Section: Application Domains

Hybrid Automated Deduction

TALARIS's main contribution in this topic has been the design of resolution and tableaux calculi for hybrid logics, calculi that were then implemented in the HyLoRes and HTab theorem provers. For example, TALARIS members have proved that the resolution calculus for hybrid logics can be enhanced with optimisations of order and selection functions without losing completeness. Moreover, a number of `effective' (i.e., directly implementable) termination proofs for the hybrid logic $\mathscr{H}(@)$ has been established, for both resolution and tableaux based approaches, and the techniques are being extended to more expressive languages. Current work includes adding a temporal reasoning component to the provers, extending the architecture to allow querying against a background theory without having to explore again the theory with each new query, and testing the hybrid provers performance against dedicated state-of-the-art provers from other domains (firs-order logic, description logics) using suitable translations.

Moreover, we are interested in providing a range of inference services beyond satisfiability checking. For example, the current version of HyLoRes and HTab includes model generation (i.e., the provers can generate a model when the input formula is satisfiable).

We have also started to explore other decision methods (e.g., game based decision methods) which are useful for non-standard semantics like topological semantics. The prover HyLoBan is an example of this work.