MHB What is the meaning of consequence in logic?

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Consequence in logic refers to the relationship between statements where one statement logically follows from another. It encompasses various forms, including material implication and logical consequence. Many textbooks tend to use "logical consequence" to describe what is often termed "semantic consequence." Understanding these distinctions is crucial for grasping logical reasoning. The discussion highlights the importance of terminology in the study of logic.
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what is the defintion of consequence in logic
 
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There is a nice little variation of the problem. The host says, after you have chosen the door, that you can change your guess, but to sweeten the deal, he says you can choose the two other doors, if you wish. This proposition is a no brainer, however before you are quick enough to accept it, the host opens one of the two doors and it is empty. In this version you really want to change your pick, but at the same time ask yourself is the host impartial and does that change anything. The host...

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