If you only need a mechanical conversion, then something like this might be a starting point

#! perl -sw
use strict;

my @stack;
while( <DATA> ) {
    print;
    s[NOT\s+][-]g;
    1 while s[(?<!\+)(\b\w+\b)\s+AND\s+][+$1 AND ]g
      or    s[\s+AND\s+(?<!\+)(\b\w+\b)][ AND +$1]g;
    s[\sAND\s][ ]g;
    s[\s+OR\s+][ ]g;
    print $_, $/;
}

__DATA__
word1 AND word2
word1 OR word2
word1 AND NOT word2
(word1 AND NOT word2) OR word3
word1 AND word2 AND word3
(word1 AND word2 OR word3) AND NOT (word4 OR word5)
(word1 AND (word2 OR (word3 AND word4 AND NOT word5)) AND word6) OR wo
+rd7
[download]

Output

D:\Perl\test>268325
word1 AND word2
+word1 +word2

word1 OR word2
word1 word2

word1 AND NOT word2
+word1 -word2

(word1 AND NOT word2) OR word3
(+word1 -word2) word3

word1 AND word2 AND word3
+word1 +word2 +word3

(word1 AND word2 OR word3) AND NOT (word4 OR word5)
(+word1 +word2 word3) -(word4 word5)

(word1 OR (word2 OR (word3 AND word4 AND NOT word5)) AND word6) OR wor
+d7
(word1 (word2 (+word3 +word4 -word5)) +word6) word7
[download]

If you want to syntax check the input before conversion then you have more work to do. Regexp::Common::balanced would be a good starting point for extracting the sub-expressions.

Might be fun to code, but it would need a much fuller explanation of what is leagal in the output format.

Eg. is -(sub condition) legal?

What about (+word1 +word2) (+word3 +word4)?

The toughest part is probably giving meaningful error messages when you encounter syntax errors.