Formal Approaches to a Definition of Agents
Biehl, Martin Andreas
This thesis is a contribution to the formalisation of the notion of an agent within the class of finite multivariate Markov chains. In accordance with the literature agents are are seen as entities that act, perceive, and are goaldirected. We present a new measure that can be used to identify entities (called i-entities). The intuition behind this is that entities are spatiotemporal patterns for which every part makes every other part more probable. The measure, complete local integration (CLI), is formally investigated within the more general setting of Bayesian networks. It is based on the specific local integration (SLI) which is measured with respect to a partition. CLI is the minimum value of SLI over all partitions. Upper bounds are constructively proven and a possible lower bound is proposed. We also prove a theorem that shows that completely locally integrated spatiotemporal patterns occur as blocks in specific partitions of the global trajectory. Conversely we can identify partitions of global trajectories for which every block is completely locally integrated. These global partitions are the finest partitions that achieve a SLI less or equal to their own SLI. We also establish the transformation behaviour of SLI under permutations of the nodes in the Bayesian network. We then go on to present three conditions on general definitions of entities. These are most prominently not fulfilled by sets of random variables i.e. the perception-action loop, which is often used to model agents, is too restrictive a setting. We instead propose that any general entity definition should in effect specify a subset of the set of all spatiotemporal patterns of a given multivariate Markov chain. Any such definition will then define what we call an entity set. The set of all completely locally integrated spatiotemporal patterns is one example of such a set. Importantly the perception-action loop also naturally induces such an entity set. We then propose formal definitions of actions and perceptions for arbitrary entity sets. We show that these are generalisations of notions defined for the perception-action loop by plugging the entity-set of the perception-action loop into our definitions. We also clearly state the properties that general entity-sets have but the perception-action loop entity set does not. This elucidates in what way we are generalising the perception-action loop. Finally we look at some very simple examples of bivariate Markov chains. We present the disintegration hierarchy, explain it via symmetries, and calculate the i-entities. Then we apply our definitions of perception and action to these i-entities.