A Tableau Method for Checking Rule Admissibility in S4
نویسندگان
چکیده
Rules that are admissible can be used in any derivations in any axiomatic system of a logic. In this paper we introduce a method for checking the admissibility of rules in the modal logic S4. Our method is based on a standard semantic ground tableau approach. In particular, we reduce rule admissibility in S4 to satisfiability of a formula in a logic that extends S4. The extended logic is characterised by a class of models that satisfy a variant of the co-cover property. The class of models can be formalised by a well-defined firstorder specification. Using a recently introduced framework for synthesising tableau decision procedures this can be turned into a sound, complete and terminating tableau calculus for the extended logic, and gives a tableau-based method for determining the admissibility of rules.
منابع مشابه
Rejecting inadmissible rules in reduced normal forms in S4
Several methods for checking admissibility of rules in the modal logic S4 are presented in [1], [15]. These methods determine admissibility of rules in S4, but they don’t determine or give substitutions rejecting inadmissible rules. In this paper, we investigate some relations between one of the above methods, based on the reduced normal form rules, and sets of substitutions which reject them. ...
متن کاملA Duplication and Loop Checking Free Proof System for S4
Most of the sequent/tableau based proof systems for the modal logic S4 need to duplicate formulas and thus are required to adopt some method of loop checking [7, 13, 10]. In what follows we present a tableau-like proof system for S4, based on D’Agostino and Mondadori’s classical KE [3], which is free of duplication and loop checking. The key feature of this system (let us call it KES4) consists...
متن کاملUnification in the normal modal logic Alt1
The unification problem in a logical system L can be defined in the following way: given a formula φ(x1, . . . , xα), determine whether there exists formulas ψ1, . . ., ψα such that φ(ψ1, . . . , ψα) is in L. The research on unification for modal logics was originally motivated by the admissibility problem for rules of inference: given a rule of inference φ1(x1, . . . , xα), . . . , φm(x1, . . ...
متن کاملTowards an Efficient Tableau Method for Boolean Circuit Satisfiability Checking
Boolean circuits offer a natural, structured, and compact representation of Boolean functions for many application domains. In this paper a tableau method for solving satisfiability problems for Boolean circuits is devised. The method employs a direct cut rule combined with deterministic deduction rules. Simplification rules for circuits and a search heuristic attempting to minimize the search ...
متن کاملSemi-analytic Tableaux For Propositional Modal Logics of Nonmonotonicity
The propositional monotonic modal logics K45, K45D, S4:2, S4R and S4F elegantly capture the semantics of many current nonmonotonic formalisms as long as (strong) de-ducibility of A from a theory ?; ? ` A; allows the use of necessitation on the members of ?: This is usually forbidden in modal logic where ? is required to be empty, resulting in a weaker notion of deducibility. Recently, Marek, Sc...
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:
- Electr. Notes Theor. Comput. Sci.
دوره 262 شماره
صفحات -
تاریخ انتشار 2010