Section: New Results
Inference Methods for Hybrid Logics
For a number of years now, members of LED have been working on inference methods for hybrid logics, both theoretically and developing applications.
HyLoRes, a resolution-based prover for hybrid logics, is a direct result of this line of research. The resolution calculus used by HyLoRes has been recently enhanced with heuristics for order and selection functions, and completeness is maintained even under these constraints, that help to greatly reduce the search space of the prover. In addition, by fixing a particular order and selection function, termination for resolution in H(@) was proved. This is the first proof of termination for an implementable decision method for H(@).
We have also explored efficient, satisfaction preserving translations into first-order logic. Such translations allow the use of modern first-order theorem provers to check for satisfiability of hybrid logic formulas. Intensive empirical testing shows this to be a viable option. The nature of the formulas obtained under our optimised translation of the hybrid input gives rise to a `layering' effect that helps the first-order prover to find a solution 
In addition to resolution methods, LED members have recently obtained results in more classical approaches to inference like axiomatics and tableaux methods. A detailed investigation of axiomatic systems for hybrid languages have recently appeared in Studia Logica  , and an article on termination techniques for hybrid logic tableaux is under way.