Canonical Form of Born-Infeld Inspired Gravity Coupled to Scalar Fields

In this short note we find canonical form of Born-Infeld inspired gravity coupled to scalar fields using Faddeev-Jackiw approach. We show that canonical form of the action splits into two parts: First part has the same form as General Relativity canonical action while the matter part has complicated form as a consequence of the structure of Born-Infeld gravity action.