Episodic Logic: Unscoped Logical Form'' (EL-ULF) is a semantic representation capturing predicate-argument structure as well as more challenging aspects of language within the Episodic Logic formalism. We present the first learned approach for parsing sentences into ULFs, using a growing set of annotated examples. The results provide a strong baseline for future improvement. Our method learns a sequence-to-sequence model for predicting the transition action sequence within a modified cache transition system. We evaluate the efficacy of type grammar-based constraints, a word-to-symbol lexicon, and transition system state features in this task. Our system is available at https://github.com/genelkim/ulf-transition-parser. We also present the first official annotated ULF dataset at https://www.cs.rochester.edu/u/gkim21/ulf/resources/.