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Questions tagged [proof]

For questions about the correctness of a proof or the nature of proofs in general.

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De Morgan for Quantifiers Formal Proof: ∀∃-intro and -elim Questions

I have a problem reading existing question's answers. I've successfully encoded the proof of one of De Morgan's Laws, ¬∃x P(x) → ∀x ¬P(x), for Quantifiers formally via cubicaltt type-checker via Curry-...
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De Morgan for Quantifiers Formal Proof: Inhabitance Question

I have a problem reading existing question's answers. I've successfully encoded the proof of one of De Morgan's Laws, ¬∃x P(x) → ∀x ¬P(x), for Quantifiers formally via cubicaltt type-checker via Curry-...
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Correct Way of Handling A Corollary of A Corollary?

I have a conclusion S that is moderately interesting. While the corollary of S is more interesting, the corollary of the corollary of S is extremely interesting. Should I just label them corollary 1 ...
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Using predicate logic, how to solve symmetric and anti reflexive

The networks is: A->B->C->D The channels used by the network are: lo, med, hi h-hi, l-lo, m-med i) A network uses one, and only one channel. ii) Networks within close proximity cannot both use the ...
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Language Proof and logic Chapter 13 problem 31

I have been working on this problem for over an hour and I think I have simply missed something. I need some help. I don't see how this is supposed to work out Here are the premises: ∀x ∀y[Likes(x,...
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Do α and β entail each other?

Show whether the following is true or false: α |= β or β |= α, for any two formulas α and β I'm assuming here that α and β are formulas, not a set of formulas. My thought is that I can prove that ...
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Testing the validity of syllogism argument

I came across a validation method for testing the validity of a syllogistic argument which seems quite easier to grasp: For example: To test the argument: no P is B some C is B Therefore, some ...
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Does anyone know of a philosophy which rectifies or considers the following question?

Let's imagine that I began to doubt the validity of one of my arguments, which leads me to question my ability to make rational arguments. And so begin to distrust my intuitive ideas about logic, then ...
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Axiomatic Proof of Symmetry and Transitivity of Identity

Given the axioms below and the rules of Modus Ponens and Universal Generalization, how can you prove that t=s → s=t for any terms s and t? Additionally, how do you prove that t = s → (s = r → t = r) ? ...
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What are some active areas of research in proof theory?

Is there any research activity going on in the field of proof theory today? If so, what are some of the most active areas, what types of questions do they deal with, and where can I go to find out ...
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Using the conception of 'reliable, unchanging' does 'truth' exist?

An 'archaic' definition for TRUE,TRUTH implies constancy, reliability, unchanging, fidelity. Using this concept of TRUTH is the following valid? There exists either that which is TRUE or that which ...