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MNLAC: uma proposta de modelagem de fluxo de navegação baseada em lógica modal

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(31) !"#$%&' () *%+,!-.+$'/. !. !"#$% &'() $%*+ "#$%&'() *+ + ,-).#/)0. ,* *-.+/- M .% /0"!1% *-.%/ 2 +34+1!51%.- 4-$ 67#89 + :;%< &==>?) (' ,* 1-<@#<8- W A 1#@-3 +/+*+<8-3 3B- 19%*%.-3 *#<.-3C &' ,*% :+/%DB- R +* W 8%/ E#+ R ⊆ W × W A 19%*%.% .+ $+/%DB- .+ %1+33!F!/!.%.+C G' ,*% H#<DB- V : W → P A 8%/ E#+ 19%*%.% .+ H#<DB- .+ J%/-$%DB-'. P. 2 #* 1-<@#<8- .+ 3I*F-/-3 4$-4-3!1!-<%!3A. K33!*A #* *-.+/- M 4-.+ 3+$ .+<-8%.-) M = (W, R, V ). LF3+$J%M3+ E#+ -3 1-<@#<8-3 W + R .+5<+* #*% +38$#8#$% $+/%1!-<%/A .+5<!.% 1-*!"#$' N+38% H-$*%A #* *-.+/- 4-.+ 3+$ .+5<!.- 1-*-) M = (F, V ). K33!*A .!OM3+ E#+ M 2 #* *-.+/- F%3+%.- <- H$%*+ FA -# E#+ F 2 - %!"#$ 3#F@%1+<8+ % M' K/2* .!33-A % H#<DB- V A 19%*%.% H#<DB- .+ J%/-$%DB-A 2 - 1-<@#<8- Φ .+ 4$-4-3!DP+3 E#+ 3B- J+$.%.+!$%3 <%3 8+/%3 .+ F 6Q/%1RF#$< +8 %/' &==&?' "#$%&'() *+1+ ,23%'() .# 45/)65'()0. S+@% M = (W, R, V ) #* *-.+/- .% /0"!1% *-.%/' S#4-<9% E#+ w ∈ W + φ 2 #*% H0$*#/% .% /0"!1% *-.%/' N+5<+M3+ E#+ #*% H0$*#/% φ 2 J+$.%.+!$% +* #* *#<.- w.

(32) !. !"! #$%&'()%*+, &) -./01' (+&'-. !"#$% " &'()!*" φ + ,"-.,&/.-" #% )!#$% w0 %! ,/1"2 w φ. 3*+) $.,,%0 $"$" " &!#45% $/ 6"*%("45% V 0 /#-5% V (w) + % 7%#1!#-% $/ -%$%, %, ,8)9%*%, :(%:%,.7.%#"., !/ ,5% 6/($"$/.(%, /) w ;<!-= / >?"# @AABCD. "#$%&'() *+,+ -./0&12/'() 3# 456789/1 #7 :8%3)1 3# 87 :)3#9); E/1" w !) )!#$% #% )%$/*% M = (W, R, V ). F)" &'()!*" φ + ,"-.,&/.-" G6/($"$/.("H /) M0 #% )!#$% w ,/0 / ,%)/#-/ ,/2 M0 w p ,/0 / ,%)/#-/ ,/0 p ∈ V (w)D M0 w 1 ⊥D M0 w ¬φ ,/0 / ,%)/#-/ ,/0 M0w 1 φD M0 w φ ∨ φ ,/0 / ,%)/#-/ ,/0 M0 w φ %! M0 w φD M0 w φ ∧ φ ,/0 / ,%)/#-/ ,/0 M0 w φ / M0 w φD M0 w φ → φ ,/0 / ,%)/#-/ ,/0 M0 w φ ,/):(/ !/ M0 w φD M0 w φ ↔ φ ,/0 / ,%)/#-/ ,/0 M0 w φ ,/0 / ,%)/#-/ ,/0 M0 w φD M0 w φ ,/0 / ,%)/#-/ ,/0 :"(" -%$% v ∈ W -"* !/ R(w, v)0 -/)%, M0 v φD M0 w ♦φ ,/0 / ,%)/#-/ ,/0 /I.,-/ !) v ∈ W -"* !/ R(w, v)0 -/)%, M0 v φD. 3*+) $.,,%0 !) 7%#1!#-% Σ $/ &'()!*", + 6/($"$/.(% /) !) /,-"$% w $/ !) )%$/*% M0 $/#%-"$% :%(2 M, w Σ. ,/0 / ,%)/#-/ ,/0 -%$%, %, )/)9(%, $/ Σ ,5% 6/($"$/.(%, /) ω D. "#$%&'() *+<+ -./0&12/'() 3# 456789/1 #7 87 :)3#9); F) )%$/*% M = (W, R, V ) ,"-.,&"J " !)" &'()!*" ,/ /) -%$%, %, )!#$%, $% )%$/*% " &'()!*" + ,"-.,&/.-" ;<!-= / >?"# @AABCD 3,,.)2 M φ. ,/0 / ,%)/#-/ ,/0 :"(" 7"$" w ∈ W 0 w φD.

