CST 329 - Module 6

 Week 6,

This week's module adds onto the first order logic, including how we can use them in proofs. Last week, I mentioned that we can refer to samples of a domain using “for all” and “there exists”, but how do we use this in a proof? Sure, we know if anything in a domain is a human, then it is mortal, but how do we use that to say Alice is a human, so she is mortal? This is where the new tools for proof come to play. We can use a universal instantiation, which allows us to use that statement referencing the domain and generalize it to something we can use, a symbolic term or representation of something. Kind of like saying Alice can represent some piece of that domain, thus allowing us to get to the conclusion we want. This works similarly with the existential quantifier “there exists”, but with its limitations because it's easy to say that Anything can include Alice, but it's not quite the same for something can be Alice.

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