A more radical approach to modelling resource bounded believers was proposed by Konolige [Konolige, 1986a]. His deduction model of belief is, in essence, a direct attempt to model the `beliefs' of symbolic AI systems. Konolige observed that a typical knowledge-based system has two key components: a database of symbolically represented `beliefs', (which may take the form of rules, frames, semantic nets, or, more generally, formulae in some logical language), and some logically incomplete inference mechanism. Konolige modelled such systems in terms of deduction structures. A deduction structure is a pair , where is a base set of formula in some logical language, and is a set of inference rules, (which may be logically incomplete), representing the agent's reasoning mechanism. To simplify the formalism, Konolige assumed that an agent would apply its inference rules wherever possible, in order to generate the deductive closure of its base beliefs under its deduction rules. We model deductive closure in a function :
where means that can be proved from using only the rules in . A belief logic can then be defined, with the semantics to a modal belief connective , where is an agent, given in terms of the deduction structure modelling 's belief system: iff .
Konolige went on to examine the properties of the deduction model at some length, and developed a variety of proof methods for his logics, including resolution and tableau systems [Geissler and Konolige, 1986]. The deduction model is undoubtedly simple; however, as a direct model of the belief systems of AI agents, it has much to commend it.