In this paper, we present a novel temporal logic, the nonmonotonic extension of Here-and-There logic, to address the difficulty of reasoning about fine-grained temporal and numerical resolution dynamical systems using logic-based approaches such as Answer Set Programming (ASP). It combines the linear temporal logic Here-and-There, an existing ASP extension, with the constraint-containing Here-and-There logic, enabling direct integration and manipulation of nonmonotonic temporal reasoning and numerical constraints. The presented scheme establishes a basic logical framework for handling high-resolution complex dynamical systems within the ASP paradigm.
