DeepAI AI Chat
Log In Sign Up

Complementation: a bridge between finite and infinite proofs

by   Gilles Dowek, et al.
State Key Laboratory of Computer Science, Institute

When a proposition has no proof in an inference system, it is sometimes useful to build a counter-proof explaining, step by step, the reason of this non-provability. In general, this counter-proof is a (possibly) infinite co-inductive proof in a different inference system. In this paper, we show that, for some decidable inference systems, this (possibly) infinite proof has a representation as a finite proof in yet another system, equivalent to the previous one.


page 1

page 2

page 3

page 4


Tight infinite matrices

We give a simple proof of a recent result of Gollin and Joó: if a possib...

The characterization of infinite Eulerian graphs, a short and computable proof

In this paper we present a short proof of a theorem by Erdős, Grünwald a...

Undecidability in Finite Transducers, Defense Systems and Finite Substitutions

In this manuscript we present a detailed proof for undecidability of the...

Irrationality and Transcendence Criteria for Infinite Series in Isabelle/HOL

We give an overview of our formalizations in the proof assistant Isabell...

Automating Reasoning with Standpoint Logic via Nested Sequents

Standpoint logic is a recently proposed formalism in the context of know...

Memoryless Determinacy of Infinite Parity Games: Another Simple Proof

The memoryless determinacy of infinite parity games was proven independe...

Generalizing inference systems by coaxioms

After surveying classical results, we introduce a generalized notion of ...