Abstract
Firstly, an extension of linear-time temporal logic (LTL), called an agents-indexed linear-time temporal logic (ALTL), is introduced as a Gentzen-type sequent calculus. ALTL is intended to appropriately express reasoning about time-dependent multi-agents within a proof system. The cut-elimination and completeness theorems for ALTL are shown. Secondly, an extension of computation tree logic (CTL), called an agents-indexed computation tree logic (ACTL), is introduced as a Kripke-type semantics. ACTL is intended to appropriately formalize reasoning about time-dependent multi-agents within an executable temporal logic by model checking. The model-checking, validity and satisfiability problems for ACTL are shown to be decidable.
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