The evolutionary history of languages can be modeled as a tree, called a phylogeny, where the leaves represent the extant languages, the internal vertices represent the ancestral languages, and the edges represent the genetic relations between the languages. Languages not only inherit characteristics from their ancestors but also sometimes borrow them from other languages. Such borrowings can be represented by additional non-tree edges. This paper addresses the problem of computing a small number of additional edges that turn a phylogeny into a "perfect phylogenetic network". To solve this problem, we use answer set programming, which represents a given computational problem as a logic program whose answer sets correspond to solutions. Using the answer set solver SMODELS, with some heuristics and optimization techniques, we have generated a few conjectures regarding the evolution of Indo-European languages.
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