Decidable Fragments of First-Order Modal Logics

نویسندگان

  • Frank Wolter
  • Michael Zakharyaschev
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.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Decidable and Undecidable Fragments of First-Order Branching Temporal Logics

In this paper we analyze the decision problem for fragments of first-order extensions of branching time temporal logics such as computational tree logics CTL and CTL or Prior’s Ockhamist logic of historical necessity. On the one hand, we show that the one-variable fragments of logics like first-order C T L —such as the product of propositional C T L with simple propositional modal logic S5, or ...

متن کامل

Decidable first-order modal logics with counting quantifiers

In this paper, we examine the computational complexity of various natural onevariable fragments of first-order modal logics with the addition of arbitrary counting quantifiers. The addition of counting quantifiers provides us a rich language with which to succinctly express statements about the quantity of objects satisfying a given property, using only a single variable. We provide optimal upp...

متن کامل

Decidable fragments of rst-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 کامل

Decidable and Undecidable Logics with a Binary Modality

We give an overview of decidability results for modal logics having a binary modality. We put an emphasis on the demonstration of proof-techniques, and hope that this will also help in finding the borderlines between decidable and undecidable fragments of usual first-order logic.

متن کامل

Dynamic Odds & Ends

Modal logic becomes action logic by adding programs as in propositional dynamic logic or the μ– calculus. Modal languages can be seen as decidable fragments of first-order logic that admit a natural bisimulation, and hence enjoy a good model theory. Recently, much stronger 'guarded fragments' of firstorder logic have been identified that enjoy the same pleasant features. The latter can serve as...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • J. Symb. Log.

دوره 66  شماره 

صفحات  -

تاریخ انتشار 2001