Bingtian Xue

Adequacy and Complete Axiomatization for Timed Modal Logic

In this paper we develop the metatheory for Timed Modal Logic (TML), which is the modal logic used for the analysis of timed transition systems (TTSs). We solve a series of long-standing open problems related to TML. Firstly, we prove that TML enjoys the Hennessy-Milner property and solve one of the open questions in the field. Secondly, we prove that the set of validities are not recursively enumerable. Nevertheless, we develop a strongly-complete proof system for TML. Since the logic is not compact, the proof system contains infinitary rules, but only with countable sets of instances. Thus, we can involve topological results regarding Stone spaces, such as the Rasiowa-Sikorski lemma, to complete the proofs.

On decidability of recursive weighted logics

In this paper, we develop and study two recursive weighted logics (RWLs)

WNetKAT: A Weighted SDN Programming and Verification Language

\mathcal {L}^w

Concurrent weighted logic

Lw and

Probabilistic Mu-Calculus: Decidability and Complete Axiomatization

\mathcal {L}^t

Decidability and Expressiveness of Recursive Weighted Logic

Lt, which are multi-modal logics that express qualitative and quantitative properties of labelled weighted transition systems (LWSs). LWSs are transition systems describing systems with quantitative aspects. They have labels with both actions and real-valued quantities representing the costs of transitions with respect to various resources. RWLs use first-order variables to measure local costs. The main syntactic operators are similar to the ones of timed logics for real-time systems.