Towards an Axiomatic Theory of Consciousness

In this paper we seek to provide elements of an axiomatic theory for a sentient consciousness as a quantified form of introspective awareness. A crucial step for its formulation is use of an interval temporal logic to give expression to on-going conditions such as those represented by the progressive aspect in natural language. In this way we are able to enrich more stative mental models so that an agent’s internal activities and its perception of external processes can be represented more faithfully. The need for agent consciousness research is briefly discussed. 1 Some Pragmatics of Consciousness Although part of the ancient mind-body problem of philosophy, the concept of consciousness itself is well enough recognised for it to be an ordinary word of our language. A conscious individual is aware, and knowing; the unconscious condition is normally recognisable. Numerous popular and contemporary books by Aleksander [1], Dennett [4], Searle [13], and others, show its explication to be contentious and a challenge to our suppositions on reality, a hazardous topic indeed for a would-be engineer of artificial intelligence. Yet we must admit the possibility that consciousness has utilitarian function, evolved to ensure survival. Our justification for addressing the subject is that artificial agents which display elements of intelligent behaviour already exist, in the popular sense of these words, but that we would doubt the real intelligence of an agent which seemed to us to have no sense of “self”, or awareness of its capabilities and its senses and their current state. So although consciousness, in a sentient albeit non-emotive sense, seems more allied to awareness than reasoning, an approximation to human consciousness could enable us to converse more naturally with an individual agent. This makes it an unusual topic of enquiry because we need an account for the first person and second person perspective as well as the more usual third person of objective science. Contention arises over whether consciousness can be considered a mental state of the human mind, for this brings presuppositions of the intentional stance and issues of its faithfulness to the human brain. But lack of faithfulness to a biological model is not a barrier to engineering, as the wheel, the fixed wing, and the computer itself demonstrate. Software agents are already designed using notions of mental state and practical reasoning which have emerged as abstractions from rational enquiry rather than any physical brain model. While agent designers may also eschew such models, and instead rely on a variety of physical and computational devices, in well known cases the management of complexity leads to design architectures with layers of abstraction, some of which are comparable with intentional models of the mind. To bypass the metaphysics of consciousness in favour of pragmatic considerations, 325 L. J. of the IGPL, Vol. 9 No. 2, pp. 325–331 2001 c ©Oxford University Press 326 Towards an Axiomatic Theory of Consciousness there is evidence to consider, the view of peers in rational enquiry, and the need for guidance in an artificial construction. Clinical reports, psychological experiment, and philosophical enquiry lead to a variety of theories which partially explain the phenomena and suggest layers of consciousness [10]. Problematic issues range from neurological syndromes such as phantom limbs, denial of paralysis, and involuntary manipulation, through issues of identity and the effect of emotion and habit, to an explication of context and presence in perception and its links with language. Our formalism arises from attempts to bridge the gap between agents designed with mental states, and credible multi-processing implementations. It may be compatible with the implementations of a psychologically motivated, but non-sentient theory like that of [2], which can be realised as a computational agent with a myriad of heterogeneous processes. But to explicate conscious behaviour we certainly require layers of conception which we hardly discuss here. 2 Refining the Intentional Stance Mental models of the intentional stance encroach on two areas of agent design. One is as an abstract basis for incorporating plans and selecting actions through meansend reasoning in software agents, notably in variants of the Belief, Desire, Intention paradigm. (See, for instance, Bratman[3], Rao and Georgeff [12]). The other area is the related basis for giving definition to standard acts of communication as realisations of speech act theory, so that there are ingredients of a coherent basis for dialogue between agents in terms of what we can loosely call knowledge interchange. (See, for instance, Labrou and Finin [8]). Our proposal for steps towards an axiomatisation of consciousness depends critically on a refinement of traditional ideas of intentionality. From the perspective of an agent designer, extant intentional theories of rational agents focus on stative concepts of belief, desire, intention, knowledge and commitment, each of which can be regarded intuitively as expressing computational data states. Agent activities, or processes, which Vendler (1967) and later workers have considered equally important for the modelling of our linguistic descriptions of behaviour, have been ignored, or rather, buried in naive computational models. But activity states like planning, learning and sleeping, and the sensing and perceiving of external conditions allow a more refined computational model of rationality. Their absence is a serious deficiency in the usual perception of mental state. However, there is also another defect. The usual axiomisation for belief, and of knowledge, presumes introspection; e.g. for knowledge, that which is known is known, that which is not known is known to be not known. These are strong conditions which make such states already too “conscious” for some forms of memory recall and learnt behaviour. The limitations of stative mental states can be overcome simply by allowing activity states as well. Both stative and activity states can be considered durative on a temporal frame. They can be distinguished informally by the observation that a stative condition is basically atemporal, but becomes homogeneous on an interval as an artifact of a temporal frame, whereas an activity is essentially durative, a process which may be composed from sub-processes. However, we gloss over finer semantic issues by emphasising one facit, an explicit progressive expression for an activity, captured by a modal operator prog to modify a singular predicate for a dynamic 2. REFINING THE INTENTIONAL STANCE 327