A Polynomial Translation from the Two-Variable Guarded Fragment with Number Restrictions to the Guarded Fragment
نویسنده
چکیده
We consider a two-variable guarded fragment with number restrictions for binary relations and give a satisfiability preserving transformation of formulas in this fragment to the three-variable guarded fragment. The translation can be computed in polynomial time and produces a formula that is linear in the size of the initial formula even for the binary coding of number restrictions. This allows one to reduce reasoning problems for many description logics to the satisfiability problem for the guarded fragment.
منابع مشابه
A Suggestion for an n-ary Description Logic
A restriction most Description Logics (DLs) have in common with most Modal Logics is their restriction to unary and binary predicates. To our knowledge, the only DLs that overcome these restrictions and allow for arbitrary n-ary relations are NaryKandor 8] and the very expressive DL DLR 2]. In the eld of Modal Logics, there are two generali-sations that allow for n-ary predicates: Polyadic Moda...
متن کاملA Suggestion for an n - ary Description
A restriction most Description Logics (DLs) have in common with most Modal Logics is their restriction to unary and binary predicates. To our knowledge, the only DLs that overcome these restrictions and allow for arbitrary n-ary relations are NaryKandor 8] and the very expressive DL DLR 2]. In the eld of Modal Logics, there are two generali-sations that allow for n-ary predicates: Polyadic Moda...
متن کاملOn the complexity of the two-variable guarded fragment with transitive guards
We investigate the complexity of the satisfiability problem for the two-variable guarded fragment with transitive guards.We prove that the satisfiability problem for the monadic version of this logic without equality is 2EXPTIME-hard. It is in fact 2EXPTIME-complete, since as shown by Szwast and Tendera, the whole guarded fragment with transitive guards is in 2EXPTIME.We also introduce a new lo...
متن کاملOne-dimensional Fragment of First-order Logic
We introduce a novel decidable fragment of first-order logic. The fragment is one-dimensional in the sense that quantification is limited to applications of blocks of existential (universal) quantifiers such that at most one variable remains free in the quantified formula. The fragment is closed under Boolean operations, but additional restrictions (called uniformity conditions) apply to combin...
متن کاملOn The Restraining Power of Guards
Guarded fragments of rst-order logic were recently introduced by Andr eka, van Benthem and N emeti; they consist of relational rst-order formulae whose quantiiers are appropriately relativized by atoms. These fragments are interesting because they extend in a natural way many propositional modal logics, because they have useful model-theoretic properties and especially because they are decidabl...
متن کامل