Cyclic induction is a powerful reasoning technique that consists in blocking the proof
development of certain subgoals already encountered during the proof process. In the …

Noetherian induction is one of the most general induction principles used in formal
reasoning. In the frame of the first-order reasoning, we propose a classification of its …

In first-order logic, the formula-based instances of the Noetherian induction principle allow to
perform effectively simultaneous, mutual and lazy induction reasoning. Compared to the …

Checking the soundness of cyclic induction reasoning for first-order logic with inductive
definitions (FOLID) is decidable but the standard checking method is based on an …

Structural and (Noetherian) cyclic induction are two instances of the Noetherian induction
principle adapted to reason on first-order logic. From a theoretical point of view, every …

Checking the soundness of the cyclic induction reasoning for first-order logic with in-ductive
definitions (FOL_ID) is decidable but the standard checking method is based on a doubly …

A cyclic proof system allows us to perform inductive reasoning without explicit inductions.
We propose a cyclic proof system for HFLN, which is a higher-order predicate logic with …

The framework of cyclic proof systems provides a reasonable proof system for logics with
inductive definitions. It also offers an effective automated proof search procedure for such …

We present in this paper the integration within the Coq proof assistant, of a method for
automatic theorem proving in geometry. We use an approach based on the validation of a …

We consider a cyclic approach to inductive reasoning in the setting of first-order logic with
inductive definitions. We present a proof system for this language in which proofs are …