Metric Boolean Algebras and an Application to Propositional Logic

Dr. Li FU
Dr. Li FU
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GuoJun Wang
GuoJun Wang
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Qinghai University for Nationalities

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Metric Boolean Algebras and an Application to Propositional Logic

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Abstract

Let B be a Boolean algebra and Ω be the set of all homomorphisms from B into D, and μ be a probability measure on Ω . We introduce the concepts of sizes of elements of B and similarity degrees of pairs of elements of B by means of μ , and then define a metric on B . As an application, we propose a kind of approximate reasoning theory for propositional logic.

References

15 Cites in Article
  1. A Csaszar (1978). General Topology.
  2. A Hamilton (1978). Logic for Mathematicians.
  3. P Halmos (1974). Measure Theory.
  4. P Johnstone (1982). Stone Space.
  5. H Rasiowa,R Sikorski (1963). The Mathematics of Metamathematics.
  6. G Wang (2000). Non -classical Mathematicical Logis and Approximate Reasoning.
  7. (2011). Dev.
  8. Eric Laurier (1999). Geographies of talk:<sup>2, 15</sup>‘Max left a message for you’<sup>16, 24</sup>.
  9. A,B ∈ D(γ Unknown Title.
  10. B Unknown Title.
  11. B Unknown Title.
  12. A,B ) = Ρ Unknown Title.
  13. B Unknown Title.
  14. B Unknown Title.
  15. B Div(Γ) sup{d(A, B)|A, B ∈ D(Γ)} ≤ D(Γ).
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Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

How to Cite This Article

Dr. Li FU. 1970. \u201cMetric Boolean Algebras and an Application to Propositional Logic\u201d. Unknown Journal GJSFR Volume 11 (GJSFR Volume 11 Issue 5).

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  • CC-BY-ND-NC 4.0
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Journal Specifications
Keywords
approximate reasoningBoolean algebraprobability measurepropositional logicsimilarity degreesize
  • Submission ReceivedJune 7, 2011
  • Peer Review Double Blind
    Handling Editor
  • Accepted July 6, 2011
  • Published July 18, 2011
Version of record

v1.2

Issue date
July 11, 2011

Language
en
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High-quality academic research articles on global topics and journals.

Metric Boolean Algebras and an Application to Propositional Logic

Dr. Li FU
Dr. Li FU <p>Qinghai University for Nationalities</p>
GuoJun Wang
GuoJun Wang
  • Submission ReceivedJune 7, 2011
  • Peer Review Double Blind
    Handling Editor
  • Accepted July 6, 2011
  • Published July 18, 2011

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