3 B was used to mean 2 disparate objects, so I added another letter to elucidate.
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These can't be simplified by the use of eliminating double negation, but the number of negatives can be reduced by applying the axiom of contrapositives

To address your first example, "A does not B unless C is true" is equivalent to "A only does B if C is true". To put that in formal logic for you:

Let D (for A'd oes' B)D be the proposition "A does B", and let CE be the proposition "C is true".

"¬D unless C"E" can clearly be rewritten "Without CE, ¬D", or in more logical notation

¬C¬E -> ¬D

By the rule of contrapositives, this is equivalent to

D -> CE

Which we can read as "D implies C"E", or "if D happens then CE must be true", or "If A does DB then C is true", or "A only does DB if C is true".

So to rewrite your first example,

...a statute does not impose criminal liability without the need for proof of mens rea unless it specifies explicitly that that is what it is doing.

becomes

...a statute only imposes criminal liability without the need for proof of mens rea if it specifies explicitly that that is what it is doing.

Here "A" is a statute, "D""B" is imposes criminal liability without the need for proof of mens rea and "C" is "it specifies explicitly that that is what it is doing".

In general it is quite dangerous to think of English in terms of the rules of formal logic, and it is quite dangerous to think of formal logic in terms of the English language semantics of the terms we use to describe it. If you want to simplify these horrible sentences, a better way would be to read it several times to make sure you fully understand it, and then write down "what it means" without directly referring to the sentence itself. (Then maybe compare the sentences to make sure you have written a sentence with the same meaning).

These can't be simplified by the use of eliminating double negation, but the number of negatives can be reduced by applying the axiom of contrapositives

To address your first example, "A does not B unless C is true" is equivalent to "A only does B if C is true". To put that in formal logic for you:

Let D (for A'd oes' B) be the proposition "A does B", and let C be the proposition "C is true".

"¬D unless C" can clearly be rewritten "Without C, ¬D", or in more logical notation

¬C -> ¬D

By the rule of contrapositives, this is equivalent to

D -> C

Which we can read as "D implies C", or "if D happens then C must be true", or "If A does D then C is true", or "A only does D if C is true".

So to rewrite your first example,

...a statute does not impose criminal liability without the need for proof of mens rea unless it specifies explicitly that that is what it is doing.

becomes

...a statute only imposes criminal liability without the need for proof of mens rea if it specifies explicitly that that is what it is doing.

Here "A" is a statute, "D" is imposes criminal liability without the need for proof of mens rea and "C" is "it specifies explicitly that that is what it is doing".

In general it is quite dangerous to think of English in terms of the rules of formal logic, and it is quite dangerous to think of formal logic in terms of the English language semantics of the terms we use to describe it. If you want to simplify these horrible sentences, a better way would be to read it several times to make sure you fully understand it, and then write down "what it means" without directly referring to the sentence itself. (Then maybe compare the sentences to make sure you have written a sentence with the same meaning).

These can't be simplified by the use of eliminating double negation, but the number of negatives can be reduced by applying the axiom of contrapositives

To address your first example, "A does not B unless C is true" is equivalent to "A only does B if C is true". To put that in formal logic for you:

Let D be the proposition "A does B", and let E be the proposition "C is true".

"¬D unless E" can clearly be rewritten "Without E, ¬D", or in more logical notation

¬E -> ¬D

By the rule of contrapositives, this is equivalent to

D -> E

Which we can read as "D implies E", or "if D happens then E must be true", or "If A does B then C is true", or "A only does B if C is true".

So to rewrite your first example,

...a statute does not impose criminal liability without the need for proof of mens rea unless it specifies explicitly that that is what it is doing.

becomes

...a statute only imposes criminal liability without the need for proof of mens rea if it specifies explicitly that that is what it is doing.

Here "A" is a statute, "B" is imposes criminal liability without the need for proof of mens rea and "C" is "it specifies explicitly that that is what it is doing".

In general it is quite dangerous to think of English in terms of the rules of formal logic, and it is quite dangerous to think of formal logic in terms of the English language semantics of the terms we use to describe it. If you want to simplify these horrible sentences, a better way would be to read it several times to make sure you fully understand it, and then write down "what it means" without directly referring to the sentence itself. (Then maybe compare the sentences to make sure you have written a sentence with the same meaning).

2 B was used to mean 2 disparate objects, so I added another letter to elucidate.
source | link

These can't be simplified by the use of eliminating double negation, but the number of negatives can be reduced by applying the axiom of contrapositives

To address your first example, "A does not B unless C is true" is equivalent to "A only does B if C is true". To put that in formal logic for you:

Let D (for A'd oes' B) be the proposition "A does B", and let C be the proposition "C is true".

"¬B"¬D unless C" can clearly be rewritten "Without C, ¬B"¬D", or in more logical notation

¬C -> ¬B¬D

By the rule of contrapositives, this is equivalent to

BD -> C

Which we can read as "B"D implies C", or "if BD happens then C must be true", or "If A does BD then C is true", or "A only does BD if C is true".

