sl: basic syntax - formulae
DESCRIPTION
SL: Basic syntax - formulae. Atomic formulae – have no connectives If P is a formula, so is ~P If P and Q are formulae, so are (P&Q), (P Q), (P Q), (P Q) nothing else is a formula. PL: Basic syntax – formulae of PL. Atomic formulae of PL are formulae - PowerPoint PPT PresentationTRANSCRIPT
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SL: Basic syntax - formulae
• Atomic formulae – have no connectives
• If P is a formula, so is ~P
• If P and Q are formulae, so are
(P&Q), (PQ), (PQ), (PQ)
• nothing else is a formula
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PL: Basic syntax – formulae of PL
• Atomic formulae of PL are formulae
• If P is a formula, so is ~P
• If P and Q are formulae, so are
(P&Q), (PQ), (PQ), (PQ)
• If P is a formula with at least one occurrence
of x and no x-quantifier, then
xPx and xPx are formulae
• nothing else is a formula
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PL: Basic syntax – definitions of important notions
• Atomic formulae
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PL: Basic syntax – definitions of important notions
• Atomic formulae
• Formulae
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PL: Basic syntax – definitions of important notions
• Atomic formulae
• Formulae
• (Main) Logical operator
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PL: Basic syntax – definitions of important notions
• Atomic formulae
• Formulae
• (Main) Logical operator
• Scope of a quantifier
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PL: Basic syntax – definitions of important notions
• Atomic formulae
• Formulae
• (Main) Logical operator
• Scope of a quantifier
• Bound/Free variable
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PL: Basic syntax – definitions of important notions
• Atomic formulae
• Formulae
• (Main) Logical operator
• Scope of a quantifier
• Bound/Free variable
• Sentence
![Page 9: SL: Basic syntax - formulae](https://reader035.vdocuments.mx/reader035/viewer/2022062323/56815a94550346895dc80dc6/html5/thumbnails/9.jpg)
PL: Basic syntax – definitions of important notions
• Atomic formulae
• Formulae
• (Main) Logical operator
• Scope of a quantifier
• Bound/Free variable
• Sentence
• Substitution instance
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Aristotle
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Aristotle’s Syllogistic
A Universal affirmative: All As are Bx(Ax Bx)
E Universal negative: No As are Bx(Ax ~Bx) or ~x(Ax & Bx)
I Particular affirmative: Some As are Bx(Ax & Bx)
O Particular negative: Some As are not Bx(Ax & ~ Bx) or ~x(Ax Bx)
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Logical Square
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Logical Squarex(Sx Px)
x(Sx & ~ Px)
or ~x(Sx Px)
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Logical Squarex(Sx Px)
x(Sx & ~ Px)
or ~x(Sx Px)
x(Sx & Px)
x(Sx ~Px) or ~x(Sx & Bx)
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All Syllogisms
First Figure: L, M, S.
1. 1. If every M is L and every S is M, then every S is L (Barbara).2. 2. If no M is L and every S is M, then no S is L (Celarent).1. 3. If every M is L and some S is M, then some S is L (Darii).1. 4. If no M is L and some S is M, then some S is not L (Ferio).
Second Figure: M, L, S.
2. 1. If no L is M and every S is 11.I, then no S is L (Cesare).2. 2. If every L is M and no S is M, then no S is L (Camestres).2. 3. If no L is M and some S is M, then some S is not L (Festino).2. 4. If every L is M and some S is not M, then some S is not L (Baroco).
Third Figure: L, S, M.
3. 1. If every M is L and every M is S, then some S is L (Darapti).3. 2. If no M is L and every M is S, then some S is not L (Felapton).3. 3. If some M is L and every M is S, then some S is L (Disamis).3. 4. If every M is L and some M is S, then some S is L (Datisi).3. 5. If some M is not L and every M is S, then some S is not L (Bocardo).3. 6. If no M is L and some M is S, then some S is not L (Ferison).
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1. 1. If every M is L and every S is M, then every S is L (Barbara).
All Ms are L
All Ss are M
So all Ss are L
Barbara
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1. 1. If every M is L and every S is M, then every S is L (Barbara).