(33) !"#$%&' () *%+,!-.+$'/. !. !"#$! % &'()*+ ,-, +.*#/#01+ )2 #3#2.$! "# 2!"#$!4 M = (W, R, V )4 1+$ 5)#6. "#$%&'( !) ). W = {w1 , w2 , w3 , w4 }. R = {(w1 , w2 ), (w1 , w4 ), (w2 , w4 ), (w4 , w3 ), (w3 , w1 )}. # + 7)089! "# :+$!*+89! V +.$';+"+ #2 ;+"+ 2)0"! "+ /#()'01# 7!*2+6 V (w1 ) = {p, q} ; V (w2 ) = {p, r} ; V (w3 ) = {p, q, s} ; V (w4 ) = {p} .. <!"#=/# ;!0;$)'* 5)# +/ /#()'01#/ 7>*2)$+/ /9! /+1'/7#'1+/ #2 M6 • M4 w p4 .!'/ p ∈ V (w )• M4 w ¬r4 .!'/ M4w 1 r4 !) /#?+4 r 09! #/1@ .*#/#01# #2 w • M 4 w p ∧ q ∧ s4 .!'/ M4 w p4 M4w q # M4w s• M4 w p ∧ q ∧ s ∧ ¬r4 .!'/ M4w p4 M4w q4 M4w s # M4w 1 s• M4 w p4 .!'/ 1!"!/ !/ 2)0"!/ +;#//A:#'/ "# w /+1'/7+B#2 p• M4 w 1 r4 .!*5)# #3'/1# )2 2)0"! +;#//A:#$ "# w 5)# 09! /+1'/7+B r C+ /+D#*4 w E• M4 w ♦r4 .!'/ #3'/1# )2 2)0"! +;#//A:#$ "# w 5)# /+1'/7+B r4 ! 2)0"! w • M p4 /'(0'F;+ 5)# #2 1!"!/ !/ 2)0"!/ "! 2!"#$! M4 p G :@$'"!4. 4. 1. 1. 1. 3. 3. 3. 3. 3. 3. 3. 3. 3. 1. 1. 1. 1. 4. 1. 1. 2.

(34) !"! #$%&'()%*+, &) -./01' (+&'-. !"#$% &'&( )*+,-* !"#$%&'( )*+* ,-./%$0(1. ./ 0%/!12* ,/ #/ /*+,-* M = (W, R, V ) 3 #/% 4,5#617!% !181!9% +, /#1+*4 w1 , w2 , w3 , . . . ∈ W : 9%- 5#,: ;%$% 7%+% i ≥ 1: (wi , wi+1 ) ∈ R' ./ 7%/!12* 3 ,47$!9* +% 4,"#!19, <*$/%( π = w1 → w2 → w3 → . . .. 2(3.&'(4 ./ 7%/!12* 3 $,;$,4,19%+* ;,-% -,9$% "$,"% π ' = 9$,72* 81%- +, #/. 7%/!12*: !1!7!%+* 1* /#1+* wi : 3 +,4!"1%+* +, πi ' 56"/78( )*9* 0%/!12*. 0*14!+,$, * /*+,-* +* >?,/;-* &'@: $,;$,4,19%+* ;,-% !"#$% &'&' = 7%/!12* π = w1 → w4 → w3 → . . .. $,;$,4,19% #/ !17$,/,19* -!1,%$ +* 9,/;*' = 7%/!12* !1!7!% 1* /#1+* w1 : +,;*!4 ;%44% %* /#1+* w4 : +,;*!4 %* /#1+* w3 : , %44!/ ;*$ +!%19,' = 9$,72* +* 7%/!12* π: !1!7!%+* 1* /#1+* w4 : *# 4,A%: 1* 4,"#1+* ,49%+* +* 7%/!12*: 3 π 2 = w4 → w3 → . . .. > * 9$,72* !1!7!%+* 1* /#1+* w3 3 π 3 = w3 → . . ..

