COMMENT ⊗   VALID 00018 PAGES
C REC  PAGE   DESCRIPTION
C00001 00001
C00003 00002		List of all sentences
C00005 00003	Need: 
C00007 00004	1. All purple mushrooms are poisonous.
C00016 00005	2a. Everybody loves somebody. ∀xεPerson ∃yεPerson. Loves(x,y)
C00017 00006	2b. Everybody loves somebody. ∃yεPerson ∀xεPerson. Loves(x,y)
C00019 00007	3. Purple mushrooms have many attributes.
C00020 00008	4. There are 23 purple mushrooms in the world.
C00021 00009	5. Purple-mushroom-23 has been accessed 12 times.
C00022 00010	6. The fact that a purple mushroom is purple is definitional.
C00023 00011	7. Block1 and Block2 together form a blivit.
C00025 00012	8. John gave Mary the book.
C00026 00013	9. Apple-23 embodies the {theory | concept} pf apple. [is an examplar]
C00027 00014	10. The color of all singleton sets is red.
C00028 00015	12. Most elephants are grey.
C00029 00016	-- Or --
C00030 00017	-- OR --
C00031 00018	14. Tower of Hanoi
C00032 ENDMK
C⊗;
	List of all sentences
  1. All purple mushrooms are poisonous.
  2. Everybody loves somebody. {Two meanings}
  3. Purple mushrooms have many attributes.
  4. There are 23 purple mushrooms in the world.
  5. Purple-mushroom-23 has been accessed 12 times.
  6. The fact that a purple mushroom is purple is definitional.
  7. The integers mod 5 form a group under addtion.
  8. John gave Mary the book.
  9. Apple-23 embodies the {theory | concept} pf apple. [is an examplar]
  10. The color of all singleton sets is red.
↓ 11. The alleged theif hated the poor violinist.
  12. Most elephants are grey.
↓ 13. John poured some of the liquid out of the bottle.
? 14. Tower of Hanoi

Need: 
4 forms of Isa:
  (1) Standard - NON-Definitional
	Expresses merely relation of set membership
  (2) Existential  - for ∃xεS 
  (3) Universal    - for ∀xεS 


New Any$SELF$Slots:  DefinitionalSlots and AttributeSlots
This may require splitting many slots into multiple slots.

Conventions:
Any---  is the set of all ---s
Typical--- is a typical element of this set of ---

Every Typical--- unit has a slot InheritableSlots, which points to slots...
	also DefinitionalSlots

If sεAny$SELF$Slot, 

TypicalDog
	TypicalExampleOf:	AnyDog
	InheritableSlots:	(Parts, ..., MyWorth)
	Parts:			(4 legs, ...)
	MyWorth:		45
	MyWorthForInstance:	33

MyWorth
	Isa:			(Any$SELF$Slot)
	StoredInTypAs:		MyWorthForInstance

Now when Dog#53 is initialized,
its MyWorth value with be 33, NOT 45 (45 is worth of TypicalDog, qua unit.)

** Note ***
Slot1
	SuperSlot:	SSlot

means
1. Domain(Slot1)=Domain(SSlot)
2. ∀xεUnit. Slot1(x) ⊂ SSlot(x)

Typical1
	SuperTypEx:	STypical

means
TypicalExampleOf( Typical1 ) ⊂ TypicalExampleOf( STypical )
1. All purple mushrooms are poisonous.

   ***	SOLN#1  ***

AnyMushroom
	SubClass: AnyPurpleMushroom

AnyPurpleThing
	SubClass: AnyPurpleMushroom

AnyPurpleMushroom
	TypicalExample: TypicalPurpleMushroom

TypicalPurpleMushroom
	Poisonous: T
	InheritableSlots: (Poisonous)

   ***	SOLN#2  ***

AnyMushroom
	UniversalExamples: {x ... }

x
	UniversalIsa:	{AnyMushroom}
	Color:		Purple
	Poisonous:	T
	DefinitionalSlots: {UniversalIsa, Color}
	InheritableSlots: (Poisonous)

Isa
	Isa:		{Slot}
	SubSlots:	{ExistentialIsa, UniversalIsa, StandardIsa}

UniversalIsa
	Isa:		{Slot}
	SuperSlots:	{Isa}

   ***	SOLN#3  ***

AnyMushroom
	UniversalExamples: {x ... }

AnyPoisonousThing
	StdExamples: {x ... }

x
	UniversalIsa:	{AnyMushroom}
	StdIsa:		{AnyPosionousThing}
	Color:		Purple
	DefinitionalSlots: {UniversalIsa, Color}
	InheritableSlots: (Poisonous)

TROUBLE - unnatural!!!

