Electronic Theses and Dissertations (PhDs)

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An Essay on Branching Time Logics
(University of the Witwatersrand, Johannesburg, 2024) Marais, Chantel
In this thesis we investigate the Priorian logics of a variety of classes of trees. These classes of trees are divided in to irreflexive and reflexive trees, and each of these has a number of subclasses, for example, dense irreflexive trees, discrete reflexive trees, irreflexive trees with branches isomorphic to the natural numbers, etc. We find finite axiomatisations for the logics of these different classes of trees and show that each logic is sound and strongly / weakly complete with respect to the respective class of trees. The methods use to show completeness vary from adapting some known constructions for specific purposes, including unravelling and bulldozing, building a network step-by-step, filtering through a finite set of formulas, as well as using some new processes, namely refining the filtration and unfolding. Once the logics have been shown to be sound and complete with respect to the different classes of trees, we also show that most of these logics are decidable, using methods that include the finite model property, mosaics and conservative extensions. Lastly, we give a glimpse into the available research on other languages used to study branching time structures, including the Peircean and Ockhamist languages, and languages that include additional modal operators like “since” and “until”