  This thesis contributes to the formalisation of the notion of an agent within
the class of finite multivariate Markov chains. Agents are seen as entities
that act, perceive, and are goal-directed.
  We present a new measure that can be used to identify entities (called
$\iota$-entities), some general requirements for entities in multivariate
Markov chains, as well as formal definitions of actions and perceptions
suitable for such entities.
  The intuition behind $\iota$-entities 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 in general
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. We prove that $\iota$-entities are blocks in specific partitions of
the global trajectory. These partitions are the finest partitions that achieve
a given SLI value. We also establish the transformation behaviour of SLI under
permutations of nodes in the network.
  We go on to present three conditions on general definitions of entities.
These are not fulfilled by sets of random variables i.e.\ the perception-action
loop, which is often used to model agents, is too restrictive. We propose that
any general entity definition should in effect specify a subset (called an an
entity-set) of the set of all spatiotemporal patterns of a given multivariate
Markov chain. The set of $\iota$-entities is such a set. Importantly the
perception-action loop also induces an entity-set.
  We then propose formal definitions of actions and perceptions for arbitrary
entity-sets. These specialise to standard notions in case of the
perception-action loop entity-set.
  Finally we look at some very simple examples.
