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\begin{document}
{\footnotesize
\begin{center}
{\normalsize Lorenzo Magnani e Rosella Gennari, {\it Manuale di logica}}

\smallskip\
\begin{tabular}{ccccccccc} \hline 
     {\rm pagina}  &  {riga}  &  {\`e} & {dovrebbe essere}\\ \hline 
     $9$              &  $-21$       &      o coloro   &      e coloro \\ 
     $9$              &  $-18$       &     $ C-(A\cup B) $  &      $ C-(A\cap B) $\\ 
     $9$              &  $-18$       &     $ C-(A\cap B) $  &      $ C-(A\cup B) $\\ 
     $9$              &  $-17$       &      o la cui lingua  &      e la cui lingua \\ 
     $11$               &  $8$       &  $<a,b>\in X$         &        $<a,b>\in R $ \\
     $11$               &  $9$       &  $<b,a>\in X $   &        $<b,a>\in R $ \\
     $13$               &  $13$      &  $ant {\tt a}$   &        $ant {\tt e}$ \\
     $13$               &  $-11$    &  per ogni naturale $n$   &
  per ogni naturale $m$ \\
     $16$               &  $11$    &  $U\in F$   &        $U\subset S$ \\
     $18$               &  $22$    &  divisibilt\`a   &       divisibilit\`a \\
     $20$               &  $5$    &  saltarla   &        saltarlo \\
     $21$               &  $1$    &  la prima definite   &        la prima definita \\
     $21$               &  $-12$    &  $a\cdot 0=a$   &        $a\cdot 0=0$ \\
     $21$               &  $-11$    &  $a\cdot (S(bn))=S(a\cdot b)+a$   &        $ a\cdot (S(bn))=a\cdot b+a$ \\
     $25$               &  $-18$    &  $ <p^{i}_{b+1},a>\in div $   &    $ <p^{b+1}_{i},a>\in div $    \\
     $25$               &  $-18$    &  $\mbox{ e }<p^{i}_{b+2},a>\not \in div$   &        $\mbox{ e }<p^{b+2}_{i},a>\not \in div$ \\
     $38$               &  Tavole 2.5 e 2.6    &  V   &        $1$ \\
     $38$               &  Tavole 2.5 e 2.6    &  F   &        $0$ \\
     $40$               &  $2$       &  valore di verit\`a 0    &       valore di verit\`a 1 \\
     $41$               &  $11$    &  [$(A\vee
B)\wedge$ non $(A\wedge B)$]   &        [$(A\vee
B)\wedge$ $\neg $$(A\wedge B)$] \\
     $44$               &  $11$    &  $<P,\neg , \rightarrow , (, )>$   &        $<P,\{\neg , \rightarrow , (, )\}> $ \\
     $45$               &  $15$    &  teorema di ricursione   &       teorema di leggibilit\`a unica\\
     $46$               &  $11$    &  $<\psi _1,\ldots ,\psi _n>$   &        $<\psi _1,\ldots ,\psi _i>$ \\
     $51$               &  $14$    & $(\neg \left( A\wedge \neg B\right))$    &  $(\neg \left( A\wedge (\neg B)\right) )$ \\
     $53$               &  $-13$    &  $Pro(P)$   &        $Pro({\cal P})$ \\
     $53$               &  $-12$    &  $ Pro(P) $   &      $ Pro({\cal P})$ \\
     $54$               &  $-13$    &  $(A\rightarrow \neg B) \vee A$
& $(A\wedge \neg B) \vee A)$\\
     $54$               &  $-9$ & ma nemmeno & (cfr. pi\'u avanti Def. 2.3.3), ma nemmeno\\
     $56$               &  Tavola 2.10    &  $(A \rightarrow \neg B) \vee B$   &        $(A \rightarrow \neg B) \vee A$ \\
     $56$               &   $-18$           & ... $\hat \nu _{1}(\alpha )=1-
\hat \nu _{1}(\beta )=1-\hat \nu _{2}(\beta )...$.   & ... $\hat \nu _{1}(\alpha )=1+
\hat \nu _{1}(\beta )=1+\hat \nu _{2}(\beta )...$.   \\
     $57$               &  $6$    &  conseguanza   &        conseguenza \\
     $59$               &  $14$    &  di ${\cal P}$   &        per $\cal P$ \\
     $60$               &  $-8$    &  $(A \rightarrow \neg B )\rightarrow \neg A $   &        $(A \rightarrow \neg A )\rightarrow \neg A $ \\
     $60$               &  $-7$    &  $(A \rightarrow B )\leftrightarrow (\neg A \rightarrow
\neg B )$   &        $(A \rightarrow B )\leftrightarrow (\neg B \rightarrow
\neg A )$ \\
     $65$               &  $13$    &  $S \cup \Gamma \subseteq D(\Gamma)$   &        $ {\rm Ax} \cup \Gamma \subseteq D(\Gamma) $ \\
