# Cirquent calculus in a nutshell

@article{Japaridze2022CirquentCI, title={Cirquent calculus in a nutshell}, author={Giorgi Japaridze and Bikal Lamichhane}, journal={ArXiv}, year={2022}, volume={abs/2108.12552} }

This paper is a brief presentation of cirquent calculus, a novel proof system for resource-conscious logics. As such, it is a refinement of sequent calculus with mechanisms that allow to explicitly account for the possibility of sharing of subexpressions/subresources between different expressions/resources. This is achieved by dealing with circuit-style constructs, termed cirquents, instead of formulas, sequents or other tree-like structures. The approach exhibits greater expressiveness…

## References

SHOWING 1-10 OF 16 REFERENCES

### Introduction to Cirquent Calculus and Abstract Resource Semantics

- Computer ScienceJ. Log. Comput.
- 2006

An abstract resource semantics is introduced and the soundness and completeness of CL5 with respect to it are shown and an implied claim of computability logic is that it is CL5 rather than affine logic that adequately materializes the resource philosophy traditionally associated with the latter.

### The Computational Complexity of Propositional Cirquent Calculus

- Computer ScienceLog. Methods Comput. Sci.
- 2015

The computational complexity of CL5 is investigated, showing it is $\Sigma_2^p$-complete and it is also shown that CL5 without the duplication rule has polynomial size proofs and is NP-complete.

### Cirquent Calculus Deepened

- Computer ScienceJ. Log. Comput.
- 2008

This article presents a detailed elaboration of a deep-inference cirquent logic, which is naturally and inherently resource conscious, and shows that classical logic, both syntactically and semantically, can be seen to be just a special, conservative fragment of this more general and, in a sense, more basic logic—the logic of resources in the form of cirquents.

### From formulas to cirquents in computability logic

- Computer ScienceLog. Methods Comput. Sci.
- 2011

The expressive power of CoL is extended in a qualitatively new way, generalizing formulas to circuit-style structures termed cirquents, which are able to account for subgame/subtask sharing between different parts of the overall game/task.

### The taming of recurrences in computability logic through cirquent calculus, Part I

- Computer ScienceArch. Math. Log.
- 2013

This paper constructs a cirquent calculus system and proves its soundness and completeness with respect to the semantics of computability logic. The logical vocabulary of the system consists of…

### Elementary-base cirquent calculus II: Choice quantifiers

- Computer ScienceLog. J. IGPL
- 2021

The present paper constructs the first-order version CL17 of CL16, also enjoying soundness and completeness, and augments that of CL18 by including choice quantifiers.

### On linear rewriting systems for Boolean logic and some applications to proof theory

- Computer ScienceLog. Methods Comput. Sci.
- 2016

This paper studies properties of systems consisting only of linear inferences and finds that the length of any 'nontrivial' derivation in such a system is bound by a polynomial, unless coNP=NP.

### Soundness and completeness of the Cirquent calculus system CL6 for computability logic

- Computer ScienceLog. J. IGPL
- 2012

The earlier article "Introduction to cirquent calculus and abstract resource semantics" by Japaridze proved soundness and completeness for the basic fragment CL5 of computability logic, which is a conservative extension of both CL5 and classical propositional logic.

### Elementary-base cirquent calculus I: Parallel and choice connectives

- Computer ScienceFLAP
- 2018

This article constructs a sound and complete axiomatization CL16 of the propositional fragment of computability logic whose logical vocabulary consists of negation and parallel and choice connectives, and whose atoms represent elementary, i.e. moveless, games.