Decidable fragments of rst-order modal logics
نویسندگان
چکیده
The paper considers the set ML1 of rst-order polymodal formulas the modal operators in which can be applied to subformulas of at most one free variable. Using the mosaic technique, we prove a general satissability criterion for formulas in ML1 which reduces the modal satissability to the classical one. The criterion is then used to single out a number of new, in a sense optimal, decidable fragments of various predicate modal logics.
منابع مشابه
Decidable Fragments of First-Order Modal Logics
The paper considers the set ML1 of rst-order polymodal formulas the modal operators in which can be applied to subformulas of at most one free variable. Using the mosaic technique, we prove a general satissability criterion for formulas in ML1 which reduces the modal satissability to the classical one. The criterion is then used to single out a number of new, in a sense optimal, decidable fragm...
متن کاملTowards First-Order Nonmonotonic Reasoning
We investigate the problem of reasoning in nonmonotonic extensions of rst-order logic. In particular, we study reasoning in rst-order MKNF, the modal logic of minimal knowledge and negation as failure introduced by Lifschitz. MKNF can be considered as a unifying framework for several nonmonotonic formalisms, including default logic, autoepistemic logic, circumscription, and logic programming. B...
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 کاملFirst Order Common Knowledge Logics
In this paper we investigate rst order common knowledge logics; i.e., modal epistemic logics based on rst order logic with common knowledge operators. It is shown that even rather weak fragments of rst order common knowledge logics are not recursively axiomatizable. This applies, for example, to fragments which allow to reason about names only; that is to say, fragments the rst order part of wh...
متن کاملFusions of Modal Logics Revisited
The fusion Ll Lr of two normal modal logics formulated in languages with disjoint sets of modal operators is the smallest normal modal logic containing Ll [ Lr. This paper proves that decidability, interpolation, uniform interpolation, and Halld encompleteness are preserved under forming fusions of normal polyadic polymodal logics. Those problems remained open in [Fine & Schurz [3]] and [Kracht...
متن کامل