The Transformation Logics
This provides a novel framework for designing temporal logics tailored to specific applications, though it appears incremental as it builds on existing operator concepts.
The authors tackled the problem of balancing expressivity and complexity in temporal logics by introducing a new family with transformation operators, particularly based on semigroups, which create hierarchies of increasing expressivity and complexity that are non-trivial to characterise in existing logics.
We introduce a new family of temporal logics designed to finely balance the trade-off between expressivity and complexity. Their key feature is the possibility of defining operators of a new kind that we call transformation operators. Some of them subsume existing temporal operators, while others are entirely novel. Of particular interest are transformation operators based on semigroups. They enable logics to harness the richness of semigroup theory, and we show them to yield logics capable of creating hierarchies of increasing expressivity and complexity which are non-trivial to characterise in existing logics. The result is a genuinely novel and yet unexplored landscape of temporal logics, each of them with the potential of matching the trade-off between expressivity and complexity required by specific applications.