Problem　Solver　Markup　Language　constructed　by　combining　OWL　and　Horn　clauses　are　studied.　The　existential　entailment　algorithm　for　the　decidable　description　logic　is　described.　In　a　nonrecursive　case,　it　is　shown　that　a　single　step　of　applying　a　Horn　clause　needs　to　be　replaced　by　a　more　sophisticated　reasoning　step　in　β-PSML.　This　step　is　isolated　and　referred　to　as　existential　entailment.　The　existential　entailment　problem　is　to　decide　whether　the　antecedent　of　a　Horn　clause,　together　with　a　description　logic　terminology,　logically　entail　the　disjunction　of　the　antecedents　of　a　set　of　Horn　clauses.