     $66$               &  $-5$    &  $T \cup \{\varphi \} $   &        $\Gamma \cup \{\varphi \}$ \\
     $68$               &  $-7$    &  $\vdash \varphi\rightarrow (\neg \varphi \rightarrow \varphi )$   &        $\vdash \varphi\rightarrow (\neg \varphi \rightarrow \psi ) $ \\
     $72$               &  $-5$    &  $T_{i_0}\subseteq T_{i_j}$,\ 
$\ldots $,\ $T_{i_n}\subseteq T_{i_j}$,   &        $T_{i_0}\subseteq T_{i_1}$,\ 
$\ldots $,\ $T_{i_n}\subseteq T_{i_j}$, \\
     $72$               &  $-6$    &  essendo F   &        essendo G \\
     $73$               &  $11$    &  ${\cal F} $   &        F \\
     $73$               &  $12$    &  ${\cal F} $   &        F & \\
     $74$               &  $8$    &  $\nu :\rightarrow \{0,1\}$   &        $\nu :{\rm P}\rightarrow \{0,1\}$ \\
     $74$               &  $-4$    &  $\Gamma ;\psi \models \varphi $   &        $\Gamma ,\psi \models \varphi $ \\
     $75$               &  $-8$    &  $\vdash ((A\rightarrow B)\rightarrow B)\rightarrow B)$   &        $\vdash (((A\rightarrow B)\rightarrow B)\rightarrow B)$ \\
     $91$               &  $22$    &  $<<{\tt a},{\tt b}>$   &        $<{\tt a},{\tt b}>$ \\
     $101$               &  $-7$    &  $ rango(f)\cap rango(g)$   &        $ rango({\cal F}_f)\cap rango({\cal F}_g)$ \\
     $101$               &  $-3$    &  $f=gt_{1}^{\prime }\ldots t_i^{\prime \prime },$   &        $f=gt_{1}^{\prime }\ldots t_i^{\prime },$ \\
     $113$               &  $7$    &  $L-interpretazione$   &        $L-struttura$ \\
     $114$               &  $5$    &  $L-interpretazione$   &        $L-struttura$ \\
     $115$               &  $15$    &  $\forall \upsilon _{1}\, \upsilon \approx c$   &        $\forall \upsilon _{1}\, \upsilon_{1} \approx c $ \\
     $121$               &  $1$    &  allora $u_{t}^{x}:=ft_{1t}^{\mbox{ }x}
\ldots t_{2t}^{\mbox{ }x}$   &        allora $u_{t}^{x}:=ft_{1t}^{\mbox{ }x}
\ldots t_{nt}^{\mbox{ }x}$ \\
     $122$               &  $-1$    &  $s_{at}^{yx}=s_{ta}^{xy}$   &        $s_{a{\hat s}(t)}^{yx}=s_{{\hat s}(t)a}^{xy}$  \\
\end{tabular}
\newpage
\begin{tabular}{ccccccccc}
     $125$               &  $15$    &  $PR(L)$   &        ${\cal PR}(L)($ \\
      $125$               &  $-3$    &  $PR(L)\subseteq Fbf(L)$   &        ${\cal PR}(L)\subseteq Fbf(L)$ \\
      $126$               &  $-17$    &  $t\approx u\rightarrow \varphi _{t}^{x}\approx \varphi _{u}^{x}$   &        $t\approx u\rightarrow \varphi _{t}^{x}\rightarrow \varphi _{u}^{x}$ \\ 
     $130$               &  $-10$    &  $T,\varphi \vdash \neg \psi $ sse $T;\psi \vdash \neg \varphi $   &        $\Gamma,\varphi \vdash \neg \psi $ sse $\Gamma,\psi \vdash \neg \varphi $\\
     $132$               &  $2$    &  $iii$   &        $ii$ \\
     $132$               &  $3$    &  $iv$   &        $iii$ \\
      $132$               &  $-13$    &  $(Rt_1\ldots
t_{n})^{-}=Rt_1^{-}\ldots t_{n}^{-}$   &        $(Rt_1\ldots
t_{n})^{-}:=Rt_1^{-}\ldots t_{n}^{-}$ \\
$134$               &  $18$    &  sse $c$ occorre in 
$\psi _{jx}^{\mbox{ }c}$   &        sse $c$ occorre in 
$\psi _{j}$\\
    $135$            &   $-4$          &           $\upsilon _{1}(R\upsilon _{1} \rightarrow Rb) \vdash Rc\rightarrow (Rc\rightarrow Rb)$           &             $\forall \upsilon _{1}(R\upsilon _{1} \rightarrow Rb) \vdash Rc\rightarrow (Rc\rightarrow Rb)$\\
    $136$            &   $1$          &           grazie allo schema $Ax2$ e al corollario 3.4.15,           &    grazie allo schema Ax2,\\
    $136$            &   $3$          &     la compattezza sintattica             &      il terzo asserto del teorema 3.4.8\\
    $136$            &   $5$          &      la 3.3.          &          quanto volevamo derivare.\\
    $136$            &     $-13$ & conlcudere    & concludere\\
