minimalizeCsf eliminates structural redundancies from complex solution formulas (csf) by recursively testing their component atomic solution formulas (asf) for redundancy and eliminating the redundant ones.
minimalizeCsf(x, ...) ## Default S3 method: minimalizeCsf(x, ct = NULL, verbose = FALSE, ..., data) ## S3 method for class 'cna' minimalizeCsf(x, n = 20, verbose = FALSE, ...)
In the default method,
Data frame, matrix or
Minimal number of csf to use.
Further arguments passed to the methods.
As of version 3.0 of the cna package, the function
minimalizeCsf is automatically executed, where needed, by the default calls of the
csf functions. In consequence, applying the stand-alone
minimalizeCsf function to an output object of
cna is no longer required. The stand-alone function is kept in the package for reasons of backwards compatibility and for developing purposes. Its automatic execution can be suppressed by calling
minimalizeCsf = FALSE, which emulates outputs of older versions of the package.
The core criterion that Boolean dependency structures must satisfy in order to be causally interpretable is redundancy-freeness. In atomic solution formulas (asf), both sufficient and necessary conditions are completely free of redundant elements. However, when asf are conjunctively combined to complex solution formulas (csf), new redundancies may arise. A csf may contain redundant parts. To illustrate, assume that a csf is composed of three asf: asf1 * asf2 * asf3. It can happen that the conjunction asf1 * asf2 * asf3 is logically equivalent to a proper part of itself, say, to asf1 * asf2. In that case, asf3 is a so-called structural redundancy in asf1 * asf2 * asf3 and must not be causally interpreted. See the package vignette (
vignette("cna")) or Baumgartner and Falk (2019) for more details.
minimalizeCsf recursively tests the
asf contained in a
csf for structural redundancies and eliminates the redundant ones. It takes a character vector
x specifying csf as input and builds all redundancy-free csf that can be inferred from
x. There are two possibilities to use
minimalizeCsf. Either the csf to be tested for structural redundancies is passed to
minimalizeCsf as a character vector (this is the default method), or
minimalizeCsf is applied directly to the output of
cna—which however, as indicated above, is superfluous as of version 3.0 of the cna package.
As a test for structural redundancies amounts to a test of logical equivalencies, it must be conducted relative to all logically possible configurations of the factors in
x. That space of logical possibilities is generated by
full.ct(x) if the
ct argument takes its default value. If all factors in
x are binary, providing a non-default
ct value is optional and without influence on the output of
minimalizeCsf. If some factors in
x are multi-value,
minimalizeCsf needs to be given the range of these values by means of the
ct can be a data frame or
configTable listing all possible value configurations.
minimalizeCsf returns an object of class "minimalizeCsf", essentially a data frame.
Falk, Christoph: identification and solution of the problem of structural redundancies
Baumgartner, Michael and Christoph Falk. 2019. “Boolean Difference-Making: A Modern Regularity Theory of Causation”. The British Journal for the Philosophy of Science.
# The default method. minimalizeCsf("(f + a*D <-> C)*(C + A*B <-> D)*(c + a*E <-> F)") minimalizeCsf("(f + a*D <-> C)*(C + A*B <-> D)*(c + a*E <-> F)", verbose = TRUE) # Same result, but with some messages. # The cna method. dat1 <- selectCases("(C + A*B <-> D)*(c + a*E <-> F)") ana1 <- cna(dat1, details = c("r"), inus.only = FALSE) csf(ana1, minimalizeCsf = FALSE) # The attribute "redundant" taking the value TRUE in ana1 shows that this csf contains # at least one redundant element. Applying minimalizeCsf() identifies and removes # the redundant element. minimalizeCsf(ana1)
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