Mixing
meaning of (r .⊃. s ⊃ r) [the syntax meaning]
Clash Royale CLAN TAG#URR8PPP
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I'm trying to to determine whether the following is a tautology, contingency, or contradictory:
(p ⊃ q) ∨ (q ⊃ p) .⊃. (r .⊃. s ⊃ r)
This is school work. I'm getting that it's a tautology, but only through looking at patterns of solutions of textbook problems and exercises. I would like to know what exactly is meant by the dot prior and after the material implication (.⊃.)?
I understand that material implication - in a truth table - has false only when p is true and q is false. I also understand the or operator where it's true when either both or one of the two, namely: p or q is true. I just need to understand what the dots are supposed to mean. I couldn't find good explanations online.
logic philosophy-of-logic symbolic-logic
asked 1 hour ago
wa7d
305
add a comment |Â
up vote
1
down vote
favorite
I'm trying to to determine whether the following is a tautology, contingency, or contradictory:
(p ⊃ q) ∨ (q ⊃ p) .⊃. (r .⊃. s ⊃ r)
This is school work. I'm getting that it's a tautology, but only through looking at patterns of solutions of textbook problems and exercises. I would like to know what exactly is meant by the dot prior and after the material implication (.⊃.)?
I understand that material implication - in a truth table - has false only when p is true and q is false. I also understand the or operator where it's true when either both or one of the two, namely: p or q is true. I just need to understand what the dots are supposed to mean. I couldn't find good explanations online.
logic philosophy-of-logic symbolic-logic
asked 1 hour ago
wa7d
305
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I'm trying to to determine whether the following is a tautology, contingency, or contradictory:
(p ⊃ q) ∨ (q ⊃ p) .⊃. (r .⊃. s ⊃ r)
This is school work. I'm getting that it's a tautology, but only through looking at patterns of solutions of textbook problems and exercises. I would like to know what exactly is meant by the dot prior and after the material implication (.⊃.)?
I understand that material implication - in a truth table - has false only when p is true and q is false. I also understand the or operator where it's true when either both or one of the two, namely: p or q is true. I just need to understand what the dots are supposed to mean. I couldn't find good explanations online.
logic philosophy-of-logic symbolic-logic
asked 1 hour ago
wa7d
305
I'm trying to to determine whether the following is a tautology, contingency, or contradictory:
(p ⊃ q) ∨ (q ⊃ p) .⊃. (r .⊃. s ⊃ r)
This is school work. I'm getting that it's a tautology, but only through looking at patterns of solutions of textbook problems and exercises. I would like to know what exactly is meant by the dot prior and after the material implication (.⊃.)?
I understand that material implication - in a truth table - has false only when p is true and q is false. I also understand the or operator where it's true when either both or one of the two, namely: p or q is true. I just need to understand what the dots are supposed to mean. I couldn't find good explanations online.
logic philosophy-of-logic symbolic-logic
logic philosophy-of-logic symbolic-logic
asked 1 hour ago
wa7d
305
asked 1 hour ago
wa7d
305
edited 54 mins ago
asked 1 hour ago
wa7d
305
asked 1 hour ago
wa7d
305
asked 1 hour ago
wa7d
305
305
add a comment |Â
add a comment |Â
2 Answers
2
active
oldest
votes
up vote
2
down vote
accepted
The dots function like parentheses: they disambiguate an otherwise ambiguous expression. In this case the expression is equivalent to:
((p ⊃ q) ∨ (q ⊃ p)) ⊃ (r ⊃ (s ⊃ r))
Note that without the dots the consequent would be:
(r ⊃ s ⊃ r)
Which is ambiguous between the following two:
((r ⊃ s) ⊃ r)
(r ⊃ (s ⊃ r))
The dots just tell you which connective is the main one.
answered 21 mins ago
Eliran H
3,80621032
I kind of wish there was a universally agreed upon notation. That would be one way to disambiguate. Thanks!
– wa7d
5 mins ago
add a comment |Â
up vote
2
down vote
The use of dots like that is an alternative to using nested parentheses. Putting dots around a connective indicates that its binding priority is lower than that of another connective in the sentence. Your sentence could also be written ((p ⊃ q) ∨ (q ⊃ p)) ⊃ (r ⊃ (s ⊃ r)).
To give a simpler example:
A ∨ B ⊃ C
is syntactically ambiguous. It could mean
(A ∨ B) ⊃ C
or
A ∨ (B ⊃ C)
An alternative way to specify the first version would be to write:
A ∨ B .⊃. C
It is a matter of style as to which you prefer, but the dot notation is not as common as it used to be.
answered 16 mins ago
Bumble
6,9882830
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
accepted
The dots function like parentheses: they disambiguate an otherwise ambiguous expression. In this case the expression is equivalent to:
((p ⊃ q) ∨ (q ⊃ p)) ⊃ (r ⊃ (s ⊃ r))
Note that without the dots the consequent would be:
(r ⊃ s ⊃ r)
Which is ambiguous between the following two:
((r ⊃ s) ⊃ r)
(r ⊃ (s ⊃ r))
The dots just tell you which connective is the main one.
answered 21 mins ago
Eliran H
3,80621032
I kind of wish there was a universally agreed upon notation. That would be one way to disambiguate. Thanks!
