Object detection is always conducted by object proposal generation and classification
sequentially. This paper handles object detection in a superpixel oriented manner instead of …

Superposition-based provers have been successfully used to discharge proof obligations
stemming from proof assistants. However, many such obligations require induction to be …

The central concept of theorem designates a claim backed by an irrefutable argument that
follows formal rules, called a proof. Proving theorems is very useful in both Computer …

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 …

CLKID^ ω ω is a sequent-based cyclic inference system able to reason on first-order logic
with inductive definitions. The current approach for verifying the soundness of CLKID^ ω ω …

We develop logic and combinatorial methods for automating the generation of sorting
algorithms for binary trees, starting from input-output specifications and producing …

Cyclic pre-proofs can be represented as sets of finite tree derivations with back-links. In the
frame of the first-order logic with inductive definitions, the nodes of the tree derivations are …

SPIKE, an induction-based theorem prover built to reason on conditional theories with
equality, is one of the few formal tools able to perform automatically mutual and lazy …

An inductive definition set (IDS, for short) of first-order predicate logic can be transformed
into a many-sorted term rewrite system (TRS, for short) such that a quantifier-free sequent is …

The construction of a theory for binary trees is presented, based on the systematic
exploration of the properties necessary for the proof-based synthesis and certification of …