     $138$               &  $14$    &  $T$   &        $\Gamma$ \\
     $138$               &  $-7$    &  $\Gamma \vdash \psi_{t}^{x}$   &        $\Gamma \vdash \neg \psi_{t}^{x}$ \\
     $144$               &  $12$    &   $\left\{ \forall x(\varphi \rightarrow \psi ),\forall x\varphi
\right\} \models \forall x\psi $    &        $\left\{ \forall x(\psi \rightarrow \varphi ),\forall x\psi
\right\} \models \forall x\varphi $ \\
     $166$               &  $-5$    &  $ D(a):=Sost(a,\hat G(\overline{a}),%
\hat G(\upsilon _{1}))$   &        $ D(a):=Sost(a,\hat G(\upsilon_{1}),%
\hat G(\overline{a}))$ {[\tiny cfr. def. di sost p. 162}] \\
     $181$               &  $11$    & $<{\cal L}, Fbf({\cal L}),S,Teo>$   &        $<{\cal L}, Fbf({\cal L}),{\rm Ax},Teo>$ \\
     $182$               &  $-19$  & $S$ & Ax\\
     $190$               &  $19$    &  $\neg (\neg \alpha \wedge \neg \beta )$,\ $\neg (\neg \alpha \wedge %
\neg \gamma )$   &        $\neg (\neg \alpha \wedge \neg \beta )$,\ $\neg (\alpha \wedge %
\neg \gamma )$ \\
     $191$               &  $13$    &  IMP   &        IMPORT,1 \\
     $197$               &   $8$          & IMPORT,1        &   $\forall$ELIM,2 {\tiny [con $t$ uguale a $x$]}  \\
     $197$               &  $-7$    &  nella premessa $\beta$   &        nella premessa $\alpha$ \\
      $198$               &  $-8$ & 10. $\gamma \wedge \beta$  \qquad $\exists$ELIM,9 &
$\forall$ELIM,4 \\
     $198$               &  $-13$    &  $\forall$ELIM,4 {\tiny [con $t$ uguale a $x$]}   &        ${\alpha}^{x}_{y}$ \\
     $198$               &  $-12$    &  $\alpha$   &        ${\alpha}^{x}_{y}$ \\
     $199$               &  $9$     &  $*7$   &        $7$ \\    
     $199$               &  $11$    &  $8$   &        $*8$ \\
     $199$               &  $15$ & $\alpha$   &        ${\alpha}^{x}_{y}$ \\    
     $200$               &  $16$    &  $\forall$INTR   &        $\approx$ELIM \\
     $202$               &  $-18$ & *7. $\alpha$  \qquad $\neg$ELIM &
[sopprimere e rinumerare la prova]    \\
     $204$               &  $7$    &  $\forall x(\gamma \rightarrow \neg \beta ),\exists x(\alpha \wedge
\beta )\vdash \exists x(\alpha \wedge \gamma )$   &        $\forall x(\gamma \rightarrow \neg \beta ),\exists x(\alpha \wedge
\beta )\vdash \exists x(\alpha \wedge \neg \gamma )$ \\
      $207$               &  $-11/13$ & **8, *9 e 10 &
**7, *8, 9    \\
     $207$               &  $-18$   &  PREMESSA  & ASS\\
     $216$               &  $-12$   &  {\it alla matrice} $\beta$
{\it e non vi occorrono variabili}. & {\it alla matrice} $\beta$.\\
     $217$            &   $17$          &        altrimenti anche
$\alpha$ lo $\ldots$ dell'algoritmo.          &      altrimenti $\alpha$ sarebbe priva di quantificatori.\\
     $233$               &  $13$    &  P$\not \models $P$\vee $Q   &        P$ \models $P$\vee $Q \\
     $244$               &  $-1$    &  p. $61$   &       p. $126$ \\
     $264$               &  $7$    &  {\it $m{^{*}}_w^{{\cal M}}(\Box \alpha )=1$ sse $ m{^{*}}_w^{{\cal M}}(\alpha )=1$}  &        
     {\it $m{^{*}}_w^{{\cal M}}(\Box \alpha )=1$ sse $ m{^{*}}_w{\prime}^{{\cal M}}(\alpha )=1$}\\
     $264$               &  $9$    &   {\it $m{^{*}}_w^{{\cal M}}(\Diamond \alpha )=1$ sse $ m{^{*}}_w^{{\cal M}}(\alpha )=1$}  &        
     {\it $m{^{*}}_w^{{\cal M}}(\Diamond \alpha )=1$ sse $ m{^{*}}_w{\prime}^{{\cal M}}(\alpha )=1$}\\
     $268$            &   $7$          &  0 \quad  1/2 \quad  1/2 \quad {\tiny [Tavola B.2]}                 &   0 \quad  1/2 \quad  0 \quad         \\
$269$            &   $3$          &  1/2 \quad  1/2 \quad  1 \quad {\tiny [Tavola B.3]}                 &   1/2 \quad  1 \quad  0  \quad        \\
     $269$               &  $9$    &  max &        $min$ \\
     $269$               &  $10$    &  $min$   &        $max$ \\

