__Definition 1__: Let R be a set of reactions, A be a set of actions, and

*r*,

*u*be reactions such that

*r*,

*u*Î R. Then

*a*such that

*a*Î A is called an

**adient action**if and only if

*r*®

*a*®

*u*

is true. R is called the

**set of beneficial stimuli**.

__Definition 2__: Let R be a set of reactions, A be a set of actions, and

*r*,

*v*be reactions such that

*r*Î R,

*v*Ï R. Then

*a*such that

*a*Î A is called an

**abient action**if and only if

*r*®

*a*®

*v*

is true. R is called the

**set of harmful stimuli**.

__Theorem 1__: If an organism perceives a stimulus as beneficial, it will respond in order to increase the duration of the stimulus. If an organism perceives a stimulus as harmful, it will respond in order to decrease the duration of the stimulus.

The above theorem is the same as the two definitions in layman's terms. More specifically, the theorem states that a stimulus can be determined as beneficial or harmful depending on the reaction of the organism to the stimulus in terms of adience and abience.

An adient response is that response which elicits more of the desired stimulus. An abient response is that response which reduces the influence of the impinging stimulus.

In the above mathematical definitions, the symbol ® means "causes" or "results in" and is logically equivalent to the symbol 'and'.

Also, an "action" is any response elicited by the agent (organism) in question. A reaction is any response elicited by the environment.

## Error