My main interests lie in the area of Automated deduction including Logic Programming and Labelled Deductive Systems. I am also interested in some related aspects of Neural Nets and in the behaviour and control of reactive agents.
Generally, I would be happy to supervise projects related to automated deduction.
The topic of Labelled deductive systems (LDS), in which non-classical logics can be given a first order semantics, is also one for which there is an interest in constructing theorem provers. In particular, the method of Compiled Labelled Deductive Systems (CLDS), jointly with Dr. Alessandra Russo, has been shown to be suitable for expressing various non-classical logics, especially Modal logics. For instance, logics for which the approach looks interesting are temporal logic, belief/default logics, hybrid logics, term modal logics and logics for concurrency. It would also be interesting to investigate the use of logic programming formulations of CLDS with negation as failure rather than classcal logic. Abduction is also an area to which the approach has been applied.
The approach mentioned above, results in a first order theory for a logic. So far, all logics investigated have been known logics and the corresponding LDS is restricted in terms of its initial configuration in order to simulate the known logic. In case the restrictions are removed, then perhaps new logics can be devised. In particular, systematic ways of combining two different theories are of interest. The two theories could use the same language or different languages.
The behaviour and control of simple reactive agents by simple logic-like programs seems simple at first sight. In particular, Teleo-reactive programs are similar to production rule programs, but with the additional feature that there is an implicit goal of the program. Predicting the emergent behaviour of agents when endowed with such TR-programs, sometimes has unexpected results. Currently, with Dr. Chris Hogger, I am investigating how to synthesise programs for these agents and to build a hierarchy of such programs. Other approaches, such as learning TR programs, perhaps using Inductive Logic Programming or Neural Nets, would be of interest.