Parameterized Dynamic Logic -- Towards A Cyclic Logical Framework for General Program Specification and Verification

Dynamic logic and its variations, because of their clear and expressive forms for capturing program properties, have been used as formalisms in program/system specification and verification for years and have many other applications. The program models of dynamic logics are in explicit forms. For different target program models, different dynamic logic theories have to be proposed to adapt different models' semantics. In this paper, we propose a parameterized `dynamic-logic-style' formalism, namely $DL_p$, for specifying and reasoning about general program models. In $DL_p$, program models and logical formulas are taken as `parameters', allowing arbitrary forms according to different interested domains. This characteristic allows $DL_p$ to support direct reasoning based on the operational semantics of program models, while still preserving compositional reasoning based on syntactic structures. $DL_p$ provides a flexible verification framework to encompass different dynamic logic theories. In addition, it also facilitates reasoning about program models whose semantics is not compositional, examples are neural networks, automata-based models, synchronous programming languages, etc. We mainly focus on building the theory of $DL_p$, including defining its syntax and semantics, building a proof system and constructing a cyclic preproof structure. We analyze and prove the soundness of $DL_p$. Case studies show how $DL_p$ works for reasoning about different types of program models.