   ***	SOLN#4  ***

AnyMushroom
	SubClass: {x ... }

X
	SuperClass: {AnyMushroom}
	TypicalExample: TypicalX
	DefinitionalSlots: {SuperClass, TypicalExample}

TypicalX
	TypicalExampleOf: {X}
	Poisonous:	   T
	Color:		Purple
?	DefinitionalSlots: {?, Color}
	InheritableSlots: (Poisonous)

2a. Everybody loves somebody. ∀xεPerson ∃yεPerson. Loves(x,y)

AnyPerson
	UniversalExamples: {x, y...}

x
	UniversalIsa:	{AnyPerson}
	Loves:		y
	DefinitionalSlots: {UniversalIsa}
	VariesThru:	AnyPerson

y
	ExistentialIsa:	{AnyPerson}
	LovedBy:	x
	DefinitionalSlots: {LovedBy, ExistentialIsa}
	VariesWith:	x
2b. Everybody loves somebody. ∃yεPerson ∀xεPerson. Loves(x,y)

   ***	SOLN#1  ***

AnyPerson
	TypicalExample:  TypicalPerson
	UniversalExamples: {y, ...}

TypicalPerson
	TypicalExampleOf: AnyPerson
	Loves:		  y

y
	ExistentialIsa:	{AnyPerson}
	LovesBy:	TypicalPerson
	DefinitionalSlots: {LovedBy, ExistentialIsa}
	VariesWith:	NIL

   ***	SOLN#2  ***

AnyPerson
	UniversalExamples: {x, y...}

x
	UniversalIsa: {AnyPerson}
	Loves:		  y
	DefinitionalSlots: {UniversalIsa}
	VariesThru:	AnyPerson

y
	ExistentialIsa:	{AnyPerson}
	LovesBy:	TypicalPerson
	DefinitionalSlots: {LovedBy, ExistentialIsa}
	VariesWith:	NIL
3. Purple mushrooms have many attributes.

AnyMushroom
	UniversalExamples: {x ... }

x
	UniversalIsa:	{AnyMushroom}
	Color:		Purple
	Poisonous:	T
	DefinitionalSlots: {UniversalIsa, Color}
	#Slots:		Many

#Slots:
	Isa:	{Any$SELF$Slot}

4. There are 23 purple mushrooms in the world.

AnyMushroom
	Cardinality:	23

Cardinality
	Isa:	{Slot}

5. Purple-mushroom-23 has been accessed 12 times.

AnyMushroom
	Examples: {Purple-mushroom-23, ...}

Purple-mushroom-23
	Isa:	{AnyMushroom}
	#Accesses:	12

#Accesses
	Isa:	{Any$SELF$Slot}

6. The fact that a purple mushroom is purple is definitional.

AnyMushroom
	UnverisalExamples: {x ... }

x
	UniversalIsa:	{AnyMushroom}
	Color:		Purple
	Poisonous:	T
	DefinitionalSlots: {UniversalIsa, Color}
	VariesThru:	AnyMushroom
7. Block1 and Block2 together form a blivit.
   Block2 and Block3 together form a blivit.
   Block1 and Block3 together form a blivit.

