Both Induction and Deduction are necessary within casual inference because they are two ways of approaching a problem and often go hand in hand. Induction goes from evidence -> hypothesis while deduction works in the forward direction; cause (hypothesis) -> effect (theory, conclusion). Artificial Intelligence has started automating Induction and Deduction, an example is Bayesian networks. 

Stages of Casual Inference: Induction and Deduction

In the case of Sherlock Holmes, deductive reasoning was his ability to investigate and then eliminate different hypotheses to eventually find the correct one and solve the case.

Sherlock Holmes' use of deductive reasoning

Consists of premises followed by a conclusions.

Syllogism

People apply mental models using their imagination to solve deductive reasoning problems. The mental model is the representation of a situation in someones mind and can help determine validity of syllogisms.

Mental model approach

In order to test a rule it is necessary to look to falsify the rule. The canonical problem experiment that shows this is the Wason four-card problem, where students are asked to test the validity of a rule given four cards and must try to turn over cards to confirm and falsify the rule to determine if its valid.

Falsification principle

Eliminating different hypothesis to draw a conclusion.  The conclusion logically follows from "premises".

University of Michigan - Ann Arbor

Logical reasoning is the process of using a rational, systematic series of steps based on sound certain mathematical procedures and statements to arrive at a conclusion. 

There are three types of the reasoning:
- Abductive Reasoning 
- Deductive Reasoning 
- Inductive Reasoning

Reasoning

Goldstein, E. B. (2014). Cognitive psychology: Connecting mind, research and everyday experience. Nelson Education.


Cognitive psychology: Connecting mind, research and everyday experience

Pearl, J., & Mackenzie, D. (2019). The Book of Why. Penguin : 
[search.lib.umich.edu/catalog/record/016899333?query=the+book+of+why&library=All+Libraries](https://search.lib.umich.edu/catalog/record/016899333?query=the+book+of+why&library=All+Libraries) 

Reference : The Book of Why (needs to be merged)

Deductive reasoning

Abductive reasoning usually starts with an incomplete set of observations and proceeds to the most possible explanation for the group of observations. It is based on making and testing hypotheses using the best information available.

Abductive reasoning is useful for forming hypotheses to be tested.

Abductive Reasoning 

Inductive reasoning is a method that moves from specific empirical observations to broader generalizations. Scientists utilize this process to formulate theories and generate hypotheses. However, a key characteristic of inductive reasoning is that its conclusions are not guaranteed to be correct, even when based on multiple, accurate observations.

Inductive Reasoning

https://en.wikipedia.org/wiki/Logical_reasoning

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