An minor investigation into lying and honesty

Introduction

This is a minor investigation into the system of lying, truthfulness and being correct or wrong. This investigation is not yet completed so is there any mistakes, and I am sure there are a lot please get it to my attention or overlook them. Preferably, the former.
This is actually an extension of a small recent report on bullshit. The final version will combine both of these.

Assumptions

1. There is a fact A.
2. There is a falsehood B.
3. There is a person X.
4. There is a person Y.

Definitions

A fact is a piece of information that is true.
A falsehood is a piece of information that is false.

Information can either be known or believed in.
1. Knowing a piece of information means the person is absolutely sure the piece of information is true. In reality, this piece of information can be true or false.
2. Believing in a piece of information means the person accepts the piece of information as being true without any proof. It might have evidence but not proof. In reality, this piece of information can be true or false.

Real value refers to the actual state of the piece of information. It can be either a fact or a falsehood.
Perception value refers to the way in which the piece of information is perceived. It can be either a true or false.

Action refers to the whether the speaker told what he perceived.

Speaker is the person who is conveying a piece of information to another person. The information may be true or false.Speaker category refers to whether the speaker was any of the following: honest or correct or liar or wrong.

The table of honesty and correctness

Real value Perceived value Resonant Action Speaker category
Fact True Yes Honest and Correct
Fact True No Liar and Correct
Fact False Yes Honest and Wrong
Fact False No Liar and Wrong
Falsehood True Yes Honest and Wrong
Falsehood True No Liar and Wrong
Falsehood False Yes Honest and Correct
Falsehood False No Liar and Correct

Properties of the table [ The method to describe the speaker ]

If the real value and perceived value are resonant, then the person is correct.

If the perceived value and the action are not resonant, then the person is lying.

Relationship between liars and bullshiters

Liars always know the truth.
Bullshiters may or may not know the truth.
So all liars are bullshiters, but all bullshiters are not liars.

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