Reasoning About Ignorance and Beliefs

When building artificial agents that have to make decisions, understanding what follows from what they know or believe is mandatory, but it is also important to understand what happens when those agents ignore some facts, where ignoring a fact is interpreted to stand for not knowing/not being aware of something. This becomes especially relevant when such agents ignore their ignorance, since this hinders their ability of seeking the information they are missing. Given this fact, it might prove useful to clarify in which circumstances ignorance is present and what might cause an agent to ignore that he/she is ignoring. This paper is an attempt at exploring those facts. In the paper, the relationship between ignorance and beliefs is analysed. In particular, three doxastic effects are discussed, showing that they can be seen as a cause of ignorance. The effects are formalized in a bi-modal formal language for knowledge and belief and it is shown how ignorance follows directly from those effects. Moreover, it is shown that negative introspection is the culprit of the passage between simply ignoring a fact and ignoring someone’s ignorance about that fact. Those results could prove useful when artificial agents are designed, since modellers would be aware of which conditions are mandatory to avoid deep forms of ignorance; this means that those artificial agents would be able to infer which information they are ignoring and they could employ this fact to seek it and fill the gaps in their knowledge/belief base.