HyLoRes: A Hybrid Logic Prover Based on Direct Resolution

In recent years, an important number of theoretical results concerning axiomatizability, proof systems (tableaux, natural deduction, etc.), interpolation, expressive power, complexity, etc. for hybrid logics has been obtained. The next natural step is to develop provers that can handle these languages. HyLoRes is a direct resolution prover for hybrid logics implementing a sound and complete algorithm for satisfiability of sentences in H (@;#). The most interesting distinguishing feature of HyLoRes is that it is not based on tableau algorithms but on (direct) resolution. 1 Hybrid logics and HyLoRes Hybrid languages are modal languages that allow direct reference to the elements of a model. The basic hybrid language (H (@)) extends the basic modal language simply by the addition of a new set of atomic symbols called nominals (usually denoted as i; j;k; : : :) which name particular points in the model (i.e., the interpretation of a nominal i in a model M = hW;R;V i is an element i 2W ), and for each nominal i a satisfiability operator @i. This extension already increases the expressive power of the language as we can now explicitly check whether the point of evaluation w is the specific point named i in the modelM : M ;w i iff w = i : And from any point in the model we can check whether a point named i satisfies a given formula φ: M ;w @iφ iffM ; i φ: The extended expressivity allows one to define elegant decision algorithms, where nominals and @ play the role of labels, or prefixes, which are usually needed during the construction of proofs in the modal setup [10, 5]. Note that they do so inside the object language. All these features we get with no increase in complexity: the complexity of the satisfiability problem for H (@) is the same as for the basic modal language, PSPACE [3]. When we move to very expressive hybrid languages containing binders, we obtain an impressive boost in expressivity, but usually we also move beyond the boundaries of decidability. Classical binders like 8 and 9 (together with @) make the language as expressive as first-order logic (FOL) while the language H (@;#) which includes the more “modal” binder # gives a logic weaker than FOL [2] (but still undecidable). See the Hybrid Logic site at http://www.hylo.net for a broad on-line bibliography.