All Ms are L A
All Ss are M A bArbArA
So all Ss are L A
Barbara
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Chrysippus
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Greece
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7.6E2
a. ( y)(By Ly)∀ ⊃
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7.6E2
a. ( y)(By Ly)∀ ⊃b. ( x)(Rx Sx)∀ ⊃
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7.6E2
a. ( y)(By Ly)∀ ⊃b. ( x)(Rx Sx)∀ ⊃c. ( z)(Rz Lz)∀ ⊃ ∼
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7.6E2
a. ( y)(By Ly)∀ ⊃b. ( x)(Rx Sx)∀ ⊃c. ( z)(Rz Lz)∀ ⊃ ∼d. ( w)(Rw & Cw)∃
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7.6E2
a. ( y)(By Ly)∀ ⊃b. ( x)(Rx Sx)∀ ⊃c. ( z)(Rz Lz)∀ ⊃ ∼d. ( w)(Rw & Cw)∃e. ( x)Bx & ( x)Rx∃ ∃
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7.6E2
a. ( y)(By Ly)∀ ⊃b. ( x)(Rx Sx)∀ ⊃c. ( z)(Rz Lz)∀ ⊃ ∼d. ( w)(Rw & Cw)∃e. ( x)Bx & ( x)Rx∃ ∃f. ( y)Oy & ( y) Oy∃ ∃ ∼
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7.6E2
a. ( y)(By Ly)∀ ⊃b. ( x)(Rx Sx)∀ ⊃c. ( z)(Rz Lz)∀ ⊃ ∼d. ( w)(Rw & Cw)∃e. ( x)Bx & ( x)Rx∃ ∃f. ( y)Oy & ( y) Oy∃ ∃ ∼g. [( z)Bz & ( z)Rz] & ( z)(Bz & Rz)∃ ∃ ∼ ∃
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7.6E2
a. ( y)(By Ly)∀ ⊃b. ( x)(Rx Sx)∀ ⊃c. ( z)(Rz Lz)∀ ⊃ ∼d. ( w)(Rw & Cw)∃e. ( x)Bx & ( x)Rx∃ ∃f. ( y)Oy & ( y) Oy∃ ∃ ∼g. [( z)Bz & ( z)Rz] & ( z)(Bz & Rz)∃ ∃ ∼ ∃h. ( w)(Rw Sw) & ( x)(Gx Ox)∀ ⊃ ∀ ⊃
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7.6E2
a. ( y)(By Ly)∀ ⊃b. ( x)(Rx Sx)∀ ⊃c. ( z)(Rz Lz)∀ ⊃ ∼d. ( w)(Rw & Cw)∃e. ( x)Bx & ( x)Rx∃ ∃f. ( y)Oy & ( y) Oy∃ ∃ ∼g. [( z)Bz & ( z)Rz] & ( z)(Bz & Rz)∃ ∃ ∼ ∃h. ( w)(Rw Sw) & ( x)(Gx Ox)∀ ⊃ ∀ ⊃i. ( y)By & [( y)Sy & ( y)Ly]∃ ∃ ∃
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7.6E2
a. ( y)(By Ly)∀ ⊃b. ( x)(Rx Sx)∀ ⊃c. ( z)(Rz Lz)∀ ⊃ ∼d. ( w)(Rw & Cw)∃e. ( x)Bx & ( x)Rx∃ ∃f. ( y)Oy & ( y) Oy∃ ∃ ∼g. [( z)Bz & ( z)Rz] & ( z)(Bz & Rz)∃ ∃ ∼ ∃h. ( w)(Rw Sw) & ( x)(Gx Ox)∀ ⊃ ∀ ⊃i. ( y)By & [( y)Sy & ( y)Ly]∃ ∃ ∃j. ( z)(Rz & Lz)∼ ∃
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7.6E2
a. ( y)(By Ly)∀ ⊃b. ( x)(Rx Sx)∀ ⊃c. ( z)(Rz Lz)∀ ⊃ ∼d. ( w)(Rw & Cw)∃e. ( x)Bx & ( x)Rx∃ ∃f. ( y)Oy & ( y) Oy∃ ∃ ∼g. [( z)Bz & ( z)Rz] & ( z)(Bz & Rz)∃ ∃ ∼ ∃h. ( w)(Rw Sw) & ( x)(Gx Ox)∀ ⊃ ∀ ⊃i. ( y)By & [( y)Sy & ( y)Ly]∃ ∃ ∃j. ( z)(Rz & Lz)∼ ∃k. ( w)(Cw Rw) & ( w)(Rw Cw)∀ ⊃ ∼ ∀ ⊃
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7.6E2
a. ( y)(By Ly)∀ ⊃b. ( x)(Rx Sx)∀ ⊃c. ( z)(Rz Lz)∀ ⊃ ∼d. ( w)(Rw & Cw)∃e. ( x)Bx & ( x)Rx∃ ∃f. ( y)Oy & ( y) Oy∃ ∃ ∼g. [( z)Bz & ( z)Rz] & ( z)(Bz & Rz)∃ ∃ ∼ ∃h. ( w)(Rw Sw) & ( x)(Gx Ox)∀ ⊃ ∀ ⊃i. ( y)By & [( y)Sy & ( y)Ly]∃ ∃ ∃j. ( z)(Rz & Lz)∼ ∃k. ( w)(Cw Rw) & ( w)(Rw Cw)∀ ⊃ ∼ ∀ ⊃l. ( z)Rx & [( y)Cy & ( y) Cy]∀ ∃ ∃ ∼
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7.6E2
