2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/145382We present a tableau-based algorithm for deciding satisfiability for propositional dynamic logic (PDL) which builds a finite rooted tree with ancestor loops and passes extra information from children to parents to separate good loops from bad loops during backtracking. It is easy to implement, with potential for parallelisation, because it constructs a pseudo-model ``on the fly'' by exploring each tableau branch independently. But its worst-case behaviour is 2EXPTIME rather than EXPTIME. A prototype implementation in the TWB (http://twb.rsise.anu.edu.au) is available.26 pages, longer version of article in Methods for Modalities 2007; improved readability of proofsLogic in Computer Sciencetext