Optimal Tableau Decision Procedures for PDL
نویسندگان
چکیده
We reformulate Pratt’s tableau decision procedure of checking satisfiability of a set of formulas in PDL. Our formulation is simpler and more direct for implementation. Extending the method we give the first ExpTime (optimal) tableau decision procedure not based on transformation for checking consistency of an ABox w.r.t. a TBox in PDL (here, PDL is treated as a description logic). We also prove the new result that the data complexity of the instance checking problem in PDL is coNP-complete.
منابع مشابه
A Cut-Free ExpTime Tableau Decision Procedure for the Logic Extending Converse-PDL with Regular Inclusion Axioms
We give the first cut-free ExpTime (optimal) tableau decision procedure for the logic CPDLreg, which extends Converse-PDL with regular inclusion axioms characterized by finite automata. The logic CPDLreg is the combination of Converse-PDL and regular grammar logic with converse. Our tableau decision procedure uses global state caching and has been designed to increase efficiency and allow vario...
متن کاملChecking Consistency of an ABox w.r.t. Global Assumptions in PDL
We reformulate Pratt’s tableau decision procedure of checking satisfiability of a set of formulas in PDL. Our formulation is simpler and more direct for implementation. Extending the method we give the first ExpTime (optimal) tableau decision procedure not based on transformation for checking consistency of an ABox w.r.t. a TBox in PDL (here, PDL is treated as a description logic). We also prov...
متن کاملClausal Tableaux for Hybrid PDL
PDL (propositional dynamic logic) [6, 11, 8] is an expressive modal logic invented for reasoning about programs. It extends basic modal logic with expressions called programs. Programs describe relations from states to states and are used to express modalities. Programs are composed with the operators familiar from regular expressions. In addition, they may employ formulas so that conditionals ...
متن کاملCorrectness of an Incremental and Worst-Case Optimal Decision Procedure for Modal Logic with Eventualities
We present a simple theory explaining the construction and the correctness of an incremental and worst-case optimal decision procedure for modal logic with eventualities. The procedure gives an abstract account of important aspects of Goré and Widmann’s PDL prover. Starting from an input formula, the procedure grows a Pratt-style graph tableau until the tableau proves or disproves the satisfiab...
متن کاملAn On-the-fly Tableau-based Decision Procedure for PDL-Satisfiability
We present a tableau-based algorithm for deciding satisfiability for propositional dynamic logic (PDL) which builds a finite rooted tree with ancestor loops and passes extra information from children to parents to separate good loops from bad loops during backtracking. It is easy to implement, with potential for parallelisation, because it constructs a pseudo-model “on the fly” by exploring eac...
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/0904.0721 شماره
صفحات -
تاریخ انتشار 2009