How Assistum works - use of fuzzy logic

How Assistum Works

Overview

A knowledge base is represented by a number of nodes joined by links.

A node describes a concept e.g. "weather" together with an Assertion or Hypothesis about it, e.g. "it is raining". It also contains a Degree of Truth (DoT) of the assertion (e.g. that it is raining) on a scale of 1 to 0 (totally true to totally false). The degree of truth maps to a scale of descriptions e.g. "raining = 1", "scattered showers = 0.5", "sunny = 0".

Some nodes or concepts are influenced by other nodes or concepts. The former are called dependent nodes, and the nodes they depend on are called influencing nodes.

The relationship between a dependent node and an influencing node is called a link between the two nodes. A link has an Affirmation weight and a Denial weight fixed by the knowledge base designer. When the knowledge base is being used on a particular instance, a link also has a current impact weight which measures the impact of the influencing node on the dependent node, given the current DoT of the influencing node and the Affirmation and Denial weights of the link between them.

How Assistum handles dependencies between Assertions - the use of weights.

The extent to which the truth of an Assertion influences the truth of another Assertion is denoted by the Affirmation Weight of the link between the Assertions. This weight can be interpreted as the extent to which the dependent Assertion is true, given that the influencing Assertion is completely true or affirmed (and with no other information).

Affirmation Weights are always in the range 0 to 1.

An affirmation weight of 1 means that if the influencing Assertion is totally true, then the dependent Assertion is also totally true (in the absence of any other information).
An affirmation weight of 0 means that if the influencing Assertion is totally true, then the dependent Assertion is totally false (in the absence of any other information).
An affirmation weight of 0.5 means that there is no impact on the dependent Assertion.
An affirmation weight of w (0 < 1) means that if the influencing Assertion is totally true, then the dependent Assertion is true to the degree w (in the absence of any other information).

The extent to which the falsity of an Assertion influences the truth of another Assertion is denoted by the Denial Weight of the link between the Assertions. This weight can be interpreted as the extent to which the dependent Assertion is true, given that the influencing Assertion is completely false or denied (and with no other information).

A denial weight of 1 means that if the influencing Assertion is totally false, then the dependent Assertion is also totally false (in the absence of any other information).
A denial weight of 0 means that if the influencing Assertion is totally false, then the dependent Assertion is totally true (in the absence of any other information).
A denial weight of 0.5 means that there is no impact on the dependent Assertion.
A denial weight of w (0 < 1) means that if the influencing Assertion is totally false, then the dependent Assertion is true to the degree w (in the absence of any other information).

The impact on the DoT of a dependent Assertion X from a fuzzy influencing Assertion A (i.e. fuzzy in that A is neither totally true or false), is the current impact weight of Link AX.

If DoT of A is > 0.5, then weight of Link AX is interpolated between Affirm Weight and Neutral Weight. If DoT of A is <0.5, then weight of Link AX is interpolated between Neutral Weight and Denial Weight.

In fuzzy logic jargon, there are two membership functions here. The first is for the truth of Assertion A. This is a linear function from DoT=1 to DoT=0.5 and has weight of "Affirm Weight-0.5." The second is for the falsity of Assertion A. This is a linear function from DoT=0 to DoT=0.5 and has weight of "0.5-Denial Weight."

How Assistum combines the impact of a number of influencing Assertions on one dependent Assertion.

Assistum distinguishes between Assertions that suggest the dependent Assertion is true (i.e. imply a DoT > 0.5) and those that suggest it is false (DoT <0.5), and it ignores all that imply a DoT of exactly 0.5.

These sets of affirming and denying Assertions are used by Assistum to construct "because" and "in spite of" explanations of a dependent Assertion.

When typing in the answers use an expression that makes sense when used in a phrase in the following format:

"Because the (Node Name) is (Answer)" e.g. "Because the walking option is probably walk."
"In spite of the (Node Name) being (Answer) e.g. "In spite of the walking option being probably walk."

Assistum takes all the affirming assertions for a dependent node and combines the current impact weights of all the affirming links to produce the overall affirming impact weight for that dependent node.

It does the same with all the denying assertions for that dependent node to produce the overall denying impact weight.

If the definite truth (or falsity) of any influencing Assertion implies that the Dependent Assertion is always true (or false), then this over-rides all the other influencing assertions.

Otherwise, Assistum combines the overall affirming and denying weights to produce the current DoT of the Dependent Assertion.