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This work provides proof-search algorithms and automated counter-model extraction for a class of logics. With this, we answer an open problem concerning syntactic decision procedures and cut-free calculi for logics. A new class of cut-free complete labelled sequent calculi , for multi-agent with at most n-many choices, is introduced. We refine the calculi through the use of propagation rules and demonstrate the admissibility of their structural rules, resulting in the auxiliary calculi . In the single-agent case, we show that the refined calculi derive theorems within a restricted class of (forestlike) sequents, allowing us to provide proof-search algorithms that decide single-agent logics. We prove that the proof-search algorithms are correct and terminate.