Logic , Sets, Groups, and Game Theory

Cause:

A thing’s material cause is the material of which it consists.
A thing’s formal cause is its form, i.e. the arrangement of that matter.
A thing’s moving cause is “the primary source of the change or rest.”
A thing’s final cause is its aim or purpose. That for the sake of which a thing is what it is.
Necessary causes:If x is a necessary cause of y, then the presence of y necessarily implies the presence of x. The presence of x, however, does not imply that y will occur.

Sufficient causes:If x is a sufficient cause of y, then the presence of x necessarily implies the presence of y. However, another cause z may alternatively cause y. Thus the presence of y does not imply the presence of x.

Contributory causes: A cause may be classified as a “contributory cause,” if the presumed cause precedes the effect, and altering the cause alters the effect. It does not require that all those subjects which possess the contributory cause experience the effect. It does not require that all those subjects which are free of the contributory cause be free of the effect. In other words, a contributory cause may be neither necessary nor sufficient but it must be contributory.

A sufficient cause is a complete causal mechanism. It can be defined as a set of events that inevitably produce disease.

A probabilistically causes B if A’s occurrence increases the probability of B. This is sometimes interpreted to reflect imperfect knowledge of a deterministic system but other times interpreted to mean that the causal system under study is inherently probabilistic, such as quantum mechanics.

Logic symbols

Set
Group
Ring
Field
Ideal
Principal Ideal
Galois Field
Lattice
Algebra
Mapping
Other links

https://www.csee.umbc.edu/portal/help/theory/group_def.shtml