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♦ $ . = C+)3-' D<E ',-$.$&/' 3" "!#$%! M = (W, R, V )2 *!"F W = {w1 , w2 , w3 , w4 }. R = {(w1 , w2 ), (w1 , w3 ), (w1 , w4 )}. $..$ "!#$%!2 V G /'% H3$F V (w1 ) = {p, q} ; V (w2 ) = {p, q} ; V (w3 ) = {q} ; V (w4 ) = {q} ;. I" 3" *'"+&1! +&+*+'#! $" w12 *!&*%3+J.$ H3$F • M2w1 ♦p. G (K%+#'2 ,!+. $>+./$ 3" *'"+&1!2 π = w1 → w2. #$ 6!-"' H3$ &! .$)3&#! "3&#! #' .$H3L&*+'2 w22 p G .'/+.6$+/!< • M, w1 q. G (K%+#'2 ,!+. $" /!#!. !. *'"+&1!. +&+*+'#!. $" w12 !. H3'+. .4!F π1 = w 1 → w 2 π2 = w 1 → w 3 π3 = w 1 → w 4. &! .$)3&#! "3&#! #$..$. *'"+&1!.2 q G .'/+.6$+/!<.

(36) !. !"! #$%&'()%*+, &) -./01' (+&'-. !"#$% &'() *+,$%-.$,/ ♦ ,  "#$%&'( )*+* 0$%1/!2!3!-%-, -. *+,$%-.$ ♦. 4 !"#$% &'5 %+$,/,12% #6 6.-,7. M = (W, R, V )8 9.6) W = {w1 , w2 , w3 , w4 }. R = {(w1 , w2 ), (w1 , w3 ), (w1 , w4 ), (w2 , w3 )}. :,//, 6.-,7.8 V ; 2%7 <#,) V (w1 ) = {p} ; V (w2 ) = {p} ; V (w3 ) = {p} ; V (w4 ) = {} ;. =6 #6 9%6!1>. !1!9!%-. ,6 w1 8 9.197#!?/, <#,) M, w1 ♦♦p. ; 3@7!-%8 +.!/ ,A!/2, #6 9%6!1>.8 π = w1 → w1 → w3. -, B.$6% <#, 1. 2,$9,!$. 6#1-. -% /,<#C19!%8. w3 8 p. ; /%2!/B,!2.'. "#$%&'( )*,* 0$%1/!2!3!-%-, -./ *+,$%-.$,/ ♦. 4 !"#$% &'D %+$,/,12% #6 6.-,7. M = (W, R, V )8 9.6) W = {w1 , w2 , w3 , w4 , w5 , w6 , w7 , w8 , w9 , w10 }.

