translate {admisc} | R Documentation |
This function interprets an expression written in a SOP - sum of products form (or in the canonical DNF - disjunctive normal form), in both crisp and multivalue sets notation. The expression is translated into a standard SOP matrix.
For crisp sets notation, upper case letters are considered the presence of a causal condition, and lower case letters are considered the absence of the respective causal condition. Tilde is recognized as a negation, even in combination with upper/lower letters.
translate(expression = "", snames = "", noflevels = NULL, data = NULL, ...)
expression |
String: a QCA expression written in sum of products form. |
snames |
A string containing the sets' names, separated by commas. |
noflevels |
Numerical vector containing the number of levels for each set. |
data |
A dataset with binary cs, mv and fs data. |
... |
Other arguments, mainly for backwards compatibility. |
An expression written in SOP - sum of products, is a "union of intersections", for example
A*B + B*c
. The DNF - disjunctive normal form is also a sum of products, with
the restriction that each product has to contain all literals. The equivalent expression is:
A*B*c + A*B*c + a*B*c
.
The same expression can be written in multivalue notation: A{1}*B{1} + B{1}*C{0}
.
Both types of expressions are valid, and yield the same result matrix.
For multivalue notation, causal conditions are expected and will be converted to upper case
by default. Expressions can contain multiple values to translate, separated by a comma. If B was
a multivalue causal condition, an expression could be: A{1} + B{1,2}*C{0}
.
In this example, all values in B equal to either 1 or 2 will be converted to 1, and the rest of the (multi)values will be converted to 0.
This function automatically detects the use of tilde “~
” as a negation for a particular
causal condition. ~A
does two things: it identifies the presence of causal
condition A
(because it was specified as upper case) and it recognizes that it
must be negated, because of the tilde. It works even combined with lower case names:
~a
, which is interpreted as A
.
To negate a multivalue condition using a tilde, the total number of levels should be supplied
(see examples below), and it works even for intersections between multiple levels of the same
causal condition. For a causal condition with 3 levels (0, 1 and 2) the following expression
~A{0,2}*A{1,2}
is equivalent with A{1}
, while A{0}*A{1}
results in the empty set.
The number of levels, as well as the set names can be automatically detected from a dataset via
the argument data
. Arguments snames
and noflevels
have
precedence over data
, when specified.
The use of the product operator *
is redundant when the set names are single
letters (for example AD + Bc
), and is also redundant for multivalue data, where
product terms can be separated by using the curly brackets notation.
When conditions are binary and their names have multiple letters (for example
AA + CC*bb
), the use of the product operator *
is preferable but the
function manages to translate an expression even without it (AA + CCbb
) by searching
deep in the space of the conditions' names, at the cost of slowing down for a high number of causal
conditions. For this reason, an arbitrary limit of 7 causal snames
is imposed, to
write an expression.
A matrix containing the implicants on the rows and the set names on the columns, with the following codes:
0 | absence of a causal condition |
1 | presence of a causal condition |
-1 | causal condition was eliminated |
The matrix was also assigned a class "translate", to avoid printing the -1 codes when signaling a minimized condition. The mode of this matrix is character, to allow printing multiple levels in the same cell, such as "1,2".
Adrian Dusa
translate("A + B*C") # same thing in multivalue notation translate("A{1} + B{1}*C{1}") # using upper/lower letters translate("A + b*C") # the negation with tilde is recognised translate("~A + b*C") # even in combination of upper/lower letters translate("~A + ~b*C") # and even for multivalue variables # in multivalue notation, the product sign * is redundant translate("C{1} + T{2} + T{1}V{0} + C{0}") # negation of multivalue sets requires the number of levels translate("~A{1} + ~B{0}*C{1}", snames = "A, B, C", noflevels = c(2, 2, 2)) # multiple values can be specified translate("C{1} + T{1,2} + T{1}V{0} + C{0}") # or even negated translate("C{1} + ~T{1,2} + T{1}V{0} + C{0}", snames = "C, T, V", noflevels = c(2,3,2)) # if the expression does not contain the product sign * # snames are required to complete the translation translate("AB + cD", snames = "A, B, C, D") # otherwise snames are not required translate("PER*FECT + str*ing") # snames are required translate("PERFECT + string", snames = "PER, FECT, STR, ING") # it works even with overlapping columns # SU overlaps with SUB in SUBER, but the result is still correct translate("SUBER + subset", "SU, BER, SUB, SET") # to print _all_ codes from the standard output matrix (obj <- translate("A + b*C")) print(obj, original = TRUE) # also prints the -1 code