Lara's Term Paper - Revision history

Lara: /* The Restricted Quantifier */

2016-06-29T09:14:09Z

The Restricted Quantifier

← Older revision		Revision as of 09:14, 29 June 2016
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	In contrast to the logical quantifiers …		In contrast to the logical quantifiers …
	* a restricted quantifier always has a '''reference quantity''' ~~and therefore points out~~ '''~~a proportion of a set~~''' and ~~not~~ the ~~proportion of everything there is~~.		* a restricted quantifier always has a '''reference quantity'''. The cardinal quantifiers can all be defined using ''exists'' and ''for all'' and only the proportional quantifiers actually require us to go beyond classical predicate logic.
	* Since common natural language quantifiers like '''''most''''', '''''few''''', '''''many''''' or '''''several''''' cannot be analyzed like the logical quantifiers in the standard form of the predicate calculus, they are expressed in the '''notation of restricted quantification'''.		* Since common natural language quantifiers like '''''most''''', '''''few''''', '''''many''''' or '''''several''''' cannot be analyzed like the logical quantifiers in the standard form of the predicate calculus, they are expressed in the '''notation of restricted quantification'''.
	* Sentences which contain restricted quantifiers are '''written with square brackets'''. This means that the noun phrase including the quantifier is always put into square brackets. Logical quantifiers can also be written in this kind of formula with square brackets.		* Sentences which contain restricted quantifiers are '''written with square brackets'''. This means that the noun phrase including the quantifier is always put into square brackets. Logical quantifiers can also be written in this kind of formula with square brackets.

Lara: /* Different Types of Quantifiers */

2016-06-29T09:10:02Z

Different Types of Quantifiers

← Older revision		Revision as of 09:10, 29 June 2016
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	* Restricted quantifiers		* Restricted quantifiers

	In predicate logic the two fundamental quantifiers are the '''logical quantifiers''' ~~(also called '''generalized quantifiers''')~~, which are the universal quantifier and the existential quantifier.		In predicate logic the two fundamental quantifiers are the '''logical quantifiers''', which are the universal quantifier and the existential quantifier.


	=== Logical Quantifiers ~~(Generalized Quantifiers)~~ ===		=== Logical Quantifiers ===

	[[File:Logical-quantifiers.png\|750px\|Logical Quantifiers]]		[[File:Logical-quantifiers.png\|750px\|Logical Quantifiers]]
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	<span style="color:#0000FF">[No x: DOG (x)] BARK (x)</span>		<span style="color:#0000FF">[No x: DOG (x)] BARK (x)</span>



	== Venn Diagrams ==		== Venn Diagrams ==

Lara: /* Definition */

2016-06-28T15:51:20Z

Definition

← Older revision		Revision as of 15:51, 28 June 2016
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	In logic, quantifiers are operators binding variables, which means that a quantifier connects parts of a sentence that classify a domain of discourse.		In logic, quantifiers are operators binding variables, which means that a quantifier connects parts of a sentence that classify a domain of discourse.

	Individual variables are ~~written as~~ “x” and ~~can refer to any individual~~.		Individual variables are symbols like “x”, "y" etc. and stand for the same entity each time they occur in a formula.


	== Different Types of Quantifiers ==		== Different Types of Quantifiers ==

Lara at 21:46, 27 June 2016

2016-06-27T21:46:11Z

← Older revision		Revision as of 21:46, 27 June 2016
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	# PROUD (s, (GRATUATE (s))		# PROUD (s, (GRATUATE (s))
	</div></div>		</div></div>



	== Exercise 3: Different Types of Quantifiers (1) ==		== Exercise 3: Different Types of Quantifiers (1) ==
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	''Check your solutions:''		''Check your solutions:''
	<div class="mw-collapsible-content">		<div class="mw-collapsible-content">

	# '''Julie reads many books.'''		# '''Julie reads many books.'''
	#* Restricted quantifier: [Many x: BOOK (x)] READ (julie, x)		#* Restricted quantifier: [Many x: BOOK (x)] READ (julie, x)
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	# '''Marcia liked most plays written by Osborne.'''		# '''Marcia liked most plays written by Osborne.'''
	#* Restricted quantifier: [Most x: PLAY (x) & WRITE (osborne, x)] LIKE (marcia, x)		#* Restricted quantifier: [Most x: PLAY (x) & WRITE (osborne, x)] LIKE (marcia, x)
			</div></div>


	~~</div></div>~~

	== Exercise 5: Logical Quantifiers ==		== Exercise 5: Logical Quantifiers ==
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	#: ∀x ∀y (ADMIRE (x, y) → ~ DESPITE (x, y))		#: ∀x ∀y (ADMIRE (x, y) → ~ DESPITE (x, y))
	</div></div>		</div></div>



