Solving Your Problem: Troubleshooting Mistakes in Code

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  • Thread starter Thread starter shivajikobardan
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    Code Troubleshooting
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SUMMARY

The discussion focuses on troubleshooting mistakes in code related to quantifier scope in logical expressions. A key point is the distinction between maximal and minimal scope of quantifiers, specifically in the expression $\forall y\,\text{Animal}(y)\Rightarrow \text{Loves}(x, y)$. The correct interpretation is that the quantifier's scope is maximal, meaning it applies to the entire expression rather than just the immediate term. This clarification is essential for accurate logical reasoning in programming and mathematical proofs.

PREREQUISITES
  • Understanding of logical expressions and quantifiers
  • Familiarity with programming concepts related to logical reasoning
  • Basic knowledge of mathematical proofs and their conventions
  • Experience with code debugging techniques
NEXT STEPS
  • Study the differences between maximal and minimal scope of quantifiers in logic
  • Learn about logical operators and their precedence in programming languages
  • Explore debugging tools and techniques for logical errors in code
  • Review mathematical proof strategies, focusing on quantifiers and their implications
USEFUL FOR

Programmers, computer scientists, and mathematicians who are involved in logical reasoning, code debugging, and mathematical proofs will benefit from this discussion.

shivajikobardan
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https://lh6.googleusercontent.com/gIpHfdMTJMBg2-cMkBWqVQYyAUKTwBCzc30JXJ054wfj06IBGeeXFdHd1-VO0J6EFrssOlAe3ntqJaVHSakLZAK8x4BI6pRL5Lb0JWUdDEuaxAm4NPAiUMvtOSLqjrOkH8r0VOv7

https://lh3.googleusercontent.com/HharKN7rVu5NqPPR9lnd4nHr1fASlCPYNvc7zkLqrhrXMRJQVI_fgsL2Vu-Zgls2ycL8QUgF6IRNIAENcyw9E5KslY-UvkOma_dT__Mcozf_dQ66aLWPvxX58qhEq37H96KUUg6F

https://lh4.googleusercontent.com/_zbkQuNFRy7N3B_u0Oz1ESBh19xov4y98iWyeWuy6-m9He33SWC3BGEnYSDjii8r-_1zmiUKeakvLZSq1dBjQ4JZugG6Z6_TLd4u0_WjGUXh8KUZm1xY2LNVd8GHrRQ8ZJh7mjQV

As you can see I am not getting correct result. What have I messed up? I want to learn it.

https://slideplayer.com/slide/4942120/
Here is full slide in case anyone wants to refer to it.
 
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The slides use the convention that the scope of a quantifier is maximal, i.e., it extends as far to the right as possible. In particular, $\forall y\,\text{Animal}(y)\Rightarrow \text{Loves}(x, y)$ means $\forall y\,(\text{Animal}(y)\Rightarrow \text{Loves}(x, y))$ and not $(\forall y\,\text{Animal}(y))\Rightarrow \text{Loves}(x, y)$, as you wrote in the first photo. This convention is not universal, however. Quite a few textbooks view the scope of a quantifier as being as small as possible.
 

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