Classical planning approaches guarantee finding a set of actions that can achieve a given goal state when possible, but require an expert to specify logical action semantics that govern the dynamics of the environment. Researchers have shown that Large Language Models (LLMs) can be used to directly infer planning steps based on commonsense knowledge and minimal domain information alone, but such plans often fail on execution. We bring together the strengths of classical planning and LLM commonsense inference to perform domain induction, learning and validating action pre- and post-conditions based on closed-loop interactions with the environment itself. We propose PSALM, which leverages LLM inference to heuristically complete partial plans emitted by a classical planner given partial domain knowledge, as well as to infer the semantic rules of the domain in a logical language based on environment feedback after execution. Our analysis on 7 environments shows that with just one expert-curated example plans, using LLMs as heuristic planners and rule predictors achieves lower environment execution steps and environment resets than random exploration while simultaneously recovering the underlying ground truth action semantics of the domain.