This is an old revision of the document!

Empirical Reasoning (2)

Uncertainty in Physical Worlds

What it is	In a dynamic world with a large number of elements and processes, presenting infinite combinatorics, knowing everything is impossible and thus predicting everything is also impossible.
Stems From	—— Unknown things ——
	Variable Values	E.g. we know it will eventually rain, but not exactly when.
	Variables	E.g. a gust of wind that hits us as we come around a skyscraper's corner.
	Goals of Others	E.g. when we meet someone in the street and move to our right, but they also move in that direction (to their left), at which point we move to our left, but they move to their right, etc., for a sequence of synchronized stalemate.
	Imprecision in Measurements	E.g. the position of your car on the road relative to other cars and the boundaries of the road.
	—— Unknowable things ——
	Chains of Events	E.g. for most things which are not possible (or utterly impractical) to measure, for any given time period.
	Living Things	E.g. bacteria, before they were hypothesized and observable through a microscope.
	Values Beyond Measurement	E.g. everything outside the reach of our senses and for which no alternative measurement mechanisms are available (e.g. telephone, telescope, microscope, etc.).
	Infinite Combinatorics	Since there is a large number of atomic elements (building blocks), many of which no-one knows about, and an infinite number of combinations that these can create, it is impossible to know any and every way in which the world may organize itself.
	Axioms of the Universe	Since agents in the physical world, even those that are extremely intelligent and knowledgeable, the very operation of their minds depends on universe and its operating principles. Even if they were to figure out the actual and complete set of rules that govern the universe, they would have to step outside of the universe to verify that it was so. But if that were possible – if they could step outside of the universe to verify that these rules were the complete and correct ruleset that governs the universe, what world would they step into? This would in essence be proof that these rules are not the complete set governing the universe, because there is another world that they can step into.

Methods For Dealing With Uncertainty

Model Creation	Model creation from experience is the key method for dealing with uncertainty. Models, combined with reasoning, can produce generalized information structures that can be used for several purposes, including prediction, explanation, planning, goal selection, classification, and many other cognitive activities.
Reasoning	Aka “rule creation” aka “generalization”. 'Induction' is another term for generalization, but it's not only reasoning through induction that matters - deduction, abduction and analogy (all defeasible, non-axiomatic) that uncertainty handling relies on.
Rules About Rules	Reasoning allows rules to be hierarchical – creating rules about rules (also called 'metarules'. This makes organization of rules become more practical.
Hierarchy	By organizing knowledge in a hierarchy, or better yet multi-dimensional hierarchies, a learner can sort through, prioritize, and select the appropriate level of detail for any situation. An example of this is that the rule “the same object can only be in one place for any particular period” has a higher priority than the rule “my mom comes home from work around 4 pm”, should there be any doubt about her spatial position.
Causal Models	A key method for dealing with uncertainty is to create models/rules about causal relations. Only one method for causal-relational model creation is known.
Causal Model Creation	The only known method for creating causal models is the combined forward-backward chaining (deduction-abduction, respectively), where the same model is tested in its usefulness for supporting both abduction and deduction. Any model which works in both directions, or better than another model, is closer to being a good (useful) representation of causal relations.

Backward & Forward Chaining in Production Systems

Matching	Rules are matched to conditions by matching – if a rule matches is found to match a pattern in a particular dataset, the rule fires. When a rule fires it means that its statements will be executed.
Production System	Sometimes 'production system' is used as a synonym to 'reasoning system'. However, while both are rule-based, reasoning systems often come with requirements and limitations that production systems are (typically) not subject to. 'Production systems' is a larger set of systems than 'reasoning systems', but the strictest sense of 'reasoning system' (e.g. first-order logic) is not part of the set of 'production systems'.
Forward Chaining	Uses matching to produce what might happen next, after a particular state is reached, starting with existing data, until an endpoint (typically a goal) is reached. The resulting chain of events can represent a predicted successful plan or simply a predicted chain of events. Forward chaining starts with a particular premise, e.g. the here-and-now, and proceeds to trace the cause-effect chain, through pattern matching, until the end-point is reached. In AI this is used to produce predictions. An example is a chain of dominos: If the first domino falls, the second domino falls, which makes the third one fall, etc. The premise is the line of dominos, spaced less than the length of one domino apart, and the effect that a falling domino has on a free-standing domino that it falls on.
Backward Chaining	Starts with a given goal or state to be achieved, and proceeds through matching to produce what could possibly have been the state just prior to that particular state. A goal-driven reasoning method for inferring unknown truths from known conclusions (goal) by moving backward from a solution to determine the initial conditions and rules. In AI this method can be used for producing plans. An example could be producing an answer to the question “How can I make the last domino fall?”
BW+FW Chaining Combination	Backward chaining is often applied in artificial intelligence (AI) and may be used along with its counterpart, forward chaining.

Center for Analysis and Design of Intelligent Agents

Table of Contents

Empirical Reasoning (2)

Uncertainty in Physical Worlds

Methods For Dealing With Uncertainty

Backward & Forward Chaining in Production Systems