Resolution for branching time temporal logics: applying the temporal resolution rule

A clausal resolution method for branching-time logic ECTL

“…No more SRES rules are applicable. Formula 12 is an eventuality clause, and therefore, we are looking for a loop in Ô (see [3] for the formulation of the loop searching procedure). The desired loop, E E Ô Ä ´ µ (given that condition Þ ½ is satisfied) can be found considering clauses 10 and 11.…”

A Formal Specification Framework for Designing and Verifying Reliable and Dependable Software for CNC Systems

“…To model systems with temporal behaviors, temporal logics are the best choice which can specify system behaviors with logical formulas including temporal constraints, events, and relationships between the two [8][9][10]. Many different forms 2 Advances in Mechanical Engineering of temporal logics have been proposed such as PTL (propositional temporal logic) [11][12][13][14][15], BTTL (branching time temporal logic) [16], ITL (interval temporal logic) [17], CTL (computational tree logic) [18], RTL (real-time logic) [19,20], LRTL (linear real-time Logic) [1][2][3], and RTTL (real-time temporal logic) [21]. Among them, LRTL and RTTL are most suitable to specify and verify hard real-time systems.…”

A clausal resolution method for extended computation tree logic ECTL

“…One of the obvious benefits of using the clausal resolution technique is the possibility of invoking a variety of welldeveloped methods and refinements used in the framework of classical logic. The algorithm to search for loops needed for temporal resolution has been introduced in [2]. With the proof that SNF ÌÄ can be served as the normal form for ECTL, the algorithm becomes fully functional for the latter.…”

“…The basic idea of invoking temporal resolution is to resolve a set of formulae characterizing a loop in Ð, a set of SNF ÌÄ clauses indicating a situation when Ð occurs at all future moments along every (an A-loop in Ð) or some path (a E-loop in Ð) from a particular point in an ECTL model, together with the clause containing Ð [2]. Below we formulate the TRES 4 rule.…”

“…In [2,3] a clausal resolution approach to CTL has been developed, extending the original definition of the method for the linear-time case [11]. In this paper, following our general aim to expand the applicability of the method to more expressive formalisms, we define it for the logic ECTL.…”