On the expressivity of the many-valued interval-based temporal logics

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Interval-Based Temporal Logics take intervals over linear orders as the primary objects of temporal analysis. The are 13 relations between the intervals known as Allen’s Relations on a linear order. We use Allen’s relation as the accessibility relation between intervals and interpret the interval structures as Kripke frames. One can think of Interval-Based Temporal Logics in a Many-Valued Interval setting where propositional variables are not just true or false but they are true or false to some extent and this extent we take as members of an algebra of truth values. Moreover, intervals can be taken to arise from many-valued linear orders. In this thesis we consider the interdefinability of modalities in the many valued interval setting. We define truth preserving morphisms that allow us to characterize the expressivity of many-valued interval-based temporal logic (MVIBTL). We use bismimulation as our primary truth preserving morphism and characterize which of the MVIBTL modalities are expressible in terms of the other modalities
A dissertation submitted in fulfilment of the requirements for the degree of Master of Science to the Faculty of Science, University of the Witwatersrand, Johannesburg, 2022
Interval-Based Temporal Logics, Many-Valued Interval setting