(37) !"#$%&' () *%+,!-.+$'/. !. !"#$% &'() *$%+,!-!.!/%/0 /1 230$%/1$. ♦. R = {(w1 , w2 ), (w1 , w3 ), (w1 , w4 ), (w2 , w5 ), (w3 , w6 ), (w3 , w7 ), (w3 , w8 ), (w4 , w9 ), (w4 , w10 )}. 40,,0 51/0617 V 8 -%6 9#0) V (w1 ) = {p} ; V (w2 ) = {p} ; V (w3 ) = {p} ; V (w4 ) = {p} ; V (w5 ) = {p} ; V (w6 ) = {p} ; V (w7 ) = {} ; V (w8 ) = {} ; V (w9 ) = {} ; V (w10 ) = {p}. :5 #5 ;%5!+<1 !+!;!%/1 05 w1 7 31/0=,0 .0$!>;%$ 9#0) • M 7 w1 ♦p. 8 .?6!/%7 31!, % 3%$-!$ /0 -1/1, 1, 0,-%/1, %6;%+@?.0!, /0 w1 7 8 31,,A.06 -$%@%$ %1 50+1, #5 ;%5!+<1 ;#B1 3$CD!51 0,-%/1 ;1+-85 p' *E5=,07 0+-F17 1, ;%5!+<1,) π1 = w 1 → w 2 → w 5 π2 = w 1 → w 3 → w 6 π3 = w1 → w4 → w10. 2, ;%5!+<1,.

(38) !. !"! #$%&'()%*+, &) -./01' (+&'-. π4 = w 1 → w 3 → w 7 π5 = w 1 → w 3 → w 8 π6 = w 1 → w 4 → w 9. !" #$%&#'$()* $ '+,*-.$ ♦p/. 0&1-,$ 2/34 5,$ #&%&6&7$7) 7" 89),$7", ♦. "#$%&'( )*+* 5,$ #&%&6&7$7) 7"# 89),$7",)#4 ♦ : 0&1-,$ 2/; $9,)#) %$ -* *"7)." M = (W, R, V )< ="*4 W = {w1 , w2 , w3 , w4 , w5 , w6 , w7 , w8 , w9 , w10 }. R = {(w1 , w2 ), (w1 , w3 ), (w1 , w4 ), (w2 , w5 ), (w3 , w6 ), (w3 , w7 ), (w3 , w8 ), (w4 , w9 ), (w4 , w10 )}. >)##) *"7)."< V ? %$. @-)4 V (w1 ) = {p} ; V (w2 ) = {} ; V (w3 ) = {p} ; V (w4 ) = {} ;.

(39) !"#$%&' () *%+,!-.+$'/. ! V (w5 ) = {} ; V (w6 ) = {p} ; V (w7 ) = {p} ; V (w8 ) = {p} ; V (w9 ) = {} ; V (w10 ) = {}. ! "! #$!%&'( %&%#%$)( *! w1 + ,()*-.* /*0%1#$0 2"*3 • M+w1 ♦p. 4 /56%)$+ ,(%. $ ,$07%0 )* $( !*&(. "! *.7$)( $6#$&85/*6 )* w1 + *! 7()(. (. #$!%&'(. p (#(00* &( *.7$)( .*9"%&7*: ;" .*<$+ &( !()*6( )$ =%9"0$ >:? (. #$!%&'(. 2"* .$7%.@$A*! $ @B0!"6$ ♦p .C(3 π1 = w 1 → w 3 → w 6 π2 = w 1 → w 3 → w 7 π3 = w 1 → w 3 → w 8. =%9"0$ >:?3 D0$&.%7%/%)$)* )( ;,*0$)(0 ♦. E ,0(,(.7$ $,0*.*&7$)$ &*.7* 70$F$6'( #(&.%)*0$ "! @0$9!*&7( )$ GB9%#$ H()$6 )*&(!%&$)( GB9%#$ D*!,(0$6: GB9%#$. 7*!,(0$%. 7*! "! $.,*#7( )%&I!%#(+ ,(%. $ /*0)$)* )* "!$ @B0!"6$ &C( 4 1J$ *! "! !()*6(+ #(!( (#(00* &$ 6B9%#$ ,0(,(.%#%(&$6 * )* ,0*)%#$)(.+ !$. )*,*&)* )* "! ,(&7( &( 7*!,( )*&70( )( !()*6( KL"7' * MN$& >OOPQ:.

