We investigate if a model can learn natural language with minimal linguistic input through interaction. Addressing this question, we design and implement an interactive language learning game that learns logical semantic representations compositionally. Our game allows us to explore the benefits of logical inference for natural language learning. Evaluation shows that the model can accurately narrow down potential logical representations for words over the course of the game, suggesting that our model is able to learn lexical mappings from scratch successfully.

Meaning Representation (AMR) has become popular for representing the meaning of natural language in graph structures. However, AMR does not represent scope information, posing a problem for its overall expressivity and specifically for drawing inferences from negated statements. This is the case with so-called "positive interpretations" of negated statements, in which implicit positive meaning is identified by inferring the opposite of the negation's focus. In this work, we investigate how potential positive interpretations (PPIs) can be represented in AMR. We propose a logically motivated AMR structure for PPIs that makes the focus of negation explicit and sketch an initial proposal for a systematic methodology to generate this more expressive structure.