a constructive inference system is a reasoning system that constructs logical models from observed information in real time.
models are topological spaces consisting of relations that preserve the logical structure between sets of variables.
the process of generating a model can be described as a game, where the objective is to create a topological space representing observations through relations-between-variables as well as relations-between-relations that are built up until the number of top-level relations reaches a minimum.
at each step of the game, the agent is given a set of assumptions, which are used to perform measurements and create a set of relations between the assumptions, reducing the number of top-level objects at play by combining assumptions via relations.
the results are passed to the following step, and the process is repeated until the set of assumptions are no longer reducible.
the original set of assumptions given at the start of the game are called the base assumptions, and describe the values assigned to certain variables.
variables are used in measurement, the second set of assumptions are therefore measured assumptions.
all assumptions after the second step are inferred assumptions, as they are produced by inferences regarding the relations between either measured or inferred assumptions.
when no more relations are inferable, meaning no rules exist for making valid inferences on the current set of assumptions, the game ends resulting in a hierarchical model where the root objects at the top are the last set of assumptions.
the number of root objects in a model indicate how well the system was able to be reduced. ideally there exists a single root object subsuming all other elements, but as the complexity of the system grows it is expected that the topological space of the model will expand as well.
rules that allow inferences to be made are held in a knowledge base, and are involved in the production of relations between relations. unlike measured assumptions which are formed by calling functions over variables, inferred relations are formed by comparing structures of other relations.
specifically, inference rules are used to assign identities to new relations which cannot be determined on the basis of measurement, but rather depend on the identity of existing relations.
core inferences are inferences which make up all other inferences. relation properties like reflexive, symmetric, and transitive properties are assigned to relations over repeated observation which allow for inferences to be made during model construction.
for example, two relations xRy and yRz have an inferred relation between them, (xRy)R(yRz), equivalent to xRz i.e. a transitive relation, if of course R has been found to be transitive.
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