What cognitive systems underlie thinking and decision making? What evidence supports the existence of these systems?

Underlying decision making are three types of reasoning: deductive reasoning, inductive reasoning and abductive reasoning. These forms of reasoning can sometimes be affected by emotion and bias, as well. 
Deductive Reasoning
This type of reasoning involves working intellectually from a general rule or premise to a specific application of this rule, and from there to a logical conclusion about the specific application. Deductive reasoning is often arranged in a syllogism that moves from a general statement to a particular one that logically follows.
A simple example of this can be made if someone were planning a trip:

Temperatures in southern Italy are very warm in the summer.Marge is planning to travel there when she finishes college in the summer.Therefore, she is packing light clothing for her trip.

Inductive Reasoning
This type of reasoning moves a specific idea to a logical conclusion about its application. Such reasoning begins with an idea that is later generalized as it is applied to other similar concepts. After details that have been observed are gathered together, a person can draw a generalization that stems logically from these details, thus using inductive reasoning.
While inductive reasoning may not always lead to the soundly logical conclusion, it often generates observations that allow creative ideas to develop that lead to new discoveries.
Abductive Reasoning
Abductive reasoning typically begins with an incomplete set of observations and proceeds to the likeliest possible explanation for the set. Abductive reasoning yields the kind of daily decision-making that does its best with the information at hand, which often is incomplete.
This is a flawed reasoning in comparison to deductive and inductive reasoning. For, it starts with a set of observations that are not complete, but enough that a person can move to a possible explanation for this set. 
https://en.wikibooks.org/wiki/Cognitive_Psychology_and_Cognitive_Neuroscience/Reasoning_and_Decision_Making

https://www.butte.edu/departments/cas/tipsheets/thinking/reasoning.html