From Kristin Andrews at the Stanford Encyclopedia of Philosophy:
The philosophical issues that relate to research on animal cognition can be categorized into three groups: questions about the assumptions on which the research is based; questions that arise about the methods used in the research programs; and questions that arise from within the specific research programs.
While the study of animal cognition is largely an empirical endeavor, the practice of science in this area relies on theoretical arguments and assumptions — for example, on the nature of mind, communication, and rationality. If nonhuman animals don’t have beliefs, and if all cognitive systems have beliefs, then animals wouldn’t be the proper subjects of cognitive studies. If animals aren’t agents because their behavior isn’t caused by propositional attitudes, and if all cognitive systems are agents, we get the same conclusion. While there are arguments against animal minds, the cognitive scientists studying animals largely accept that animals are minded, cognitive systems. Animal consciousness, however, it is a topic that some scientists are less willing to engage with.
Many of the research programs investigating particular cognitive capacities in different species raise philosophical questions and have implications for philosophical theories, insofar as they impose additional empirical constraints for naturalistically minded philosophers. Traditional research paradigms in animal cognition are similar to those in human cognition, and include an examination of perception, learning, categorization, memory, spatial cognition, numerosity, communication, language, social cognition, theory of mind, causal reasoning, and metacognition.