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I'm generally confused about how to work this out, these are the questions that have been given to me, and I just don't know where to start on them:

  1. Consider the set of natural deduction rules, is the set of natural deduction without the rule RAA sound, and complete?

How do I go about figuring this out? check if the set of rules are still sound and complete?

  1. State whether this new rule:

--
⊥

is sound, and complete? How would I also go about figuring this out? I'm guessing it wouldn't be sound because true doesn't evaluate to false.

craisdais
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1 Answers1

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I think your question is more directly addressed here: https://en.wikipedia.org/wiki/Paraconsistent_logic . Some laws of logic are weakened or dismissed yet allow for non-trivial conclusions.

Foundational bases for classical logic can be uprooted, like the idea that statements must either be true or false: Deviant Logic

Variations on the Law of Excluded Middle have implications in programming.

In addition to varying the foundational rules of logic themselves, you can vary commonly accepted axiomsrr. Non-Euclidean Geometry was discovered when Gauss and others rejected the parallel principle and were able to develop consistent theorems.

TurlocTheRed
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