Decidability and Undecidability Results for Propositional Schemata
نویسندگان
چکیده
We define a logic of propositional formula schemata adding to the syntax of propositional logic indexed propositions (e.g., pi) and iterated connectives ∨ or ∧ ranging over intervals parameterized by arithmetic variables (e.g., ∧n i=1 pi, where n is a parameter). The satisfiability problem is shown to be undecidable for this new logic, but we introduce a very general class of schemata, called bound-linear, for which this problem becomes decidable. This result is obtained by reduction to a particular class of schemata called regular, for which we provide a sound and complete terminating proof procedure. This schemata calculus (called stab) allows one to capture proof patterns corresponding to a large class of problems specified in propositional logic. We also show that the satisfiability problem becomes again undecidable for slight extensions of this class, thus demonstrating that bound-linear schemata represent a good compromise between expressivity and decidability.
منابع مشابه
Program Schemata vs. Automata for Decidability of Program Logics
A new technique for decidability of program logics is introduced. This technique is applied to the most expressive propositional program logic Mu-Calculus.
متن کاملPropositional interval neighborhood logics: Expressiveness, decidability, and undecidable extensions
In this paper, we investigate the expressiveness of the variety of propositional interval neighborhood logics (PNL), we establish their decidability on linearly ordered domains and some important sub-classes, and we prove undecidability of a number of extensions of PNL with additional modalities over interval relations. All together, we show that PNL form a quite expressive and nearly maximal d...
متن کاملA New Proof of Exponential Decidability for the Propositional -calculus with Program Converse
The propositional-Calculus (C) is a powerful propositional program logic with xpoints. C decidability with exponential upper bound was sketched for the rst time in 1988 by E. A. Emerson and Ch. S. Jutla on base of automata-theoretic technique, while a complete proof was published in 1999 only. Meanwhile M. Vardi sketched in 1998 an automata-theoretic proof of exponential decidability for the pr...
متن کاملGame Theoretic Decidability and Undecidability∗
We study the possibility of prediction/decision making in a finite 2—person game with pure strategies, following the Nash(-Johansen) noncooperative solution theory. We adopt the epistemic logic KD as the base logic to capture individual decision making from the viewpoint of logical inference. Since some infinite regresses naturally arise in this theory, we use a fixed-point extension EIR of KD ...
متن کاملUndecidability of a Very Simple Modal Logic with Binding
We show undecidability of the satisfiability problem of what is arguably the simplest non-sub-Boolean modal logic with an implicit notion of binding. This work enriches the series of existing results of undecidability of modal logics with binders, which started with Hybrid Logics and continued with Memory Logics. 1 Modal Logics, Names and Binders Modal Logics are languages that are able to desc...
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:
- J. Artif. Intell. Res.
دوره 40 شماره
صفحات -
تاریخ انتشار 2011