A Tableau Calculus for a Temporal Logic with Temporal Connectives

The paper presents a tableau calculus for a linear time tem poral logic for reasoning about processes and events in concurrent sys tems The logic is based on temporal connectives in the style of Transac tion Logic BK and explicit quanti cation over states The language extends rst order logic with sequential and parallel conjunction parallel disjunction and temporal implication Explicit quanti cation over states via state variables allows to express temporal properties which cannot be formulated in modal logics Using the tableau representation of temporal Kripke structures presented for CTL in MS which represents states by pre x terms explicit quan ti cation over states is integrated into the tableau calculus by an adap tation of the rule from rst order tableau calculi to the linear ordering of the universe of states Complementing the CTL calculus the paper shows that this tableau representation is both suitable for modal temporal logics and for logics using temporal connectives