Proving the Decidability of the Pdl×pdl Product Logic

The propositional dynamic logic (PDL) is an adequate tool to write down programs. In a previous article we used PDL to formulate cryptographic protocols as parallel programs. In these protocols at least two agents/individuals exchange messages, so we needed to use product logic to formulate the parallel actions. Ágnes Kurucz proved that S5×S5×S5 — which is the simplest triple product logic — is undecidable, hence it follows that PDL×PDL×PDL is undecidable, too. It is easy to show that the PDL logic (without the star operator) is decidable, so it is an interesting problem, that the PDL×PDL product logic is decidable or not.