This paper proposes two methods for realising automated reasoning about agent-based systems. The framework for modelling intelligent agent behaviour that we focus on is a core of KARO logic, an expressive combination of various modal logics including propositional dynamic logic, a modal logic of knowledge, a modal logic of wishes, and additional non-standard operators. The first method we present is based on a translation of core KARO logic to first-order logic combined with first-order resolution. The second method uses an embedding of core KARO logic into a combination of branching-time temporal logic $\ml{CTL}$ and multi-modal $\ml{S5}$ plus a clausal resolution calculus for these combined logics. We discuss the advantages and shortcomings of each approach and suggest ways to extend each variant to cover more of the KARO framework.