A clausal resolution method for CTL branching-time temporal logic

A clausal resolution method for branching-time logic ECTL

“…A significant part of this argument is either similar to the corresponding proofs given in [1,2] for CTL and ECTL or extend these proofs for new cases of ECTL · formulae. Therefore, we will only state such claims referring the reader to [1,2] while we sketch here proofs for new techniques used for ECTL · transformations. Note also that in our previous paper ([2]) we have not established the proof for the claim analogous to Lemma 3 (see below).…”

“…In order to achieve a refutation, we apply two types of resolution rules already defined in [1,4]: step resolution (SRES) and temporal resolution (TRES). The SRES rules are used between formulae which refer to the same initial moment of time or same next moment along some or all paths.…”

“…For the full set of rules preserved from the CTL the reader is referred to [1,4]. In the presentation below we omit the outer 'A ' connective that surrounds the conjunction of pre-clauses and, for convenience, consider a set of pre-clauses rather than the conjunction.…”

“…The justification of this labelling is based upon fixpoint characterization of basic CTL modalities and was explained in [1,2] except for the new specific ECTL · formulae in AE E form. The latter can be explained simply based upon the SNF ÌÄ semantics.…”

“…As a normal form for ECTL · , similarly to ECTL, we utilise a clausal normal form, defined for the logic CTL, SNF ÌÄ , which was developed in [1,4]. …”