– wa7d
5 mins ago
add a comment |Â
up vote
2
down vote
accepted
The dots function like parentheses: they disambiguate an otherwise ambiguous expression. In this case the expression is equivalent to:
((p ⊃ q) ∨ (q ⊃ p)) ⊃ (r ⊃ (s ⊃ r))
Note that without the dots the consequent would be:
(r ⊃ s ⊃ r)
Which is ambiguous between the following two:
((r ⊃ s) ⊃ r)
(r ⊃ (s ⊃ r))
The dots just tell you which connective is the main one.
answered 21 mins ago
Eliran H
3,80621032
I kind of wish there was a universally agreed upon notation. That would be one way to disambiguate. Thanks!
– wa7d
5 mins ago
add a comment |Â
up vote
2
down vote
accepted
up vote
2
down vote
accepted
The dots function like parentheses: they disambiguate an otherwise ambiguous expression. In this case the expression is equivalent to:
((p ⊃ q) ∨ (q ⊃ p)) ⊃ (r ⊃ (s ⊃ r))
Note that without the dots the consequent would be:
(r ⊃ s ⊃ r)
Which is ambiguous between the following two:
((r ⊃ s) ⊃ r)
(r ⊃ (s ⊃ r))
The dots just tell you which connective is the main one.
answered 21 mins ago
Eliran H
3,80621032
The dots function like parentheses: they disambiguate an otherwise ambiguous expression. In this case the expression is equivalent to:
((p ⊃ q) ∨ (q ⊃ p)) ⊃ (r ⊃ (s ⊃ r))
Note that without the dots the consequent would be:
(r ⊃ s ⊃ r)
Which is ambiguous between the following two:
((r ⊃ s) ⊃ r)
(r ⊃ (s ⊃ r))
The dots just tell you which connective is the main one.
answered 21 mins ago
Eliran H
3,80621032
answered 21 mins ago
Eliran H
3,80621032
answered 21 mins ago
Eliran H
3,80621032
answered 21 mins ago
Eliran H
3,80621032
3,80621032
I kind of wish there was a universally agreed upon notation. That would be one way to disambiguate. Thanks!
– wa7d
5 mins ago
add a comment |Â
I kind of wish there was a universally agreed upon notation. That would be one way to disambiguate. Thanks!
– wa7d
5 mins ago
I kind of wish there was a universally agreed upon notation. That would be one way to disambiguate. Thanks!
– wa7d
5 mins ago
I kind of wish there was a universally agreed upon notation. That would be one way to disambiguate. Thanks!
– wa7d
5 mins ago
add a comment |Â
up vote
2
down vote
The use of dots like that is an alternative to using nested parentheses. Putting dots around a connective indicates that its binding priority is lower than that of another connective in the sentence. Your sentence could also be written ((p ⊃ q) ∨ (q ⊃ p)) ⊃ (r ⊃ (s ⊃ r)).
To give a simpler example:
A ∨ B ⊃ C
is syntactically ambiguous. It could mean
(A ∨ B) ⊃ C
or
A ∨ (B ⊃ C)
An alternative way to specify the first version would be to write:
A ∨ B .⊃. C
It is a matter of style as to which you prefer, but the dot notation is not as common as it used to be.
answered 16 mins ago
Bumble
6,9882830
add a comment |Â
up vote
2
down vote
The use of dots like that is an alternative to using nested parentheses. Putting dots around a connective indicates that its binding priority is lower than that of another connective in the sentence. Your sentence could also be written ((p ⊃ q) ∨ (q ⊃ p)) ⊃ (r ⊃ (s ⊃ r)).
To give a simpler example:
A ∨ B ⊃ C
is syntactically ambiguous. It could mean
(A ∨ B) ⊃ C
or
A ∨ (B ⊃ C)
An alternative way to specify the first version would be to write:
A ∨ B .⊃. C
It is a matter of style as to which you prefer, but the dot notation is not as common as it used to be.
answered 16 mins ago
Bumble
6,9882830
add a comment |Â
up vote
2
down vote
up vote
2
down vote
The use of dots like that is an alternative to using nested parentheses. Putting dots around a connective indicates that its binding priority is lower than that of another connective in the sentence. Your sentence could also be written ((p ⊃ q) ∨ (q ⊃ p)) ⊃ (r ⊃ (s ⊃ r)).
To give a simpler example:
A ∨ B ⊃ C
is syntactically ambiguous. It could mean
(A ∨ B) ⊃ C
or
A ∨ (B ⊃ C)
An alternative way to specify the first version would be to write:
A ∨ B .⊃. C
It is a matter of style as to which you prefer, but the dot notation is not as common as it used to be.
answered 16 mins ago
Bumble
6,9882830
The use of dots like that is an alternative to using nested parentheses. Putting dots around a connective indicates that its binding priority is lower than that of another connective in the sentence. Your sentence could also be written ((p ⊃ q) ∨ (q ⊃ p)) ⊃ (r ⊃ (s ⊃ r)).
To give a simpler example:
A ∨ B ⊃ C
is syntactically ambiguous. It could mean
(A ∨ B) ⊃ C
or
A ∨ (B ⊃ C)
An alternative way to specify the first version would be to write:
A ∨ B .⊃. C
It is a matter of style as to which you prefer, but the dot notation is not as common as it used to be.
answered 16 mins ago
Bumble
6,9882830
answered 16 mins ago
Bumble
6,9882830
answered 16 mins ago
Bumble
6,9882830
answered 16 mins ago
Bumble
6,9882830
6,9882830
add a comment |Â
add a comment |Â
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