Questions tagged [logical-validity]

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13 questions
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Calculus methods and computability

We know about calculability of a function or computability. We looks for the ability to solve a specific problem / compute a function with calculus method. But if we define a calculus method, is ...
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Undecidable predicate logic is decidable by people?

Logic in computer science (By Michael Huth,Mark Ryan, second edition, page 132) says Every φ can, in principle, be discovered to be valid or not, if you are prepared to work arbitrarily hard at ...
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Show the Invalidity of the sequence

∃x (P(x) → Q(x)), ∃x P(x) ⊨ ∃x Q(x) I am trying to find the invalidity of the following sequents. A = Set of natural number P(x) : x is odd Q(x) : x is not divisible by 2 What i don't understand ...
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Using the rules of inferences

I know the rules of inferences and logical equivalence but I cannot seem to validate this argument. I rewrote the first premise as $\neg p\vee q$ other from that I am stuck. Any help will be ...
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definition of formula validity

I read in some sources that valid formulas are tautologies (valid under every evaluation). In the others, I read that these are formulas that have conclusions true when premises are true. Are these ...
The following predicate logic formula is invalid (i.e. not a tautology): $\Bigl[\forall x \,\exists y {\,.\,} P(x,y)\Bigr] \implies \Bigl[\exists y \, \forall x {\,.\,} P(x,y)\Bigr]$ Which of the ...