We present three methods to check CTRSs for non-confluence: (1) an ad hoc method for 4-CTRSs, (2) a specialized method for unconditional critical pairs, and finally, (3) a method that employs conditional narrowing to find non-confluence witnesses. We shortly describe our implementation of these methods in ConCon [8], then look into their certification with CeTA [11], and finally conclude with e...

In the logic based framework of knowledge representation and reasoning many operators have been defined in order to capture different kinds of change: revision, update, merging and many others. There are close links between revision, update, and merging. Merging operators can be considered as extensions of revision operators to multiple belief bases. And update operators can be considered as po...

Proofs of coherence in category theory, starting from Mac Lane’s original proof of coherence for monoidal categories, are sometimes based on confluence techniques analogous to what one finds in the lambda calculus, or in term-rewriting systems in general. This applies to coherence results that assert that a category is a preorder, i.e. that “all diagrams commute”. This note is about this analog...

Driven by the interest of reasoning about probabilistic programming languages, we set out to study a notion of unicity of normal forms for them. To provide a tractable proof method for it, we define a property of distribution confluence which is shown to imply the desired unicity (even for infinite sequences of reduction) and further properties. We then carry over several criteria from the clas...

We extend the well-known results about the process of confluence for the Gauss hypergeometric differential equation to the case of general hypergeometric systems. We see that the process of confluence comes from the geometry of the set of regular elements of the Lie algebra of complex general linear group. As a consequence, we give a geometric and group-theoretic view on the process of confluen...