What is a decidable fragment?
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I read everywhere that description logics are decidable fragments of first-order logic. What does this mean? What is a decidable fragment of first-order logic?
terminology definition first-order-logic
edited Dec 20 '18 at 15:29
Shaun
8,932113681
asked Dec 20 '18 at 14:08
DeeDee
1184
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add a comment |
$begingroup$
I read everywhere that description logics are decidable fragments of first-order logic. What does this mean? What is a decidable fragment of first-order logic?
terminology definition first-order-logic
edited Dec 20 '18 at 15:29
Shaun
8,932113681
asked Dec 20 '18 at 14:08
DeeDee
1184
$endgroup$
add a comment |
$begingroup$
I read everywhere that description logics are decidable fragments of first-order logic. What does this mean? What is a decidable fragment of first-order logic?
terminology definition first-order-logic
edited Dec 20 '18 at 15:29
Shaun
8,932113681
asked Dec 20 '18 at 14:08
DeeDee
1184
$endgroup$
I read everywhere that description logics are decidable fragments of first-order logic. What does this mean? What is a decidable fragment of first-order logic?
terminology definition first-order-logic
terminology definition first-order-logic
edited Dec 20 '18 at 15:29
Shaun
8,932113681
asked Dec 20 '18 at 14:08
DeeDee
1184
edited Dec 20 '18 at 15:29
Shaun
8,932113681
asked Dec 20 '18 at 14:08
DeeDee
1184
edited Dec 20 '18 at 15:29
Shaun
8,932113681
edited Dec 20 '18 at 15:29
Shaun
8,932113681
edited Dec 20 '18 at 15:29
Shaun
8,932113681
8,932113681
asked Dec 20 '18 at 14:08
DeeDee
1184
asked Dec 20 '18 at 14:08
DeeDee
1184
asked Dec 20 '18 at 14:08
DeeDee
1184
1184
add a comment |
add a comment |
2 Answers
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oldest
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A decidable logic is one where, given a statement, you can compute whether or not that statement is true in the logic.
A fragment of a logic is a subset of that logic obtained by imposing syntactic restrictions. The fragment has the same semantics, but possibly fewer well-formed formulae.
So a decidable fragment of first-order logic is a syntactically-restricted subset of first-order logic in which truth is computable.
answered Dec 20 '18 at 14:22
Patrick StevensPatrick Stevens
28.6k52874
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add a comment |
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It is a "subset" of first-order logic that is decidable.
Another example is Monadic predicate calculus :
in which all relation symbols are monadic (that is, they take only one argument), and there are no function symbols. This means that all atomic formulas are thus of the form $P(x)$.
In the case of a logical system, decidability means that :
there is an effective method for determining whether arbitrary formulas are theorems of the logical system. For example, propositional logic is decidable, because the truth-table method can be used to determine whether an arbitrary propositional formula is logically valid.
answered Dec 20 '18 at 14:23
Mauro ALLEGRANZAMauro ALLEGRANZA
65.2k448112
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add a comment |
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2 Answers
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2 Answers
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$begingroup$
A decidable logic is one where, given a statement, you can compute whether or not that statement is true in the logic.
A fragment of a logic is a subset of that logic obtained by imposing syntactic restrictions. The fragment has the same semantics, but possibly fewer well-formed formulae.
So a decidable fragment of first-order logic is a syntactically-restricted subset of first-order logic in which truth is computable.
answered Dec 20 '18 at 14:22
Patrick StevensPatrick Stevens
28.6k52874
$endgroup$
add a comment |
$begingroup$
A decidable logic is one where, given a statement, you can compute whether or not that statement is true in the logic.
A fragment of a logic is a subset of that logic obtained by imposing syntactic restrictions. The fragment has the same semantics, but possibly fewer well-formed formulae.
So a decidable fragment of first-order logic is a syntactically-restricted subset of first-order logic in which truth is computable.
answered Dec 20 '18 at 14:22
Patrick StevensPatrick Stevens
28.6k52874
$endgroup$
add a comment |
$begingroup$
A decidable logic is one where, given a statement, you can compute whether or not that statement is true in the logic.
