Abstract
The hybrid logic \(\mathcal{H}(@)\) is obtained by adding nominals and the satisfaction operator @ to the basic modal logic. The resulting logic gains expressive power without increasing the complexity of the satisfiability problem, which remains within PSpace. A resolution calculus for \(\mathcal{H}(@)\) was introduced in [5], but it did not provide strategies for ordered resolution and selection functions. Additionally, the problem of termination was left open.
In this paper we address both issues. We first define proper notions of admissible orderings and selection functions and prove the refutational completeness of the obtained ordered resolution calculus using a standard “candidate model” construction [10]. Next, we refine some of the nominal-handling rules and show that the resulting calculus is sound, complete and can only generate a finite number of clauses, establishing termination. Finally, the theoretical results were tested empirically by implementing the new strategies into HyLoRes [6,18], an experimental prototype for the original calculus described in [5]. Both versions of the prover were compared and we discuss some preliminary results.
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Areces, C., Gorín, D. (2005). Ordered Resolution with Selection for \(\mathcal{H}(@)\) . In: Baader, F., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2005. Lecture Notes in Computer Science(), vol 3452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-32275-7_9
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DOI: https://doi.org/10.1007/978-3-540-32275-7_9
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