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Electronic Notes in Theoretical Computer Science (ENTCS)
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ETLs are temporal logics employing ω-automata as temporal connectives. This paper presents sound and complete axiom systems for ETLl, ETLf, and ETLr, respectively. Axioms and rules reflecting temporal behaviors of looping, finite and repeating automaton connectives are provided. Moreover, by encoding temporal operators into automaton connectives and instantiating the axioms and rules relating to automaton connectives, one may derive axiom systems for given ETL fragments.