a. ( y)(By Ly)∀ ⊃b. ( x)(Rx Sx)∀ ⊃c. ( z)(Rz Lz)∀ ⊃ ∼d. ( w)(Rw & Cw)∃e. ( x)Bx & ( x)Rx∃ ∃f. ( y)Oy & ( y) Oy∃ ∃ ∼g. [( z)Bz & ( z)Rz] & ( z)(Bz & Rz)∃ ∃ ∼ ∃h. ( w)(Rw Sw) & ( x)(Gx Ox)∀ ⊃ ∀ ⊃i. ( y)By & [( y)Sy & ( y)Ly]∃ ∃ ∃j. ( z)(Rz & Lz)∼ ∃k. ( w)(Cw Rw) & ( w)(Rw Cw)∀ ⊃ ∼ ∀ ⊃l. ( z)Rx & [( y)Cy & ( y) Cy]∀ ∃ ∃ ∼m. ( y)Ry [( y)By ( y)Gy]∀ ∨ ∀ ∨ ∀
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7.6E2
a. ( y)(By Ly)∀ ⊃b. ( x)(Rx Sx)∀ ⊃c. ( z)(Rz Lz)∀ ⊃ ∼d. ( w)(Rw & Cw)∃e. ( x)Bx & ( x)Rx∃ ∃f. ( y)Oy & ( y) Oy∃ ∃ ∼g. [( z)Bz & ( z)Rz] & ( z)(Bz & Rz)∃ ∃ ∼ ∃h. ( w)(Rw Sw) & ( x)(Gx Ox)∀ ⊃ ∀ ⊃i. ( y)By & [( y)Sy & ( y)Ly]∃ ∃ ∃j. ( z)(Rz & Lz)∼ ∃k. ( w)(Cw Rw) & ( w)(Rw Cw)∀ ⊃ ∼ ∀ ⊃l. ( z)Rx & [( y)Cy & ( y) Cy]∀ ∃ ∃ ∼m. ( y)Ry [( y)By ( y)Gy]∀ ∨ ∀ ∨ ∀n. ( x)Lx & ( x)(Lx Bx)∼ ∀ ∀ ⊃
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7.6E2
a. ( y)(By Ly)∀ ⊃b. ( x)(Rx Sx)∀ ⊃c. ( z)(Rz Lz)∀ ⊃ ∼d. ( w)(Rw & Cw)∃e. ( x)Bx & ( x)Rx∃ ∃f. ( y)Oy & ( y) Oy∃ ∃ ∼g. [( z)Bz & ( z)Rz] & ( z)(Bz & Rz)∃ ∃ ∼ ∃h. ( w)(Rw Sw) & ( x)(Gx Ox)∀ ⊃ ∀ ⊃i. ( y)By & [( y)Sy & ( y)Ly]∃ ∃ ∃j. ( z)(Rz & Lz)∼ ∃k. ( w)(Cw Rw) & ( w)(Rw Cw)∀ ⊃ ∼ ∀ ⊃l. ( z)Rx & [( y)Cy & ( y) Cy]∀ ∃ ∃ ∼m. ( y)Ry [( y)By ( y)Gy]∀ ∨ ∀ ∨ ∀n. ( x)Lx & ( x)(Lx Bx)∼ ∀ ∀ ⊃o. ( w)(Rw & Sw) & ( w)(Rw & Sw)∃ ∃ ∼
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7.6E2
a. ( y)(By Ly)∀ ⊃b. ( x)(Rx Sx)∀ ⊃c. ( z)(Rz Lz)∀ ⊃ ∼d. ( w)(Rw & Cw)∃e. ( x)Bx & ( x)Rx∃ ∃f. ( y)Oy & ( y) Oy∃ ∃ ∼g. [( z)Bz & ( z)Rz] & ( z)(Bz & Rz)∃ ∃ ∼ ∃h. ( w)(Rw Sw) & ( x)(Gx Ox)∀ ⊃ ∀ ⊃i. ( y)By & [( y)Sy & ( y)Ly]∃ ∃ ∃j. ( z)(Rz & Lz)∼ ∃k. ( w)(Cw Rw) & ( w)(Rw Cw)∀ ⊃ ∼ ∀ ⊃l. ( z)Rx & [( y)Cy & ( y) Cy]∀ ∃ ∃ ∼m. ( y)Ry [( y)By ( y)Gy]∀ ∨ ∀ ∨ ∀n. ( x)Lx & ( x)(Lx Bx)∼ ∀ ∀ ⊃o. ( w)(Rw & Sw) & ( w)(Rw & Sw)∃ ∃ ∼p. [( w)Sw & ( w)Ow] & ( w)(Sw & Ow)∃ ∃ ∼ ∃
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7.6E2
a. ( y)(By Ly)∀ ⊃b. ( x)(Rx Sx)∀ ⊃c. ( z)(Rz Lz)∀ ⊃ ∼d. ( w)(Rw & Cw)∃e. ( x)Bx & ( x)Rx∃ ∃f. ( y)Oy & ( y) Oy∃ ∃ ∼g. [( z)Bz & ( z)Rz] & ( z)(Bz & Rz)∃ ∃ ∼ ∃h. ( w)(Rw Sw) & ( x)(Gx Ox)∀ ⊃ ∀ ⊃i. ( y)By & [( y)Sy & ( y)Ly]∃ ∃ ∃j. ( z)(Rz & Lz)∼ ∃k. ( w)(Cw Rw) & ( w)(Rw Cw)∀ ⊃ ∼ ∀ ⊃l. ( z)Rx & [( y)Cy & ( y) Cy]∀ ∃ ∃ ∼m. ( y)Ry [( y)By ( y)Gy]∀ ∨ ∀ ∨ ∀n. ( x)Lx & ( x)(Lx Bx)∼ ∀ ∀ ⊃o. ( w)(Rw & Sw) & ( w)(Rw & Sw)∃ ∃ ∼p. [( w)Sw & ( w)Ow] & ( w)(Sw & Ow)∃ ∃ ∼ ∃q. ( x)Ox & ( y)(Ly Oy)∃ ∀ ⊃ ∼
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1 Everyone that Michael likes likes either Henry or Sue
2 Michael likes everyone that both Sue and Rita like
3 Michael likes everyone that either Sue or Rita like
4 Rita doesn’t like Michael but she likes everyone that Michael likes
5 Grizzly bears are dangerous but black bears are not
6 Grizzly bears and polar bears are dangerous but black bears are not
7 Every self-respecting polar bear is a good swimmer
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1 Everyone that Michael likes likes either Henry or Sue
