Open Daily: 10am - 10pm | Alley door pickup 10am - 7pm 3038 Hennepin Ave Minneapolis, MN
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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Abstraction Logic (Founder's Edition): A New Foundation for Reasoning, Computing, and Understanding

Abstraction Logic (Founder's Edition): A New Foundation for Reasoning, Computing, and Understanding

Obua, Steven

Paperback

General ComputersGeneral Science

ISBN13: 9798328992961
Publisher: Independently Published
Published: Jan 1 2025
Pages: 134
Weight: 0.57
Height: 0.35 Width: 6.00 Depth: 9.00
Language: English

Abstraction logic is a new logic combining exceptional simplicity with astonishing generality. It combines the best features of first-order logic and higher-order logic, while avoiding their respective drawbacks. It manages to do so because it is based on a simple understanding of the mathematical universe, its operations and, in particular, its operators. Abstraction algebra encodes this understanding as a formal language, generalising abstract algebra. It is the right setting for the treatment of alpha equivalence. Abstraction logic then turns abstraction algebra into a logic by considering truth values as a partially ordered substructure of the mathematical universe. A key property of this logic is that formulas are merely terms. Among the presented proof systems are natural deduction, which is sound if truth values form a complete lattice, and sequent calculus, which is sound if truth values form a complete bi-Heyting algebra. By constructing the Rasiowa model, we prove that natural deduction is a complete proof system for abstraction logic.

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