5. Resolution - Discrete Mathematics - Vol 1
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5. Resolution

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.

12 sections

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Sections

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  1. 5
    Discrete Mathematics

    This section introduces resolution in discrete mathematics, focusing on the...

  2. 5.1

    This lecture covers the resolution rule in logic, its application in PROLOG,...

  3. 5.2

    This section introduces the resolution rule in logical arguments and its...

  4. 5.3
    Understanding The Resolution Rule

    This section introduces the resolution rule, a fundamental element in...

  5. 5.4
    Application Of Resolution Rule

    This section covers the resolution rule in propositional logic, explaining...

  6. 5.5
    Proof Of Validity Of Resolution

    The section introduces the resolution rule as a central inference rule in...

  7. 5.6
    Resolving More Than Two Clauses

    This section introduces the concept of resolution in propositional logic,...

  8. 5.7
    Example Of Resolution Tree

    This section introduces the concept of the resolution rule and explains its...

  9. 5.8
    Key Properties Of Resolution

    This section introduces the resolution rule, a key inference method in...

  10. 5.9
    Proof By Resolution Refutation

    This section introduces the resolution inference rule and the proof strategy...

  11. 5.10
    Example Of Argument Validation

    This section covers the resolution rule, an essential inference tool in...

  12. 5.11

    This section introduces the resolution inference rule in discrete...

What we have learnt

  • The resolution rule allows for canceling out common literals in clauses to derive conclusions.
  • The resolvent of a set of clauses helps identify unsatisfiability, which is critical in logical proofs.
  • Proof by resolution refutation can determine the validity of arguments by checking the unsatisfiability of premises when combined with the negation of the conclusion.

Key Concepts

-- Resolution Rule
A logical rule that allows the cancellation of a common literal present in both a positive and negative form across two clauses to derive a new clause.
-- Resolvent
The resulting clause derived from resolving two clauses using the resolution rule.
-- Proof by Resolution Refutation
A method for proving the validity of an argument by demonstrating that the conjunction of premises and the negation of the conclusion is unsatisfiable.
-- Unsatisfiability
A condition where no truth assignment exists that makes all clauses true, indicating that the set of clauses is inconsistent.

Additional Learning Materials

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