Answer Set Programming (ASP), a well-known declarative programming paradigm, has recently found practical application in Process Mining, particularly in tasks involving declarative specifications of business processes. Declare is the most popular declarative process modeling language. It provides a way to model processes by sets of constraints, expressed in Linear Temporal Logic (LTL), that valid traces must satisfy. Existing ASP-based solutions encode a Declare constraint by the corresponding LTL formula or its equivalent automaton, derived using well-established techniques. In this paper, we propose a novel encoding for Declare constraints, which models their semantics directly as ASP rules, without resorting to intermediate representations. We evaluate the effectiveness of the novel approach on two Process Mining tasks by comparing it to alternative ASP encodings and a Python library for Declare.