#7%/0#/-(./+",(-#./'9$'9';(. 2)2
)*3A +",(-#./0#/1#"0%0/0#/"#$ 2))
<* 0#0:&&'89/9%;:"%-/#9/"# 2<3
<*5 #-/.'.;#7%/%&# 2<3
<*5*5 #-'7'9%&'89/0#-/:9'1#".%- 2<3
<*5*2 '9;"(0:&&'89/0#-/#B'.;#9&'%- 2<)
<*5*4 '9;"(0:&&'89/0#-/:9'1#".%- 4CC
<*5*> #-'7'9%&'89/0#-/#B'.;#9&'%- 4C4
<*2 &(9&#!;(./,+.'&(./0#/%&# 45C
<*2*5 0#"'1%,'-'0%0 45C
<*2*2 1%-'0#D 452
<*2*4 ;#("#7%. 45>
<*2*> #E:'1%-#9&'% 453
<*2*@ '9&(9.'.;#9&'% 45)
<*4A #-/.'.;#7%/%&#A 425
<*>A #-/.'.;#7%/%&#F 42@
;#"&#"%/!%";#
-%/-86'&%/7(0%-/!"(!(.'&'(9%-
5C* '9;"(0:&&'89/%/-%/-86'&%/7(0%- 445
5C*5 #9:9&'%0(./9#&#.%"'(.G/!(.',-#./?/&(9;'96#9;#. 445
5C*2 !"(!'#0%0#./-86'&%./0#/-%./7(0%-'0%0#. 443
5C*4 7(0%-'0%0#./9(/%-H;'&%. 44)
5C*> -(./%B'(7%./0#/-%/-86'&%/7(0%-/!"(!(.'&'(9%- 4>5
5C*@ .#7+9;'&%/0#/-%/-86'&%/7(0%- 4>3
5C*@*5 .#7+9;'&%/-#',9'D'%9% 4>3
5C*@*2 .#7+9;'&%/I"'!I#%9% 4><
55* +",(-#./0#/1#"0%0/7(0%-#. 4@3
55*5 "#6-%./!%"%/#-/.'.;#7%/I 4@3
55*2 #B;#9.'(9#./.'7!-#./0#/I 434
!
!"#$%$&'(#) *- *+,-+,-+./*-01+/$'#'