x(Lmx LxsLxh)
2 Michael likes everyone that both Sue and Rita like
3 Michael likes everyone that either Sue or Rita like
4 Rita doesn’t like Michael but she likes everyone that Michael likes
5 Grizzly bears are dangerous but black bears are not
6 Grizzly bears and polar bears are dangerous but black bears are not
7 Every self-respecting polar bear is a good swimmer
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1 Everyone that Michael likes likes either Henry or Sue
x(Lmx LxsLxh)
2 Michael likes everyone that both Sue and Rita like
x(Lsx&Lrx Lmx)
3 Michael likes everyone that either Sue or Rita like
4 Rita doesn’t like Michael but she likes everyone that Michael likes
5 Grizzly bears are dangerous but black bears are not
6 Grizzly bears and polar bears are dangerous but black bears are not
7 Every self-respecting polar bear is a good swimmer
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1 Everyone that Michael likes likes either Henry or Sue
x(Lmx LxsLxh)
2 Michael likes everyone that both Sue and Rita like
x(Lsx&Lrx Lmx)
3 Michael likes everyone that either Sue or Rita like
x(LsxLrx Lmx)
4 Rita doesn’t like Michael but she likes everyone that Michael likes
5 Grizzly bears are dangerous but black bears are not
6 Grizzly bears and polar bears are dangerous but black bears are not
7 Every self-respecting polar bear is a good swimmer
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1 Everyone that Michael likes likes either Henry or Sue
x(Lmx LxsLxh)
2 Michael likes everyone that both Sue and Rita like
x(Lsx&Lrx Lmx)
3 Michael likes everyone that either Sue or Rita like
x(LsxLrx Lmx)
4 Rita doesn’t like Michael but she likes everyone that Michael likes
~Lrm & x(Lmx Lrx)
5 Grizzly bears are dangerous but black bears are not
6 Grizzly bears and polar bears are dangerous but black bears are not
7 Every self-respecting polar bear is a good swimmer
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1 Everyone that Michael likes likes either Henry or Sue
x(Lmx LxsLxh)
2 Michael likes everyone that both Sue and Rita like
x(Lsx&Lrx Lmx)
3 Michael likes everyone that either Sue or Rita like
x(LsxLrx Lmx)
4 Rita doesn’t like Michael but she likes everyone that Michael likes
~Lrm & x(Lmx Lrx)
5 Grizzly bears are dangerous but black bears are not
x(Gx Dx) & x(Bx ~Dx)
6 Grizzly bears and polar bears are dangerous but black bears are not
7 Every self-respecting polar bear is a good swimmer
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1 Everyone that Michael likes likes either Henry or Sue
x(Lmx LxsLxh)
2 Michael likes everyone that both Sue and Rita like
x(Lsx&Lrx Lmx)
3 Michael likes everyone that either Sue or Rita like
x(LsxLrx Lmx)
4 Rita doesn’t like Michael but she likes everyone that Michael likes
~Lrm & x(Lmx Lrx)
5 Grizzly bears are dangerous but black bears are not
x(Gx Dx) & x(Bx ~Dx)
