FILO -- automated unification in $mathcal{FL}_0$
This paper addresses the unifiability decision problem for the description logic $mathcal{FL}_0$. We present the first fully automated, executable Java tool dedicated to this task. The method leverages $mathcal{FL}_0$’s syntactic and semantic properties to design novel algorithms for symbolic normalization, pattern matching, and variable constraint propagation—operating entirely without external solvers. Given any pair of $mathcal{FL}_0$ concepts, the tool correctly decides unifiability and, if affirmative, constructs an explicit unifier. It is the first $mathcal{FL}_0$-specific tool supporting TBox-free pure concept unification with guaranteed completeness in unifier construction. By bridging a longstanding gap in the automated reasoning toolchain for $mathcal{FL}_0$, it complements existing systems such as UEL and FL0wer. Empirical evaluation on standard benchmark suites confirms both theoretical completeness and practical efficiency.