A fragment of a logic is a subset of that logic obtained by imposing syntactic restrictions. The fragment has the same semantics, but possibly fewer well-formed formulae.
So a decidable fragment of first-order logic is a syntactically-restricted subset of first-order logic in which truth is computable.
answered Dec 20 '18 at 14:22
Patrick StevensPatrick Stevens
28.6k52874
$endgroup$
A decidable logic is one where, given a statement, you can compute whether or not that statement is true in the logic.
A fragment of a logic is a subset of that logic obtained by imposing syntactic restrictions. The fragment has the same semantics, but possibly fewer well-formed formulae.
So a decidable fragment of first-order logic is a syntactically-restricted subset of first-order logic in which truth is computable.
answered Dec 20 '18 at 14:22
Patrick StevensPatrick Stevens
28.6k52874
answered Dec 20 '18 at 14:22
Patrick StevensPatrick Stevens
28.6k52874
answered Dec 20 '18 at 14:22
Patrick StevensPatrick Stevens
28.6k52874
answered Dec 20 '18 at 14:22
Patrick StevensPatrick Stevens
28.6k52874
28.6k52874
add a comment |
add a comment |
$begingroup$
It is a "subset" of first-order logic that is decidable.
Another example is Monadic predicate calculus :
in which all relation symbols are monadic (that is, they take only one argument), and there are no function symbols. This means that all atomic formulas are thus of the form $P(x)$.
In the case of a logical system, decidability means that :
there is an effective method for determining whether arbitrary formulas are theorems of the logical system. For example, propositional logic is decidable, because the truth-table method can be used to determine whether an arbitrary propositional formula is logically valid.
answered Dec 20 '18 at 14:23
Mauro ALLEGRANZAMauro ALLEGRANZA
65.2k448112
$endgroup$
add a comment |
$begingroup$
It is a "subset" of first-order logic that is decidable.
Another example is Monadic predicate calculus :
in which all relation symbols are monadic (that is, they take only one argument), and there are no function symbols. This means that all atomic formulas are thus of the form $P(x)$.
In the case of a logical system, decidability means that :
there is an effective method for determining whether arbitrary formulas are theorems of the logical system. For example, propositional logic is decidable, because the truth-table method can be used to determine whether an arbitrary propositional formula is logically valid.
answered Dec 20 '18 at 14:23
Mauro ALLEGRANZAMauro ALLEGRANZA
65.2k448112
$endgroup$
add a comment |
$begingroup$
It is a "subset" of first-order logic that is decidable.
Another example is Monadic predicate calculus :
in which all relation symbols are monadic (that is, they take only one argument), and there are no function symbols. This means that all atomic formulas are thus of the form $P(x)$.
In the case of a logical system, decidability means that :
there is an effective method for determining whether arbitrary formulas are theorems of the logical system. For example, propositional logic is decidable, because the truth-table method can be used to determine whether an arbitrary propositional formula is logically valid.
answered Dec 20 '18 at 14:23
Mauro ALLEGRANZAMauro ALLEGRANZA
65.2k448112
$endgroup$
It is a "subset" of first-order logic that is decidable.
Another example is Monadic predicate calculus :
in which all relation symbols are monadic (that is, they take only one argument), and there are no function symbols. This means that all atomic formulas are thus of the form $P(x)$.
In the case of a logical system, decidability means that :
there is an effective method for determining whether arbitrary formulas are theorems of the logical system. For example, propositional logic is decidable, because the truth-table method can be used to determine whether an arbitrary propositional formula is logically valid.
answered Dec 20 '18 at 14:23
Mauro ALLEGRANZAMauro ALLEGRANZA
65.2k448112
answered Dec 20 '18 at 14:23
Mauro ALLEGRANZAMauro ALLEGRANZA
65.2k448112
answered Dec 20 '18 at 14:23
Mauro ALLEGRANZAMauro ALLEGRANZA
65.2k448112
answered Dec 20 '18 at 14:23
Mauro ALLEGRANZAMauro ALLEGRANZA
65.2k448112
65.2k448112
add a comment |
add a comment |
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