Discrete Mathematics - Vol 1 | 5. Resolution by Abraham | Learn Smarter
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5. Resolution

The chapter explores the resolution inference rule, a vital concept in logic used extensively in programming, particularly in AI applications like PROLOG. It defines how pairs of clauses with common literals can be resolved to form new conclusions, along with the introduction of proof by resolution refutation as a method for validating arguments. The content also delves into resolving sets of clauses and discusses the significance of unsatisfiability in the context of resolution.

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Sections

  • 5

    Discrete Mathematics

    This section introduces resolution in discrete mathematics, focusing on the resolution inference rule and its application in proof by resolution refutation.

    Learning Practice

  • 5.1

    Lecture -05

    This lecture covers the resolution rule in logic, its application in PROLOG, and the concept of proof by resolution refutation.

    Learning Practice

  • 5.2

    Resolution

    This section introduces the resolution rule in logical arguments and its significance in validating argument forms using resolution refutation.

    Learning Practice

  • 5.3

    Understanding The Resolution Rule

    This section introduces the resolution rule, a fundamental element in logical inference, especially in AI programming languages like PROLOG.

    Learning Practice

  • 5.4

    Application Of Resolution Rule

    This section covers the resolution rule in propositional logic, explaining its function as an inference rule and introducing the concept of proof by resolution refutation.

    Learning Practice

  • 5.5

    Proof Of Validity Of Resolution

    The section introduces the resolution rule as a central inference rule in logic, detailing how it can be used to prove the validity of arguments through resolution refutation.

    Learning Practice

  • 5.6

    Resolving More Than Two Clauses

    This section introduces the concept of resolution in propositional logic, focusing on resolving more than two clauses and proving argument validity through resolution refutation.

    Learning Practice

  • 5.7

    Example Of Resolution Tree

    This section introduces the concept of the resolution rule and explains its importance in propositional logic and proof strategies.

    Learning Practice

  • 5.8

    Key Properties Of Resolution

    This section introduces the resolution rule, a key inference method in discrete mathematics, along with its properties and proof strategy applied in logical reasoning.

    Learning Practice

  • 5.9

    Proof By Resolution Refutation

    This section introduces the resolution inference rule and the proof strategy known as proof by resolution refutation, emphasizing their applications in logic and AI.

    Learning Practice

  • 5.10

    Example Of Argument Validation

    This section covers the resolution rule, an essential inference tool in logic, outlining its application in validating arguments through proof by resolution refutation.

    Learning Practice

  • 5.11

    Summary

    This section introduces the resolution inference rule in discrete mathematics and its application in proving argument validity.

    Learning Practice

References

ch5.pdf

Class Notes

Memorization

What we have learnt

  • The resolution rule allows ...
  • The resolvent of a set of c...
  • Proof by resolution refutat...

Final Test

Revision Tests