Nominal Substitution at work with the Global and Converse Modalities

This paper represents a continuation of a previous work, where a practical approach to the treatment of nominal equalities in tableaux for basic Hybrid Logic HL(@) was proposed. Its peculiarity is a substitution rule accompanied by nominal deletion. The main advantage of such a rule, compared with other approaches, is its efficiency, that has been experimentally verified for the HL(@) fragment. The integration of substitution and nominal deletion with more expressive languages is not a trivial task. In this work the previously proposed tableaux calculus for HL(@) is extended to hybrid logic with the global and converse modalities, taking into account also practical considerations. Though termination, in this case, relies on loop checks, the computational advantages of the substitution rule persist in this richer framework.