Abstract
LTL is frequently used to express specifications in many domains such as embedded systems or business processes. Witnesses can help to understand why an LTL specification is satisfiable, and a number of approaches exist to make understanding a witness easier. In the case of unsatisfiable specifications unsatisfiable cores (UCs), i.e., parts of an unsatisfiable formula that are themselves unsatisfiable, are a well established means for debugging. However, little work has been done to help understanding a UC of an unsatisfiable LTL formula. In this paper we suggest to enhance a UC of an unsatisfiable LTL formula with information about the time points at which the subformulas of the UC are relevant for unsatisfiability. In previous work we showed how to obtain a UC in LTL by translating the LTL formula into a clausal normal form, applying temporal resolution, extracting a clausal UC from the resolution proof, and mapping the clausal UC back to a UC in LTL. In this paper we extend that method by extracting information at which time points the clauses of a clausal UC are relevant for unsatisfiability from a resolution proof and by transferring that information to a UC in LTL. We implement our method in TRP++, and we experimentally evaluate it.
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