It is argued that if we take grounding to be univocal, then there is a serious tension between truthgrounding and one commonly assumed structural principle for grounding, namely transitivity. The primary claim of the paper is that truth-grounding cannot be transitive. Accordingly, it is either the case that grounding is not transitive or that truth-grounding is not grounding, or both.

The rationalizability of a choice function by means of a transitive relation has been analyzed thoroughly in the literature. However, not much seems to be known when transitivity is weakened to quasi-transitivity or acyclicity. We describe the logical relationships between the different notions of rationalizability involving, for example, the transitivity, quasi-transitivity, or acyclicity of t...

Recent progress in symbolic dynamics of cellular automata (CA) shows that many CA exhibit rich and complicated Bernoulli-shift properties, such as positive topological entropy, topological transitivity and even mixing. Noticeably, some CA are only transitive, but not mixing on their subsystems. Yet, for one-dimensional CA, this paper proves that not only the shift transitivity guarantees the CA...