Nothing

```
.generalization <- function(LHS, RHS, attributes) {
# A -> B and C -> D,
# with A subset of C (axiom C -> A)
# and D subset of B (axiom B -> D)
# => remove C -> D
RHS_subsets <- .subset(RHS)
LHS_subsets <- Matrix::t(.subset(LHS))
ALL_subsets <- LHS_subsets & RHS_subsets
# Find A subset of C
condition1 <- Matrix::colSums(ALL_subsets) > 1
subsets <- Matrix::which(condition1)
marked_as_single <- rep(TRUE, ncol(LHS))
if (length(subsets) > 0) {
for (k in seq_along(subsets)) {
# Index for A -> B
this_row <- subsets[k]
if (!marked_as_single[this_row]) next
# Select C -> D with A subset of C and B superset of D
idx_subset <- which_at_col(ALL_subsets@i,
ALL_subsets@p,
this_row)
idx_subset <- setdiff(idx_subset, this_row)
marked_as_single[idx_subset] <- FALSE
}
}
# Add singles
singles <- which(marked_as_single)
LHS <- LHS[, singles]
RHS <- RHS[, singles]
return(list(lhs = Matrix::Matrix(LHS, sparse = TRUE),
rhs = Matrix::Matrix(RHS, sparse = TRUE)))
}
```

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