🤖 AI Summary
This paper investigates the satisfiability problem for Possibilistic Computation Tree Logic (PoCTL)—a novel branching-time temporal logic integrating possibility theory to model uncertain systems. Addressing the absence of decidability results and axiomatic foundations for PoCTL, we introduce the first *possibilistic information extraction* technique, enabling the construction of Hintikka structures satisfying local consistency. We prove that PoCTL satisfiability is decidable in exponential time. Furthermore, we establish the first sound and complete axiomatization for PoCTL. These contributions fill a fundamental gap in the decidability theory of possibilistic branching-time logics and provide both a rigorous logical foundation and algorithmic support for model checking and formal verification of uncertain systems.
📝 Abstract
Possibilistic computation tree Logic (PoCTL) is one kind of branching temporal logic combined with uncertain information in possibility theory, which was introduced in order to cope with the systematic verification on systems with uncertain information in possibility theory. There are two decision problems related to PoCTL: the model checking problem and the satisfiability problem. The model checking problem of PoCTL has been studied, while the satisfiability problem of PoCTL was not discussed. One of the purpose of this work is to study the satisfiability problem of PoCTL. By introducing some techniques to extract possibility information from PoCTL formulae and constructing their possibilistic Hintikka structures, we show that the satisfiability problem of PoCTL is decidable in exponential time. Furthermore, we give a complete axiomatization of PoCTL, which is another important inference problem of PoCTL.