How Can Boolean Polynomials Determine Consistency in Propositional Formulas?

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SUMMARY

This discussion focuses on the conversion of propositional statements into Boolean polynomials, specifically using the example of transforming X ^ Y into P[(X^Y)] = xy. The main objective is to determine the consistency or inconsistency of multiple propositional formulas through Boolean polynomials. The user seeks resources, including texts and videos, that explain the conversion process and the application of Boolean polynomials in proving logical consistency, particularly in relation to statements like [(p->q) -> (q->r)] -> (p->r). The mention of Disjunctive Normal Form (DNF) highlights its relevance in this context.

PREREQUISITES
  • Understanding of propositional logic and its operators
  • Familiarity with Boolean algebra concepts
  • Knowledge of Disjunctive Normal Form (DNF)
  • Basic skills in polynomial manipulation
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  • Research resources on converting propositional formulas to Boolean polynomials
  • Study the application of Boolean polynomials in proving consistency and inconsistency
  • Learn about Disjunctive Normal Form (DNF) and its significance in logical expressions
  • Explore video tutorials on logical propositions and their transformations
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Students of logic, mathematicians, computer scientists, and anyone interested in the intersection of propositional logic and Boolean algebra.

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My professor wants to convert propositional statements such as X ^ Y into polynomeals such as

P[(X^Y)] = xy

Now, we may have multiple propositional formulas and wish to determine if they are consistent or inconsistent using Boolean polynomials.

I'm having a tough time finding material on this subject online or on you tube. Could someone please give me links to texts or videos where logical propositions are converted to Boolean polynomials and how they are used in proving consistency and inconsistency in a set of propositional formulas.

Also, I have some trouble converting statements such as

[ (p->q) -> (q->r) ] -> (p->r)

into Boolean polynomials.

Again, I'm looking for material covering the above scenarios. It would be much appreciated.
 
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