Term
| atomic sentences consist of what? |
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Definition
| Names and predicates (predicates state what the subject does) Ex: Max SAW Claire |
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Term
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Definition
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Term
| Using FOL, interpret the meaning of: Cube(b), Larger(c,f), Between(b,c,d) |
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Definition
b is a cube,
c is larger than f,
b is between c and d. |
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Term
| Define individual constant |
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Definition
| Symbols used to refer to a fixed object. Ex: A persons name |
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Term
| Names in FOL are represented by what letters of the alphabet? |
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Definition
| Letters a - f (and subscript name1 and name2) |
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Term
| Three things to remember about individual constants: |
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Definition
Every individual constant must name an object that actually exists
No individual constant can name more than one object
An object can have more than one name, or no name at all |
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Term
| Define predicate symbols (also known as relational symbols) used in FOL |
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Definition
| symbols used to express some property of an object or a relationship between objects Ex: Small(max) - meaning Max is small (where small is the predicates symbol) |
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Term
| Logical subjects: arguments of the predicate |
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Definition
Ex: Max likes Claire (Max & Claire are logical subjects)
("likes" is the predicate referencing the subject) |
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Term
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Definition
the number of arguments referenced by the predicate
Ex arity of 1: Home(max)
Ex arity of 2: Smaller(c,b)
Ex arity of 3: Between(b,a,c) |
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Term
| determinate property in FOL means what? |
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Definition
| that there is a precise interpretation. unlike in normal English where terms can be vague Ex: at what age do you stop being young. |
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Term
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Definition
Infix: the arguments are placed on either side of the predicate Ex: a=b
Prefix: the arguments are after the predicate Ex: Smaller(a,b) |
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Term
| Function symbols: (also known as terms) |
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Definition
| noun phrases used to form complex subjects (very similar to names). Ex: Max's father likes tennis - "Max's father" is the function symbol |
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Term
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Definition
noun phrases that refer to an individuals. Ex: Max's father or Father(max)
(works just like individual constants/names do) |
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Term
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Definition
Ex: Taller(father(max),max)
is
Max's father is taller than Max |
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Term
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Definition
Only has two types of predicates (things that link subjects):
The identity symbol: "=" and the membership symbol: "∈" |
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Term
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Definition
"∈" Symbold:
Ex: a = 2 and b = {2,4,6} So "a" is a member of the set "b"
So: a ∈ a is False
a ∈ b is True
b ∈ a is False
b ∈ b is False |
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Term
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Definition
Uses: 0,1
(=,<) for predicates
(+,x) for functions |
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Term
| Inductive definitions (FOL Arithmetic) |
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Definition
The names 0,1 are terms
If t1 , t2 are terms, then the expression (t1+t2) and (t1xt2) are also terms |
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Term
| FOL Arithmetic atomic sentences |
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Definition
One times One is less than one plus one is the same as
(1x1)<(1+1) |
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