AnyBlivit
	EssentialParts:	{Whiggit, Whatever}
	Examples:	{Blivit-0, Blivit-32, Blivit-95 ...}

Blivit-0
	Isa:		(AnyBlivit)
	Whiggit:	Block1
	Whatever:	Block2

Blivit-32
	Isa:		(AnyBlivit)
	Whiggit:	Block2
	Whatever:	Block3
	APartOf:	Block3

Blivit-95
	Isa:		(AnyBlivit)
	Whiggit:	Block1
	Whatever:	Block3

Block1
	Isa:		{AnyBlock, AnyWhiggit}
	WhiggitFor:	(Blivit-0, Blivit-32)
	APartOf:	(Blivit-0, Blivit-32)

Block2
	Isa:		{AnyBlock, AnyWhiggit, AnyWhatever}
	WhateverFor:	(Blivit-0)
	WhiggitFor:	(Blivit-32)
	APartOf:	(Blivit-0, Blivit-32)

Block3
	Isa:		{AnyBlock, AnyWhatever}
	WhiggitFor:	(Blivit-32, Blivit-95)
	APartOf:	(Blivit-32, Blivit-95)

APartOf
	Isa:		(AnySlot)
	SubSlots:	(WhiggitFor, WhateverFor)

Whiggit
	Isa:		(AnySlot)
	Inverse:	WhiggitFor

Whatever
	Isa:		(AnySlot)
	Inverse:	WhateverFor

WhiggitFor
	Isa:		(AnySlot)
	SuperSlots:	(APartIn)
	Inverse:	Whiggit

WhateverFor
	Isa:		(AnySlot)
	SuperSlots:	(APartIn)
	Inverse:	Whatever
8. John gave Mary the book.

AnyGivingEvent
	Examples:	{GE-41, ...}

GE-41
	Giver:		John
	Recipient:	Mary
	Object:		Book

John
	GiverIn:	GE-41

Mary
	RecipientIn:	GE-41

Book
	ObjectIn:	GE-41

GiverIn
	Isa:		{Slot}
	SuperSlots:	{ParticipatesIn}

RecipientIn
	Isa:		{Slot}
	SuperSlots:	{ParticipatesIn}

ObjectIn
	Isa:		{Slot}
	SuperSlots:	{ParticipatesIn}
9. Apple-23 embodies the {theory | concept} pf apple. [is an examplar]

AnyApple
	Examplar:	Apple-23

Apple-23
	ExamplarOf:	AnyApple

Examplar
	Isa:	{Slot}
	?

x = Examplar( S ) means:

1. x ε S
2. ∀yεS. ∀sεT.  s(y) = s(x) most of the time.
	where T = InheritableSlots(TypicalExample(S)).
	[Rewording: ∀sεT. |{yεS | s(y) = s(x)}| ≥ 80% of |S| ]
10. The color of all singleton sets is red.

AnySet
	UniversalExamples:	{x, ...}

x
	UniversalIsa:	{AnySet}
	Cardinality:	1
	DefinitionalSlots: {UniversalIsa, Cardinality}
	Color:		Red
12. Most elephants are grey.

AnyElephant
	TypicalExample:	TypicalElephant

TypicalElephant
	Propositions:	{Prop-41, ...}

Grey
	Isa:		{AnyColor}
	Propositions:	{Prop-41, ...}

Prop-41
	Relation:	Color
	Value:		Grey
	Modality:	MostAre
	FromUnit:	TypicalElephant

Propositions
	Isa:		{Slot}
	Datatype:	... (*P AnyProp) ...

AnyProp
	TypicalExample:	TypicalProp

TypicalProp
	TypicalExampleOf:	AnyProp
	SensibleSlots:		{Relation, Value, FromUnit, Modality, Tense, ...}
-- Or --

AnyElephant
	TypicalExample:	TypicalElephant

TypicalElephant
	Color:	{(Prop Prop-41), ...}

Grey
	Isa:		{AnyColor}
	ColorOf:	{(Prop Prop-41), ...}

Prop-41
	Relation:	Color
	Value:		Grey
	Modality:	MostAre
	FromUnit:	TypicalElephant

-- OR --

AnyElephant
	UniversalExamples:	{x, ...}

x
	UniversalIsa:		{AnyElephant}
	QualifiedBy:		Most
	DefinitionalSlots:	{UniversalIsa, NatureOfQualification}
	Color:			Grey

Most
	?

--------------

AnyElephant
	UniversalExamples:	{x, ...}

AnyGreyThing
	StdExamples:		{x, ...}

x
	UniversalIsa:		{AnyElephant}
	QualifiedBy:		Most
	DefinitionalSlots:	{UniveralIsa, QualifiedBy}
	StdIsa:			{AnyGreyThing}
	Isa:			{AnyGreyThing, AnyElephant}
14. Tower of Hanoi
??