Propositional Dynamic Logic with Program Quantifiers
نویسنده
چکیده
We consider an extension QPDL of Segerberg-Pratt’s Propositional Dynamic Logic PDL, with program quantification, and study its expressive power and complexity. A mild form of program quantification is obtained in the calculus μPDL, extending PDL with recursive procedures (i.e. context free programs), which is known to be Π 1 -complete. The unrestricted program quantification we consider leads to complexity equivalent to that of second-order logic (and second-order arithmetic), i.e. outside the analytical hierarchy. However, the deterministic variant of QPDL has complexity Π 1 .
منابع مشابه
Idempotent Transductions for Modal Logics
We investigate the extension of modal logics by bisimulation quantifiers and present a class of modal logics which is decidable when augmented with bisimulation quantifiers. These logics are refered to as the idempotent transduction logics and are defined using the programs of propositional dynamic logic including converse and tests. This is a nontrivial extension of the decidability of the pos...
متن کاملAn Arithmetical Hierarchy in Propositional Dynamic Logic
Propositional dynamic logic (PDL), as introduced by Fischer and Ladner (1979) is the propositional part of the dynamic logic of Pratt (1976). Our aim in this paper is to answer a basic question: Does every alternation of modalities add to the expressive power of the logic? We give a positive answer to the question by building models where modalities behave (somewhat) like quantifiers in first-o...
متن کاملEquality propositional logic and its extensions
We introduce a new formal logic, called equality propositional logic. It has two basic connectives, $boldsymbol{wedge}$ (conjunction) and $equiv$ (equivalence). Moreover, the $Rightarrow$ (implication) connective can be derived as $ARightarrow B:=(Aboldsymbol{wedge}B)equiv A$. We formulate the equality propositional logic and demonstrate that the resulting logic has reasonable properties such a...
متن کاملCompleteness of second-order propositional S4 and H in topological semantics
We add propositional quantifiers to the propositional modal logic S4 and to the propositional intuitionsitic logic H, introducing axiom schemes that are the natural analogs to axiom schemes typically used for first-order quantifiers in classical logic. We show that the resulting logics are sound and complete for a topological semantics extending, in a natural way, the topological semantics for ...
متن کاملDecidability of Quantified Propositional Intuitionistic Logic and S4 on Trees of Height and Arity ≤ω
Quantified propositional intuitionistic logic is obtained from propositional intuitionistic logic by adding quantifiers ∀p, ∃p, where the propositional variables range over upward-closed subsets of the set of worlds in a Kripke structure. If the permitted accessibility relations are arbitrary partial orders, the resulting logic is known to be recursively isomorphic to full second-order logic (K...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Electr. Notes Theor. Comput. Sci.
دوره 218 شماره
صفحات -
تاریخ انتشار 2008