Identifying all predicate-argument relations in a sentence has been a fundamental research target in NLP. While traditionally these relations were modeled via formal schemata, the recent QA-SRL paradigm (and its extensions) present appealing advantages of capturing such relations through intuitive natural language question-answer (QA) pairs. In this paper, we extend the QA-based semantics framework to cover adjectival predicates, which carry important information in many downstream settings yet have been scarcely addressed in NLP research. Firstly, based on some prior literature and empirical assessment, we propose capturing four types of core adjectival arguments, through corresponding question types. Notably, our coverage goes beyond prior annotations of adjectival arguments, while also explicating valuable implicit arguments. Next, we develop an extensive data annotation methodology, involving controlled crowdsourcing and targeted expert review. Following, we create a high-quality dataset, consisting of 9K adjective mentions with 12K predicate-argument instances (QAs). Finally, we present and analyze baseline models based on text-to-text language modeling, indicating challenges for future research, particularly regarding the scarce argument types. Overall, we suggest that our contributions can provide the basis for research on contemporary modeling of adjectival information.