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A temporal logic of belief and actions (TLBA) is considered. The TLBA allows us to express informational and dynamic properties of computational agents. The considered fragment of TLBA allows one: (1) to present a deduction-based structured decision procedure; (2) to separate a decision procedure for so-called induction-free formulas and (3) to use only logical axioms for such formulas. The main new technical tool of the presented decision procedure is separation rules which incorporatedoi:10.15388/informatica.2004.067 fatcat:jasy3mrrzfbrtat4wxmajzodmq