\end{tabular}
\end{center}

\noindent Inserire in basso alla pagina 278 l'item [64] Moore, R., Possible-world semantics for autoepistemic
logic, in {\em Proc. AAAI Workshop on Non-Monotonic Reasoning}, New
Paltz, NY, 1984, pp. 344-354.}

\smallskip\
{\footnotesize
\noindent A pagina 199 sostituire le righe 18-31 con

\begin{tabular}{p{5.5cm}p{5cm}}

$^{**}$13 $\neg \alpha$ & $\exists$ELIM,10,12\\
\end{tabular}

/FINE: $\exists $ELIM/

\begin{tabular}{p{5.5cm}p{5cm}}

$^{**}$14. $\alpha$ & IMPORT10 \\

$^{*}$15. $\neg\exists x\alpha$ & $\neg$INTR,9,13,14 \\
\end{tabular}

/FINE: $\neg $INTR per provare $\neg \exists x\alpha$\\

\begin{tabular}{p{5.5cm}p{5cm}}
16. $(\forall x\neg\alpha\rightarrow\neg\exists x\alpha)$ & $\rightarrow$INTR,8,15   \\ 
17. $\neg\exists x\alpha\leftrightarrow\forall x\neg\alpha)$   & $\leftrightarrow$INTR,7,16
\end{tabular}
}

 

\end{document}