	== Exercise 6: Restricted Quantifiers ==		== Exercise 6: Restricted Quantifiers ==
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	#: [Most x: TRAVELLER (x) & (ENTER (x, a) V LEAVE (x, a))] VISIT (x, s)<br/>		#: [Most x: TRAVELLER (x) & (ENTER (x, a) V LEAVE (x, a))] VISIT (x, s)<br/>
	:: ''or:'' [Most x: TRAVELLER (x) & (ENTER (x, a) or LEAVE (x, a))] VISIT (x, s)		:: ''or:'' [Most x: TRAVELLER (x) & (ENTER (x, a) or LEAVE (x, a))] VISIT (x, s)
			</div></div>


	~~</div></div>~~

	== Exercise 7: First-Order Logic "Mix" ==		== Exercise 7: First-Order Logic "Mix" ==
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	#: ∀x (STUDENT (x) → FLUNK (x) → ~ ∃x (STUDENT (x) & GLAD (x))		#: ∀x (STUDENT (x) → FLUNK (x) → ~ ∃x (STUDENT (x) & GLAD (x))
	</div></div>		</div></div>



	== Exercise 8: Paraphrasing into Plain English ==		== Exercise 8: Paraphrasing into Plain English ==
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	# One man loves every woman.		# One man loves every woman.
	</div></div>		</div></div>



	== Exercise 9: Scopal Ambiguity ==		== Exercise 9: Scopal Ambiguity ==
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	#: ∃x (PERSON (x) → ∀y (PERSON (y) & LOVE (y, x))		#: ∃x (PERSON (x) → ∀y (PERSON (y) & LOVE (y, x))
	</div></div>		</div></div>



	= Participants =		= Participants =

Lara: /* Exercise 9: Scopal Ambiguity */

2016-06-27T21:28:50Z

Exercise 9: Scopal Ambiguity

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 == Exercise 9: Scopal Ambiguity ==
-''Exercise...''<br/>
+''1. In which way is the following sentence ambiguous?''<br/>
 = Participants =

Lara: /* Exercise 8: Paraphrasing into Plain English */

2016-06-27T21:12:16Z

Exercise 8: Paraphrasing into Plain English

← Older revision		Revision as of 21:12, 27 June 2016
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			'''''Example:'''''<br/>
			∃x (CHILD (x) & SLEEP (x))<br/>
			A child sleeps. / A child slept. ''(also in the following answers several writings are correct)''


			# ∀x (STUDENT (x) → KNOW (x, mary))
			# ∃x (KILL (robert, x))
			# ~ ∃x (KNOW (x, bill))
			# ∀x ~ (FORGET (x, lisa))
			# ADMIRE (burt, frank) & DESPITE (frank, burt)
			# [Most x: DOG (x)] DOMESTIC (x)
			# ∀x ~ (NEWSPAPER (x) & READ (john, x))
			# ∀x ((SKODA (x) & RED (X)) → WORK (x))
			# [Four x: APPLE (x)] EAT (marcia, x) & EAT (clive, x)
			# ∀y (∃x (MAN (x) & (WOMAN (y) → LOVE (x, y))))


			<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
			''Check your solutions:''
			<div class="mw-collapsible-content">
			# Every student knows Mary. (All students know Mary.)
			# Robert kills somebody.
			# Nobody knows Bill.
			# Nobody forgets Lisa.
			# Burt admires Frank but Frank despite Burt.
			# Most dogs are domestic.
			# John reads no newspaper. (John doesn’t read any newspaper.)
			# All red sodas work.
			# Marcia and Clive eat four apples each.
			# One man loves every woman.
			</div></div>

	== Exercise 9: Scopal Ambiguity ==		== Exercise 9: Scopal Ambiguity ==

Lara: /* Exercise 2: Logical Metalanguage "Warm-Up" */

2016-06-27T20:32:53Z

Exercise 2: Logical Metalanguage "Warm-Up"

← Older revision		Revision as of 20:32, 27 June 2016
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	''Check your solutions:''		''Check your solutions:''
	<div class="mw-collapsible-content">		<div class="mw-collapsible-content">

	# SMOKE (bill) <span style="color:#008080"> ''or:'' SMOKE (b) </span> <span style="color:#6A5ACD"> ''or:'' S (b) </span> ''(also in the following answers these writings are all correct)''		# SMOKE (bill) <span style="color:#008080"> ''or:'' SMOKE (b) </span> <span style="color:#6A5ACD"> ''or:'' S (b) </span> ''(also in the following answers these writings are all correct)''
	# CRAZIER (p, r)		# CRAZIER (p, r)
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	# PROUD (s, the new car)		# PROUD (s, the new car)
	# PROUD (s, (GRATUATE (s))		# PROUD (s, (GRATUATE (s))

