DeepAI AI Chat
Log In Sign Up

Cirquent calculus in a nutshell

by   Giorgi Japaridze, et al.

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.


page 1

page 2

page 3

page 4


A repetition-free hypersequent calculus for first-order rational Pavelka logic

We present a hypersequent calculus G^3Ł∀ for first-order infinite-valued...

Schematic Refutations of Formula Schemata

Proof schemata are infinite sequences of proofs which are defined induct...

A Symmetric Lambda-Calculus Corresponding to the Negation-Free Bilateral Natural Deduction

Filinski constructed a symmetric lambda-calculus consisting of expressio...

The Logic for a Mildly Context-Sensitive Fragment of the Lambek-Grishin Calculus

While context-free grammars are characterized by a simple proof-theoreti...

Introducing Proof Tree Automata and Proof Tree Graphs

In structural proof theory, designing and working on large calculi make ...

A polynomial time algorithm for the Lambek calculus with brackets of bounded order

Lambek calculus is a logical foundation of categorial grammar, a linguis...

The em-convex rewrite system

We introduce and study em (or "emergent"), a lambda calculus style rewri...