Introduction to clarithmetic II
arXiv:1004.3236 · doi:10.1016/j.ic.2016.02.002
Abstract
The earlier paper "Introduction to clarithmetic I" constructed an axiomatic system of arithmetic based on computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html), and proved its soundness and extensional completeness with respect to polynomial time computability. The present paper elaborates three additional sound and complete systems in the same style and sense: one for polynomial space computability, one for elementary recursive time (and/or space) computability, and one for primitive recursive time (and/or space) computability.
References in corpus (14)
- Sequential operators in computability logic
- Introduction to Cirquent Calculus and Abstract Resource Semantics
- Propositional computability logic I
- Cirquent calculus deepened
- Computability Logic: a formal theory of interaction
- From truth to computability I
- The intuitionistic fragment of computability logic at the propositional level
- Intuitionistic computability logic
- Many concepts and two logics of algorithmic reduction
- The logic of interactive Turing reduction
- Toggling operators in computability logic
- Towards applied theories based on computability logic
- Introduction to clarithmetic I
- A logical basis for constructive systems
Cited by in corpus (9)
- The taming of recurrences in computability logic through cirquent calculus, Part I
- Toggling operators in computability logic
- From formulas to cirquents in computability logic
- On the system CL12 of computability logic
- Introduction to clarithmetic I
- Build your own clarithmetic I: Setup and completeness
- Build your own clarithmetic II: Soundness
- A PSPACE-Complete First Order Fragment of Computability Logic
- Computational Complexity of Interactive Behaviors