Temporal alethic-deontic logic and semantic tableaux. (English) Zbl 1264.03054
Summary: The purpose of this paper is to describe a set of temporal alethic-deontic systems, i.e., systems that include temporal, alethic and deontic operators. All in all we consider 2,147,483,648 systems. All systems are described both semantically and proof-theoretically. We use a kind of possible worlds semantics, inspired by the so-called \(\mathrm{T} \times \mathrm{W}\) semantics, to characterize our systems semantically and semantic tableaux to characterize them proof-theoretically. We also show that all systems are sound and complete with respect to their semantics.
Keywords:
\(\mathrm{T} \times \mathrm{W}\) logics; temporal logic; modal logic; deontic logic; semantic tableaux; historical necessity; the ought-implies-can principle; the means-end principleReferences:
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