	</div></div>		</div></div>

Lara: /* Exercise 7: First-Order Logic Mix */

2016-06-27T20:30:15Z

Exercise 7: First-Order Logic Mix

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	</div></div>		</div></div>

	== Exercise 7: First-Order Logic Mix ==		== Exercise 7: First-Order Logic "Mix" ==

	''Translate the sentences below into first-order logic.''<br/>		''Translate the sentences below into first-order logic.''<br/>

Lara: /* Exercise 7: First-Order Logic Mix */

2016-06-27T20:28:48Z

Exercise 7: First-Order Logic Mix

← Older revision		Revision as of 20:28, 27 June 2016
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	''Check your solutions:''		''Check your solutions:''
	<div class="mw-collapsible-content">		<div class="mw-collapsible-content">
	# Kate was a liberal but Andrew was a socialist.		# '''Kate was a liberal but Andrew was a socialist.'''
	#: LIBERAL (k) & SOCIAL (a) <span style="color:#008080"> ''or:'' LIBERAL (kate) & SOCIAL (andrew)) </span> <span style="color:#6A5ACD"> ''or:'' L (k) & S (a)) </span> ''(also in the following answers these writings are all correct)''		#: LIBERAL (k) & SOCIAL (a) <span style="color:#008080"> ''or:'' LIBERAL (kate) & SOCIAL (andrew)) </span> <span style="color:#6A5ACD"> ''or:'' L (k) & S (a)) </span> ''(also in the following answers these writings are all correct)''
	# You can if you try.		# '''You can if you try.'''
	#: TRY (x) → CAN (x)		#: TRY (x) → CAN (x)
	# Every baby cried.		# '''Every baby cried.'''
	#: ∀x (BABY (x) → CRY (x))		#: ∀x (BABY (x) → CRY (x))
	# Someone is conservative.		# '''Someone is conservative.'''
	#: ∃x (CONSERVATIVE (x))		#: ∃x (CONSERVATIVE (x))
	# John likes many animals.		# '''John likes many animals.'''
	#: [Many x: ANIMAL] LIKE (john, x)		#: [Many x: ANIMAL] LIKE (john, x)
	# No honest politicians are businessmen.		# '''No honest politicians are businessmen.'''
	#: ~∃x ((POLITICIAN (x) & HONEST (x)) & BUSINESSMAN (x))		#: ~∃x ((POLITICIAN (x) & HONEST (x)) & BUSINESSMAN (x))
	# If Thomas snores, then Maria hates Thomas		# '''If Thomas snores, then Maria hates Thomas'''
	#: SNORE (thomas) → HATE (maria, thomas)		#: SNORE (thomas) → HATE (maria, thomas)
	# Thomas doesn’t snore.		# '''Thomas doesn’t snore.'''
	#: ~ (SNORE (thomas))		#: ~ (SNORE (thomas))
	# All dishes which Anna cooks are delicious.		# '''All dishes which Anna cooks are delicious.'''
	#: ∀x (DISH (x) & COOK (anna, x)) → DELICIOUS (x))		#: ∀x (DISH (x) & COOK (anna, x)) → DELICIOUS (x))
	# Four politicians are honest.		# '''Four politicians are honest.'''
	#: [Five x: POLITICIAN] HONEST (x)		#: [Five x: POLITICIAN] HONEST (x)
	# No guy likes Lisa.		# '''No guy likes Lisa.'''
	#: ~ ∃x (GUY (x) & LIKE (x, lisa)) <span style="color:#008080"> ''or:'' ∀x ~ (GUY (x) → LIKE (x, lisa)) </span>		#: ~ ∃x (GUY (x) & LIKE (x, lisa)) <span style="color:#008080"> ''or:'' ∀x ~ (GUY (x) → LIKE (x, lisa)) </span>
	# All students who know John know Mary.		# '''All students who know John know Mary.'''
	#: ∀x (STUDENT (x) & KNOW (x, john)) → KNOW (x, mary))		#: ∀x (STUDENT (x) & KNOW (x, john)) → KNOW (x, mary))
	# Several students who drink tequila dance.		# '''Several students who drink tequila dance.'''
	#: [Several x: STUDENT (x) & DRINK (x, tequila)] DANCE (x)		#: [Several x: STUDENT (x) & DRINK (x, tequila)] DANCE (x)
	# Not many books James owned were expensive.		# '''Not many books James owned were expensive.'''
	#: [Not many x: BOOK (x) & OWN (james, x)] EXPENSIVE (x)		#: [Not many x: BOOK (x) & OWN (james, x)] EXPENSIVE (x)
	# Some tourists who visit London are rich.		# '''Some tourists who visit London are rich.'''
	#: ∃x (TOURIST (x) & VISIT (x, london) & RICH (x))		#: ∃x (TOURIST (x) & VISIT (x, london) & RICH (x))
	# Nobody loves everybody.		# '''Nobody loves everybody.'''
	#: ~ (∃x (∀y (LOVE (x, y))))		#: ~ (∃x (∀y (LOVE (x, y))))
	# If everybody loves everybody, then everybody loves him/herself.		# '''If everybody loves everybody, then everybody loves him/herself.'''
	#: ∀x (∀y (LOVE (x, y) → LOVE (x, x)))		#: ∀x (∀y (LOVE (x, y) → LOVE (x, x)))
	# If all students flunk, no student will be glad.		# '''If all students flunk, no student will be glad.'''
	#: ∀x (STUDENT (x) → FLUNK (x) → ~ ∃x (STUDENT (x) & GLAD (x))		#: ∀x (STUDENT (x) → FLUNK (x) → ~ ∃x (STUDENT (x) & GLAD (x))
	</div></div>		</div></div>

