Abstraction Logic

[Steven Obua]

I have discovered a logic that is situated between first-order logic and second-order logic, and which I consider being the proper extension of propositional calculus, not first-order logic. I call this logic Abstraction Logic. This work generalises decades old work by Rasiowa who used an algebraic approach for non-classical logic (that’s also the name of her book). While Rasiowa treats quantifiers in a special way, abstraction logic treats them as normal constants, but does not use type theory for that purpose, but a simple shape specification. Where Rasiowa uses abstract algebras to show completeness of various propositional calculi, I use abstraction algebras to show completeness of abstraction logic, which gives new proofs to the completeness of intuitionistic and classical logic, albeit based on standard methods. I think my approach is new, but I am bracing myself to hear otherwise from you :-)

Here is the link to my paper: https://doi.org/10.47757/abstraction.logic.1 <https://doi.org/10.47757/abstraction.logic.1>

And here is the abstract:

Abstraction Logic is introduced as a foundation for Practical Types and Practal. It combines the simplicity of first-order logic with direct support for variable binding constants called abstractions. It also allows free variables to depend on parameters, which means that first-order axiom schemata can be encoded as simple axioms. Conceptually abstraction logic is situated between first-order logic and second-order logic. It is sound and complete with respect to an intuitive and simple algebraic semantics.

Best, 

Steven Obua

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https://obua.com
steven at obua.com


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