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In Conradie, Goranko, and Vakarelov (2006, Logical Methods in Computer Science, 2) we introduced a new algorithm, SQEMA, for computing first-order equivalents and proving the canonicity of modal formulae of the basic modal language. Here we extend SQEMA, first to arbitrary and reversive polyadic modal languages, and then to hybrid polyadic languages too. We present the algorithm, illustrate it with some examples, and prove its correctness with respect to local equivalence of the input anddoi:10.1093/logcom/exl026 fatcat:eepiz3dtjfdfhjjmwo3i735lou