Lara: /* Exercise 6: Restricted Quantifiers */

2016-06-27T20:27:10Z

Exercise 6: Restricted Quantifiers

← Older revision		Revision as of 20:27, 27 June 2016
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	''Check your solutions:''		''Check your solutions:''
	<div class="mw-collapsible-content">		<div class="mw-collapsible-content">
			# '''Anna has read most books on psychoanalysis.'''
	# [Most x: BOOK (x) & PSYCHOANALYSIS (x)] READ (a, x)		#: [Most x: BOOK (x) & PSYCHOANALYSIS (x)] READ (a, x)
	# [Few x: KNOW (x, b)] SUPPORT (x, b)		# '''Few who knew him supported Baxter.'''
	# [Some x: STUDENT (x) & HEAR (x, c)] INTERVIEW (h, x)		#: [Few x: KNOW (x, b)] SUPPORT (x, b)
	# [Every x: FINGERPRINT (x) & DUST (m, x)] SHOW (k, x, l)		# '''Some students who heard both concerts were interviewed by Holmes.'''
	# [Three x: APPLE (x)] PEEL (m, x) & QUARTER (m, x)		#: [Some x: STUDENT (x) & HEAR (x, c)] INTERVIEW (h, x)
	# [An x: PEANUT (x)] EAT (r, x)		# '''Kyle showed Lucie every fingerprint he dusted.'''
	# [Every x: SCULPTURE (x) & MAKE (r, x)] SIGN (v, x)		#: [Every x: FINGERPRINT (x) & DUST (m, x)] SHOW (k, x, l)
	# [Four x: APPLE (x)] EAT (m, x) & EAT (c, x)		# '''Mary peeled and quartered three apples.'''
	# [Several x: PAINTING (x) & VALUABLE (x)] RESTORE (j, x) & SELL (j, x)		#: [Three x: APPLE (x)] PEEL (m, x) & QUARTER (m, x)
	# [Most x: BULB (x) & DRY (x)] ~GROW (x)		# '''Ryan ate a peanut.'''
	# [Most x: TRAVELLER (x) & (ENTER (x, a) V LEAVE (x, a))] VISIT (x, s)<br/>		#: [An x: PEANUT (x)] EAT (r, x)
			# '''Victor signs every sculpture he makes.'''
			#: [Every x: SCULPTURE (x) & MAKE (r, x)] SIGN (v, x)
			# '''Mary and Charles ate four apples each.'''
			#: [Four x: APPLE (x)] EAT (m, x) & EAT (c, x)
			# '''Jane restored and sold several valuable paintings.'''
			#: [Several x: PAINTING (x) & VALUABLE (x)] RESTORE (j, x) & SELL (j, x)
			# '''Most bulbs will not grow if they are dry.'''
			#: [Most x: BULB (x) & DRY (x)] ~GROW (x)
			# '''Most travellers entering or leaving Australia visit Sydney.'''
			#: [Most x: TRAVELLER (x) & (ENTER (x, a) V LEAVE (x, a))] VISIT (x, s)<br/>
	:: ''or:'' [Most x: TRAVELLER (x) & (ENTER (x, a) or LEAVE (x, a))] VISIT (x, s)		:: ''or:'' [Most x: TRAVELLER (x) & (ENTER (x, a) or LEAVE (x, a))] VISIT (x, s)