  Simulations, along with other similar applications like virtual worlds and
video games, require computational models of intelligence that generate
realistic and credible behavior for the participating synthetic characters.
Cognitive architectures, which are models of the fixed structure underlying
intelligent behavior in both natural and artificial systems, provide a
conceptually valid common basis, as evidenced by the current efforts towards a
standard model of the mind, to generate human-like intelligent behavior for
these synthetic characters. Sigma is a cognitive architecture and system that
strives to combine what has been learned from four decades of independent work
on symbolic cognitive architectures, probabilistic graphical models, and more
recently neural models, under its graphical architecture hypothesis. Sigma
leverages an extended form of factor graphs towards a uniform grand unification
of not only traditional cognitive capabilities but also key non-cognitive
aspects, creating unique opportunities for the construction of new kinds of
cognitive models that possess a Theory-of-Mind and that are perceptual,
autonomous, interactive, affective, and adaptive. In this paper, we will
introduce Sigma along with its diverse capabilities and then use three distinct
proof-of-concept Sigma models to highlight combinations of these capabilities:
(1) Distributional reinforcement learning models in; (2) A pair of adaptive and
interactive agent models that demonstrate rule-based, probabilistic, and social
reasoning; and (3) A knowledge-free exploration model in which an agent
leverages only architectural appraisal variables, namely attention and
curiosity, to locate an item while building up a map in a Unity environment.
