Terminology for free variables
up vote
2
down vote
favorite
Suppose you have a proof along the lines of
$$begin{array} {rc}
text{Assume:} & x > 2 \
& vdots \
& text{Some logic stuff} \
& vdots \
text{Conclude:} & x > 1 \
end{array}$$
Two common ways for this to be interpreted are (1) $(forall x~.~x > 2) to (forall x~.~x > 1)$ and (2) $forall x~.~(x > 2 to x > 1)$. Logics that intend the first way include PRA and Hilbert style FOL. Logics that intend the second way include Fitch style Natural Deduction.
Is there common terminology to distinguish the two approaches to interpreting how the free variables are shared between propositions in a proof? Or if you have reason to think there are no such common terms, what would you suggest?
logic terminology quantifiers sequent-calculus
asked 18 hours ago
DanielV
17.7k42752
add a comment |
up vote
2
down vote
favorite
Suppose you have a proof along the lines of
$$begin{array} {rc}
text{Assume:} & x > 2 \
& vdots \
& text{Some logic stuff} \
& vdots \
text{Conclude:} & x > 1 \
end{array}$$
Two common ways for this to be interpreted are (1) $(forall x~.~x > 2) to (forall x~.~x > 1)$ and (2) $forall x~.~(x > 2 to x > 1)$. Logics that intend the first way include PRA and Hilbert style FOL. Logics that intend the second way include Fitch style Natural Deduction.
Is there common terminology to distinguish the two approaches to interpreting how the free variables are shared between propositions in a proof? Or if you have reason to think there are no such common terms, what would you suggest?
logic terminology quantifiers sequent-calculus
asked 18 hours ago
DanielV
17.7k42752
add a comment |
up vote
2
down vote
favorite
up vote
2
down vote
favorite
Suppose you have a proof along the lines of
$$begin{array} {rc}
text{Assume:} & x > 2 \
& vdots \
& text{Some logic stuff} \
& vdots \
text{Conclude:} & x > 1 \
end{array}$$
Two common ways for this to be interpreted are (1) $(forall x~.~x > 2) to (forall x~.~x > 1)$ and (2) $forall x~.~(x > 2 to x > 1)$. Logics that intend the first way include PRA and Hilbert style FOL. Logics that intend the second way include Fitch style Natural Deduction.
Is there common terminology to distinguish the two approaches to interpreting how the free variables are shared between propositions in a proof? Or if you have reason to think there are no such common terms, what would you suggest?
logic terminology quantifiers sequent-calculus
asked 18 hours ago
DanielV
17.7k42752
Suppose you have a proof along the lines of
$$begin{array} {rc}
text{Assume:} & x > 2 \
& vdots \
& text{Some logic stuff} \
& vdots \
text{Conclude:} & x > 1 \
end{array}$$
Two common ways for this to be interpreted are (1) $(forall x~.~x > 2) to (forall x~.~x > 1)$ and (2) $forall x~.~(x > 2 to x > 1)$. Logics that intend the first way include PRA and Hilbert style FOL. Logics that intend the second way include Fitch style Natural Deduction.
Is there common terminology to distinguish the two approaches to interpreting how the free variables are shared between propositions in a proof? Or if you have reason to think there are no such common terms, what would you suggest?
logic terminology quantifiers sequent-calculus
logic terminology quantifiers sequent-calculus
asked 18 hours ago
DanielV
17.7k42752
asked 18 hours ago
DanielV
17.7k42752
asked 18 hours ago
DanielV
17.7k42752
asked 18 hours ago
DanielV
17.7k42752
asked 18 hours ago
DanielV
17.7k42752
17.7k42752
add a comment |
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2995394%2fterminology-for-free-variables%23new-answer', 'question_page');
}
);
Post as a guest
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
