The model checking problem for propositional intuitionistic logic with one variable is AC^1-complete
نویسندگان
چکیده
We investigate the complexity of the model checking problem for propositional intuitionistic logic. We show that the model checking problem for intuitionistic logic with one variable is complete for logspace-uniform AC1, and for intuitionistic logic with two variables it is P-complete. For superintuitionistic logics with one variable, we obtain NC1-completeness for the model checking problem and for the tautology problem. 1998 ACM Subject Classification F.2 Analysis of algorithms and problem complexity, F.4 Mathematical logic and formal languages
منابع مشابه
An Ac-complete Model Checking Problem for Intuitionistic Logic∗
We show that the model checking problem for intuitionistic propositional logic with one variable is complete for logspace-uniform AC1. The basic tool we use is the connection between intuitionistic logic and Heyting algebras, investigating its complexity theoretical aspects. For superintuitionistic logics with one variable, we obtain NC1-completeness for the model checking problem.
متن کاملThe model checking problem for intuitionistic propositional logic with one variable is AC1-complete
We show that the model checking problem for intuitionistic propositional logic with one variable is complete for logspace-uniform AC. As basic tool we use the connection between intuitionistic logic and Heyting algebra, and investigate its complexity theoretical aspects. For superintuitionistic logics with one variable, we obtain NC-completeness for the model checking problem.
متن کاملIntuitionistic implication makes model checking hard
We investigate the complexity of the model checking problem for intuitionistic and modal propositional logics over transitive Kripke models. More specific, we consider intuitionistic logic IPC, basic propositional logic BPL, formal propositional logic FPL, and Jankov’s logic KC. We show that the model checking problem is P-complete for the implicational fragments of all these intuitionistic log...
متن کاملTruth Values and Connectives in Some Non-Classical Logics
The question as to whether the propositional logic of Heyting, which was a formalization of Brouwer's intuitionistic logic, is finitely many valued or not, was open for a while (the question was asked by Hahn). Kurt Gödel (1932) introduced an infinite decreasing chain of intermediate logics, which are known nowadays as Gödel logics, for showing that the intuitionistic logic is not finitely (man...
متن کاملThe Complexity of Model Checking for Intuitionistic Logics and Their Modal Companions
We study the model checking problem for logics whose semantics are defined using transitive Kripke models. We show that the model checking problem is P-complete for the intuitionistic logic KC. Interestingly, for its modal companion S4.2 we also obtain P-completeness even if we consider formulas with one variable only. This result is optimal since model checking for S4 without variables is NC-c...
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:
دوره شماره
صفحات -
تاریخ انتشار 2011