A Simplest Undecidable Modal Logic
نویسندگان
چکیده
Modal logics are widely used in computer science. The complexity of their satisfiability problems has been an active field of research since the 1970s. We prove that even very “simple” modal logics can be undecidable: We show that there is an undecidable modal logic that can be obtained by restricting the allowed models with a first-order formula in which only universal quantifiers appear.
منابع مشابه
Undecidability of Compass Logic
It is known that the tiling technique can be used to give simple proofs of unde-cidability of various two-dimensional modal and temporal logics. However, up until now, the simplest two-dimensional temporal logic, the compass logic of Venema, has eluded such treatment. We present a new coding of an enumeration of the tiling plane which enables us to show that the compass logic is undecidable.
متن کاملProving the Decidability of the Pdl×pdl Product Logic
The propositional dynamic logic (PDL) is an adequate tool to write down programs. In a previous article we used PDL to formulate cryptographic protocols as parallel programs. In these protocols at least two agents/individuals exchange messages, so we needed to use product logic to formulate the parallel actions. Ágnes Kurucz proved that S5×S5×S5 — which is the simplest triple product logic — is...
متن کاملUndecidability of first-order intuitionistic and modal logics with two variables
We prove that the two-variable fragment of first-order intuitionistic logic is undecidable, even without constants and equality. We also show that the twovariable fragment of a quantified modal logic L with expanding first-order domains is undecidable whenever there is a Kripke frame for L with a point having infinitely many successors (such are, in particular, the first-order extensions of pra...
متن کاملLinear Logic as a Logic of Computations
The question at issue is to develop a computational interpretation of Linear Logic [S] and to establish exactly its expressive power. We follow the bottom-up approach. This involves starting with the simplest of the systems we are interested in, and then expanding them step-by-step. We begin with the !-Horn fragment of Linear Logic, which uses only positive literals, the linear implication -, t...
متن کاملBounded Petri Net Synthesis from Modal Transition Systems is Undecidable
In this paper, the synthesis of bounded Petri nets from deterministic modal transition systems is shown to be undecidable. The proof is built from three components. First, it is shown that the problem of synthesising bounded Petri nets satisfying a given formula of the conjunctive nucalculus (a suitable fragment of the mu-calculus) is undecidable. Then, an equivalence between deterministic moda...
متن کاملذخیره 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 ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1105.0845 شماره
صفحات -
تاریخ انتشار 2011