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(58) !"! #$%&'() *) #%&+) *$ ,$-&.. !. !"# $ %&'()*+% ,$ !"#!$ %$ &'!'()$!*+),('+ - .$,$ /(012#2'% 31).2%)$4 ,$ 5/6%/( 7 '/$)#3%/8$,% (8 18$ '(4$9 :(##$ '/$)#3%/8$*+%- 7 .%)#2,(/$,$ $ 3%/8$ .%8% %# 2'()# #(/+% ,2#!%#'%# )$ 2)'(/3$.( ;)$4 ( .%8% (4(# #(/+% 2)'(/42<$,%#9 =%/ (>(8!4%- % &-') )$ 5/6%/( ,$ ?2<1/$ @9A BC426(2/$ (' $49 DEAE,- C426(2/$ DEAAF !%##12 %# #(<12)'(# 2'()# /(4$.2%)$,%#G. &#."$!+' /012,(' • 3!'"'45# 6!78,"# &#."$!+' • 69$.%':$.)# &#."$!+' • ;$2$45# <+8=!,# • &#."$!+' 3!8># /'!),(82'! •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(60) !. ! ! "#$%&%'($ )* +,%-#.*/-. "#$%&'#(. ! "#$! %$ #$&' ( %$)*#'%*+ )$,#$ #-'.'&/*+ 0$&* ,$1 )*!$ 0-$2$%"%* 0$&'. &$#-' i3 4, %$)*#'56$, ' ,$71"- 2*--$,0*)%$! ' "#$), %$ #$&'8. iRevista, iF orum, iP erf il, iM ural, iBiblioteca, iCriatividade, iM ensagens, iAgendamento, iGravar, iP articular, iF echar, iM inimizar. )*+,-&'# ./0/ 123,&4*5 67-89:*-5 * "'# 67-89:*-5;. 9, "#$), %$ #$&' ,:* 2&',,";2'%*, $!8 • • •. <#$! 2&"2=>$& ?@*#'5:*8 α1AB <#$! ):* 2&"2=>$& ?@*#'5:*8 α2A3 9, "#$), 2&"2=>$", ,:* -$C1","#*, %' !"#!$ %$ &'!'()$!*+),('+ C1$ -$0-$,$)#'!+ $! 1!' #$&'+ 1!' D1)5:* '#">' C1$ %",0'-' 1! $>$)#*3 9, "#$), 2&"2=>$", ,:* %">"%"%*, $!8 <. <. •. <#$! 2&"2=>$& C1$ 7$-' #$&'8 E,,$, "#$),+ '* ,*D-$-$! * 2&"C1$ %* !*1,$+ %",0'-'! 1! $>$)#* C1$ 2-"' 1!' )*>' #$&'3 ! "#$! %$,,$ #"0* ( %$)*#'%*+ )$,#$ #-'.'&/*+ 0*- α113 <#$! 2&"2=>$& C1$ ):* 7$-' #$&'8 E,,$, "#$),+ '* ,*D-$-$! * 2&"C1$ %* !*1,$+ %",0'-'! 1! $>$)#* C1$ ):* 2-"' #$&'3 <,#* (+ $&$ %",0'-' 1! $>$)#* ")#$-)* %$ 1!' #$&'3 ! "#$! %$,,$ #"0* ( %$)*#'%*+ )$,#$ #-'.'&/*+ 0*- α123. ! "#$! ):* 2&"2=>$& ( 1! "#$! %$ #$&' C1$ ,$ $)2*)#-' %$,'#">'%*3 91 ,$F'+ $,#= 0-$,$)#$ )' #$&'+ !', '* 2&"2'- 2*! * !*1,$ )$&$+ )$)/1! $>$)#* ( %",0'-'%*3 @$,#$ #-'.'&/*+ 1! "#$! %$,,$ #"0* ( %$)*#'%* 0*- α23. )*+,-&'# ././ 1=*7%;. !' #$&' ( 1! >(-#"2$ %* -!'.# %$ /$0'+ $ 2*--$,0*)%$ ' 1! !1)%* )' ,$!G)#"2' %' HI7"2' J*%'&3 !' #$&' ( 2*!0*,#' %$ "#$), 2&"2=>$", $ ):* 2&"2=>$",+ ,$)%* %$)*#'%' 0$&' &",#' /$0' + #'& C1$8 T ela = [α11 , α12 , α2 ]. @$,,' )*#'5:*+.

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