2 Grizzly bears and polar bears are dangerous but black bears are not
x(Gx Px Dx) & x(Bx ~Dx)
7 Every self-respecting polar bear is a good swimmer
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1 Everyone that Michael likes likes either Henry or Sue
x(Lmx LxsLxh)
2 Michael likes everyone that both Sue and Rita like
x(Lsx&Lrx Lmx)
3 Michael likes everyone that either Sue or Rita like
x(LsxLrx Lmx)
4 Rita doesn’t like Michael but she likes everyone that Michael likes
~Lrm & x(Lmx Lrx)
5 Grizzly bears are dangerous but black bears are not
x(Gx Dx) & x(Bx ~Dx)
2 Grizzly bears and polar bears are dangerous but black bears are not
x(Gx Px Dx) & x(Bx ~Dx)
3 Every self-respecting polar bear is a good swimmer
x(Px & Rxx Sx)
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UD = people
9 Anyone who likes Sue likes Rita
x(Lxs Lxr)
10 Everyone who likes Sue likes Rita
11 If anyone likes Sue, Michael does
12 If everyone likes Sue, Michael does
13 If anyone likes Sue, he or she likes Rita
14 Michael doesn’t like everyone
15 Michael doesn’t like anyone
16 If someone likes Sue, then s/he likes Rita
17 If someone likes Sue, then someone likes Rita
![Page 46: SL: Basic syntax - formulae](https://reader035.vdocuments.mx/reader035/viewer/2022062323/56815a94550346895dc80dc6/html5/thumbnails/46.jpg)
UD = people
9 Anyone who likes Sue likes Rita
x(Lxs Lxr)
10 Everyone who likes Sue likes Rita
the same as 9
11 If anyone likes Sue, Michael does
12 If everyone likes Sue, Michael does
13 If anyone likes Sue, he or she likes Rita
14 Michael doesn’t like everyone
15 Michael doesn’t like anyone
16 If someone likes Sue, then s/he likes Rita
17 If someone likes Sue, then someone likes Rita
![Page 47: SL: Basic syntax - formulae](https://reader035.vdocuments.mx/reader035/viewer/2022062323/56815a94550346895dc80dc6/html5/thumbnails/47.jpg)
UD = people
9 Anyone who likes Sue likes Rita
x(Lxs Lxr)
10 Everyone who likes Sue likes Rita
the same as 9
11 If anyone likes Sue, Michael does
xLxs Lms
12 If everyone likes Sue, Michael does
13 If anyone likes Sue, he or she likes Rita
14 Michael doesn’t like everyone
15 Michael doesn’t like anyone
16 If someone likes Sue, then s/he likes Rita
17 If someone likes Sue, then someone likes Rita
![Page 48: SL: Basic syntax - formulae](https://reader035.vdocuments.mx/reader035/viewer/2022062323/56815a94550346895dc80dc6/html5/thumbnails/48.jpg)
UD = people
9 Anyone who likes Sue likes Rita
x(Lxs Lxr)
10 Everyone who likes Sue likes Rita
the same as 9
11 If anyone likes Sue, Michael does
xLxs Lms
12 If everyone likes Sue, Michael does
xLxs Lms
13 If anyone likes Sue, he or she likes Rita
14 Michael doesn’t like everyone
15 Michael doesn’t like anyone
16 If someone likes Sue, then s/he likes Rita
17 If someone likes Sue, then someone likes Rita
