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Results tagged with logic
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user 141236
Questions related to mathematical logic and its use in computer science
1
vote
Determine if the following arithmetics are sentences
According to ref here:
A formula in first-order logic with no free variable occurrences is called a first-order sentence. … And unlike most programming languages, in logic with identity we normally just use $=$ as identity relation symbol in the alphabet and we add functional symbols if needed to express functions such as + …
- 330
0
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Proof of a logical theorem
This problem sounds quite abstract and I'll sketch a proof below. To prove the final material conditional is a tautology, we only need to prove $\psi(p_0, \ldots p_n, p) \wedge \psi(p_0, \ldots p_n, q …
- 330
1
vote
Incomplete definition of function- first order logic
First of all in your above 3 "recursive definitions" linking $\Sigma$ with $\Sigma_2$, clearly the function $g$ in $\Sigma_2$ doesn't have any role in defining the values of $f(t)$ in $\Sigma$, the va …
- 330
0
votes
Problem with formalism in first order logic
You can always find a relation to replace any total or even partial function albeit it inevitably complicates the original wff with additional quantifiers and conjuncts, so usually you'd much better o …
- 330