This paper proposes a new method to rank the cases classified by a decision tree. The method applies a posteriori without modification of the tree and doesn’t use additional training cases. It consists in computing the distance of the cases to the decision boundary induced by the decision tree, and to rank them according to this geometric score. When the data are numeric it is very easy to impl...

We present a novel approach to constraintbased causal discovery, that takes the form of straightforward logical inference, applied to a list of simple, logical statements about causal relations that are derived directly from observed (in)dependencies. It is both sound and complete, in the sense that all invariant features of the corresponding partial ancestral graph (PAG) are identified, even i...

This paper improves several well-known results concerning the descriptional complexity of grammars regulated by context conditions. Specifically, it proves that every recursively enumerable language is generated (A) by a context-conditional grammar of degree (2, 1) with no more than seven conditional productions and eight nonterminals, (B) by a generalized forbidding grammar of degree two with ...

Weighted labelled transition systems (WLTSs) are an established (meta-)model aiming to provide general results and tools for a wide range of systems such as non-deterministic, stochastic, and probabilistic systems. In order to encompass processes combining several quantitative aspects, extensions of the WLTS framework have been further proposed, state-to-function transition systems (FuTSs) and ...

The presence of deterministic relations pose problems for current algorithms that learn the causal structure of a system based on the observed conditional independencies. Deterministic variables lead to information equivalences; two sets of variables have the same information about a third variable. Based on information content, one cannot decide on the direct causes. Several edges model equall...

In 1952, Heinrich Scholz published a question in the Journal of Symbolic Logic asking for a characterization of spectra, i.e., sets of natural numbers that are the cardinalities of finite models of first order sentences. Günter Asser asked whether the complement of a spectrum is always a spectrum. These innocent questions turned out to be seminal for the development of finite model theory and d...