Reactive Valuations
Bert Christiaan Regenboog
Abstract:
In sequential logic there is an order in which the atomic propositions
in an expression are evaluated. This order allows the same atomic
proposition to have diﬀerent values depending on which atomic
propositions have already been evaluated. In the sequential
propositional logic introduced by Bergstra and Ponse in [5], such
valuations are called "reactive" valuations, in contrast to "static"
valuations as are common in e.g. ordinary propositional logic. There
are many classes of these reactive valuations e.g., we can deﬁne a
class of reactive valuations such that the value for each atomic
proposition remains the same until another atomic proposition is
evaluated.
This Master of Logic thesis consists of a study of some of the
properties of this logic.
We take a closer look at some of the classes of reactive valuations
mentioned in [5]. We particularly focus on the relation between the
axiomatization and the semantics. Consequently, the main part of this
thesis focuses on proving soundness and completeness. Furthermore, we
show that the axioms in the provided axiomatizations are independent
i.e., there are no redundant axioms present. Finally, we show
ω-completeness for two classes of reactive valuations.