![Page 49: SL: Basic syntax - formulae](https://reader035.vdocuments.mx/reader035/viewer/2022062323/56815a94550346895dc80dc6/html5/thumbnails/49.jpg)
UD = people
9 Anyone who likes Sue likes Rita
x(Lxs Lxr)
10 Everyone who likes Sue likes Rita
the same as 9
11 If anyone likes Sue, Michael does
xLxs Lms
12 If everyone likes Sue, Michael does
xLxs Lms
13 If anyone likes Sue, he or she likes Rita
x(Lxs Lxr)
14 Michael doesn’t like everyone
15 Michael doesn’t like anyone
16 If someone likes Sue, then s/he likes Rita
17 If someone likes Sue, then someone likes Rita
![Page 50: SL: Basic syntax - formulae](https://reader035.vdocuments.mx/reader035/viewer/2022062323/56815a94550346895dc80dc6/html5/thumbnails/50.jpg)
UD = people
9 Anyone who likes Sue likes Rita
x(Lxs Lxr)
10 Everyone who likes Sue likes Rita
the same as 9
11 If anyone likes Sue, Michael does
xLxs Lms
12 If everyone likes Sue, Michael does
xLxs Lms
13 If anyone likes Sue, he or she likes Rita
x(Lxs Lxr)
14 Michael doesn’t like everyone ~xLmx
15 Michael doesn’t like anyone
16 If someone likes Sue, then s/he likes Rita
17 If someone likes Sue, then someone likes Rita
![Page 51: SL: Basic syntax - formulae](https://reader035.vdocuments.mx/reader035/viewer/2022062323/56815a94550346895dc80dc6/html5/thumbnails/51.jpg)
UD = people
9 Anyone who likes Sue likes Rita
x(Lxs Lxr)
10 Everyone who likes Sue likes Rita
the same as 9
11 If anyone likes Sue, Michael does
xLxs Lms
12 If everyone likes Sue, Michael does
xLxs Lms
13 If anyone likes Sue, he or she likes Rita
x(Lxs Lxr)
14 Michael doesn’t like everyone ~xLmx
15 Michael doesn’t like anyone ~xLmx
16 If someone likes Sue, then s/he likes Rita
17 If someone likes Sue, then someone likes Rita
![Page 52: SL: Basic syntax - formulae](https://reader035.vdocuments.mx/reader035/viewer/2022062323/56815a94550346895dc80dc6/html5/thumbnails/52.jpg)
UD = people
9 Anyone who likes Sue likes Rita
x(Lxs Lxr)
10 Everyone who likes Sue likes Rita
the same as 9
11 If anyone likes Sue, Michael does
xLxs Lms
12 If everyone likes Sue, Michael does
xLxs Lms
13 If anyone likes Sue, he or she likes Rita
x(Lxs Lxr)
14 Michael doesn’t like everyone ~xLmx
15 Michael doesn’t like anyone ~xLmx
16 If someone likes Sue, then s/he likes Rita x(Lxs Lxr)
17 If someone likes Sue, then someone likes Rita
![Page 53: SL: Basic syntax - formulae](https://reader035.vdocuments.mx/reader035/viewer/2022062323/56815a94550346895dc80dc6/html5/thumbnails/53.jpg)
UD = people
9 Anyone who likes Sue likes Rita
x(Lxs Lxr)
10 Everyone who likes Sue likes Rita
the same as 9
11 If anyone likes Sue, Michael does
xLxs Lms
12 If everyone likes Sue, Michael does
xLxs Lms
13 If anyone likes Sue, he or she likes Rita
x(Lxs Lxr)
14 Michael doesn’t like everyone ~xLmx
15 Michael doesn’t like anyone ~xLmx
16 If someone likes Sue, then s/he likes Rita x(Lxs Lxr)
17 If someone likes Sue, then someone likes Rita xLxs xLxr