Cirquent calculus in a nutshell

TL;DR

This paper introduces cirquent calculus, a new proof system that enhances traditional logic frameworks by explicitly modeling resource sharing through circuit-like structures, improving expressiveness and efficiency.

Contribution

It presents cirquent calculus as a novel, resource-aware proof system that refines sequent calculus with circuit constructs for better expressiveness and resource management.

Findings

Provides a formal definition of cirquent calculus.

Demonstrates increased expressiveness over traditional systems.

Shows potential for more efficient proof procedures.

Abstract

This paper is a brief and informal 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, flexibility and efficiency compared to the more traditional proof-theoretic approaches.