So to rewrite your first example,

...a statute does not impose criminal liability without the need for proof of mens rea unless it specifies explicitly that that is what it is doing.

becomes

...a statute only imposes criminal liability without the need for proof of mens rea if it specifies explicitly that that is what it is doing.

Here "A" is a statute, "B""D" is imposes criminal liability without the need for proof of mens rea and "C" is "it specifies explicitly that that is what it is doing".

In general it is quite dangerous to think of English in terms of the rules of formal logic, and it is quite dangerous to think of formal logic in terms of the English language semantics of the terms we use to describe it. If you want to simplify these horrible sentences, a better way would be to read it several times to make sure you fully understand it, and then write down "what it means" without directly referring to the sentence itself. (Then maybe compare the sentences to make sure you have written a sentence with the same meaning).

These can't be simplified by the use of eliminating double negation, but the number of negatives can be reduced by applying the axiom of contrapositives

To address your first example, "A does not B unless C is true" is equivalent to "A only does B if C is true". To put that in formal logic for you:

Let B be the proposition "A does B", and let C be the proposition "C is true".

"¬B unless C" can clearly be rewritten "Without C, ¬B", or in more logical notation

¬C -> ¬B

By the rule of contrapositives, this is equivalent to

B -> C

Which we can read as "B implies C", or "if B happens then C must be true", or "If A does B then C is true", or "A only does B if C is true".

So to rewrite your first example,

...a statute does not impose criminal liability without the need for proof of mens rea unless it specifies explicitly that that is what it is doing.

becomes

...a statute only imposes criminal liability without the need for proof of mens rea if it specifies explicitly that that is what it is doing.

Here "A" is a statute, "B" is imposes criminal liability without the need for proof of mens rea and "C" is "it specifies explicitly that that is what it is doing".

In general it is quite dangerous to think of English in terms of the rules of formal logic, and it is quite dangerous to think of formal logic in terms of the English language semantics of the terms we use to describe it. If you want to simplify these horrible sentences, a better way would be to read it several times to make sure you fully understand it, and then write down "what it means" without directly referring to the sentence itself. (Then maybe compare the sentences to make sure you have written a sentence with the same meaning).

These can't be simplified by the use of eliminating double negation, but the number of negatives can be reduced by applying the axiom of contrapositives

To address your first example, "A does not B unless C is true" is equivalent to "A only does B if C is true". To put that in formal logic for you:

Let D (for A'd oes' B) be the proposition "A does B", and let C be the proposition "C is true".

"¬D unless C" can clearly be rewritten "Without C, ¬D", or in more logical notation

¬C -> ¬D

By the rule of contrapositives, this is equivalent to

D -> C

Which we can read as "D implies C", or "if D happens then C must be true", or "If A does D then C is true", or "A only does D if C is true".

So to rewrite your first example,

...a statute does not impose criminal liability without the need for proof of mens rea unless it specifies explicitly that that is what it is doing.

becomes

...a statute only imposes criminal liability without the need for proof of mens rea if it specifies explicitly that that is what it is doing.

Here "A" is a statute, "D" is imposes criminal liability without the need for proof of mens rea and "C" is "it specifies explicitly that that is what it is doing".

In general it is quite dangerous to think of English in terms of the rules of formal logic, and it is quite dangerous to think of formal logic in terms of the English language semantics of the terms we use to describe it. If you want to simplify these horrible sentences, a better way would be to read it several times to make sure you fully understand it, and then write down "what it means" without directly referring to the sentence itself. (Then maybe compare the sentences to make sure you have written a sentence with the same meaning).

1
source | link

These can't be simplified by the use of eliminating double negation, but the number of negatives can be reduced by applying the axiom of contrapositives

To address your first example, "A does not B unless C is true" is equivalent to "A only does B if C is true". To put that in formal logic for you:

Let B be the proposition "A does B", and let C be the proposition "C is true".

"¬B unless C" can clearly be rewritten "Without C, ¬B", or in more logical notation

¬C -> ¬B

By the rule of contrapositives, this is equivalent to

B -> C

Which we can read as "B implies C", or "if B happens then C must be true", or "If A does B then C is true", or "A only does B if C is true".

So to rewrite your first example,

...a statute does not impose criminal liability without the need for proof of mens rea unless it specifies explicitly that that is what it is doing.

becomes

...a statute only imposes criminal liability without the need for proof of mens rea if it specifies explicitly that that is what it is doing.

Here "A" is a statute, "B" is imposes criminal liability without the need for proof of mens rea and "C" is "it specifies explicitly that that is what it is doing".

In general it is quite dangerous to think of English in terms of the rules of formal logic, and it is quite dangerous to think of formal logic in terms of the English language semantics of the terms we use to describe it. If you want to simplify these horrible sentences, a better way would be to read it several times to make sure you fully understand it, and then write down "what it means" without directly referring to the sentence itself. (Then maybe compare the sentences to make sure you have written a sentence with the same meaning).