Metric Boolean Algebras and an Application to Propositional Logic

Dr. Li FU

Metric Boolean Algebras and an Application to Propositional Logic

Dr. Li FU * §

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§ QingHai Nationalities University

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

Reference Format

A Csaszar (1978). General Topology.
A Hamilton (1978). Logic for Mathematicians.
P Halmos (1974). Measure Theory.
P Johnstone (1982). Stone Space.
H Rasiowa,R Sikorski (1963). The Mathematics of Metamathematics.
G Wang (2000). Non -classical Mathematicical Logis and Approximate Reasoning.
(2011). Dev.
Eric Laurier (1999). Geographies of talk:<sup>2, 15</sup>‘Max left a message for you’<sup>16, 24</sup>.
A,B ∈ D(γ Unknown Title.
B Unknown Title.
B Unknown Title.
A,B ) = Ρ Unknown Title.
B Unknown Title.
B Unknown Title.
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. FU, Dr. FU. 1970. "Metric Boolean Algebras and an Application to Propositional Logic". Global Journal of Science Frontier Research GJSFR Volume 11 (GJSFR Volume 11 Issue 5).

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GJSFR Volume 11 Issue 5

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Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

Keywords

approximate reasoning Boolean algebra probability measure propositional logic similarity degree size

Classification

GJSFR Classification 03G05

54E35

60A10

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

English

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Article Matrices

Total Score: 181

Country: China

Subject: Global Journal of Science Frontier Research

Authors: Dr. Li FU , GuoJun Wang (PhD/Dr. count: 1)

View Count (all-time): 333

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Total Downloads (simulated): 389

Publish Date: 2011 07, Mon

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Total Views: 6.1K

Total Downloads: 389

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