ar X iv : c s . A I / 04 02 03 5 v 1 16 F eb 2 00 4 MEMORY AS A MONADIC CONTROL CONSTRUCT IN PROBLEM - SOLVING

Recent advances in programming languages study and design have established a standard way of grounding computational systems representation in category theory. These formal results led to a better understanding of issues of control and side-effects in functional and imperative languages. This framework can be successfully applied to the investigation of the performance of Artificial Intelligence (AI) inference and cognitive systems. In this paper, we delineate a categorical formalisation of memory as a control structure driving performance in inference systems. Abstracting away control mechanisms from three widely used representations of memory in cognitive systems (scripts, production rules and clusters) we explain how categorical triples capture the interaction between learning and problem-solving. 1. Reminding as computation What are the basic issues in the design of memory systems? Memory systems must have the ability to cope with new information. Any new input that is to be processed by a memory system should cause some adjustment in that system. Memory systems are the quintessential state semantics. A dynamic memory system is one that is altered by every experience it processes, and, in addition, it must be capable of finding what it has in it. Retrieval of memorised information, for instance through reminding, is a of course a critical feature of the system. More specifically the role of reminding in the overall architecture is the critical design issue. To be reminded of something we must have come across it while we were processing the new input. But to have done so, the memory system either had to be looking for this reminded event or else it must have run into it accidentally. Following Schank and Abelson’s seminal work [14], reminding relies on an amalgamation of both scenarii: a memory system is not consciously looking for a particular episode in memory, because it doesn’t explicitly know of that episode’s existence; it knows however where episodes like the one it is currently processing are likely to be stored. Reminding then occurs when the memory system has found the most appropriate structure in memory that will help in processing a new input. When no one episode is that closely related to an input, we can still process it, but no reminding occurs. This implies that an expert memory system is constantly receiving new inputs and evalutating them in terms of previously processed inputs. It understands in terms of what it already understood. Date: August 4, 2003. 1991 Mathematics Subject Classification. Primary 68Q55, 18C50; Secondary 18C15, 18C20.