  We argue that an explainable artificial intelligence must possess a rationale
for its decisions, be able to infer the purpose of observed behaviour, and be
able to explain its decisions in the context of what its audience understands
and intends. To address these issues we present four novel contributions.
Firstly, we define an arbitrary task in terms of perceptual states, and discuss
two extremes of a domain of possible solutions. Secondly, we define the
intensional solution. Optimal by some definitions of intelligence, it describes
the purpose of a task. An agent possessed of it has a rationale for its
decisions in terms of that purpose, expressed in a perceptual symbol system
grounded in hardware. Thirdly, to communicate that rationale requires natural
language, a means of encoding and decoding perceptual states. We propose a
theory of meaning in which, to acquire language, an agent should model the
world a language describes rather than the language itself. If the utterances
of humans are of predictive value to the agent's goals, then the agent will
imbue those utterances with meaning in terms of its own goals and perceptual
states. In the context of Peircean semiotics, a community of agents must share
rough approximations of signs, referents and interpretants in order to
communicate. Meaning exists only in the context of intent, so to communicate
with humans an agent must have comparable experiences and goals. An agent that
learns intensional solutions, compelled by objective functions somewhat
analogous to human motivators such as hunger and pain, may be capable of
explaining its rationale not just in terms of its own intent, but in terms of
what its audience understands and intends. It forms some approximation of the
perceptual states of humans.
