Hardegree,
Intermediate Logic
; Unit 1: Translations in Function Logic
1
of 8
UNIT 1: TRANSLATIONS IN FUNCTION LOGIC
1.
Directions for all Exercise Sets in Unit 1
Using the suggested abbreviations (the capitalized words), translate each of the following into the
language of function logic.
Symbolize all and only
capitalized words.
Important:
Write down your lexicon.
In each case, clearly indicate what each predicate letter, each function letter, and each proper-noun letter
symbolizes.
Examples:
V
[
α
]
:
α
is a voter
R
[
α
,
β
]
:
α
respects
β
S
[
α
,
β
,
γ
]
:
α
sold
β
to
γ
m
(
α
)
:
the mother of
α
f
(
α
)
:
α
’s father
s
(
α
,
β
)
:
the sum of
α
and
β
p
(
α
,
β
)
:
α
plus
β
j
:
Jay
In writing down the lexicon, use lower case Greek letters as generic arguments (place holders); in
particular, use ‘
α
’ for one-place functors, ‘
α
’, ‘
β
’ for two-place functors, and ‘
α
’,‘
β
’,‘
γ
’ for three-place
functors.
[brief note on Greek alphabet:
α
is alpha,
β
is beta,
γ
is gamma,
δ
is delta; and, of course, the
word ‘alphabet’ comes from ‘
αβ
’]
Also, in quantified sentences, identify the universe of discourse (the domain over which the quantifiers
range) .
For example,
U : things (the most general domain)
U : persons
U : numbers
etc.
Alternatively, you may write:
2200
x
: every thing
2200
x
: every person
2200
x
: every number
etc.
Final Note
:
You may use numerals (‘1’, ‘2’, etc.) to symbolize themselves.