From objective Bayesian epistemology to inductive logic

The main aim of this project is to revive inductive logic (the logic of inference under uncertainty) by building on recent developments in epistemology (the theory of knowledge and belief).

Inductive logic has potential application to any area in which one needs to reason about structure, but where evidence is limited and uncertainty is rife. For example, bioinformatics requires formal methods for reasoning about biological structure in the presence of only partial knowledge of genetic function and biochemical processes; natural language processing requires formal methods for reasoning about sentence structure and meaning in the presence of statistical evidence of previously processed sentences.

However, after intensive research in the 1950s-70s, the inductive logic programme faced important philosophical critiques from which it never fully recovered. Thus, while there are a few small pockets of researchers still working on logics for reasoning under uncertainty, the inductive logic programme is widely held to have failed.

In the 1980s-90s, new methods for handling uncertainty were developed - probabilistic network methods - which are computational rather than logical techniques. These new methods filled the need for computationally feasible tools for manipulating and reasoning with probabilities, and research on inductive logic remained on the sidelines. However, while probabilistic networks can handle uncertainty in an elegant way, they were not developed for reasoning about structure at the same time. There are attempts to extend the probabilistic network formalism to cope with richer structure, but these methods are complex and disparate and no clear contender has emerged.

Now is the right time to revive the inductive logic programme. This is for three reasons. First, the need for inductive logic remains: there is still a need throughout the sciences to reason about structure under uncertainty and inductive logic is the natural formalism for fulfilling that need. Second, recent work in epistemology has offered the possibility of developing a new approach to inductive logic that may survive the traditional critique of inductive logic. In particular, ideas emerging from probabilistic epistemology may offer a coherent approach to inductive logic (see, e.g., 'In defence of objective Bayesianism', Oxford University Press 2010). Third, recent work in forging connections between probabilistic logics and probabilistic networks has led to the possibility of developing computationally tractable methods for performing calculations in inducitve logic (see, e.g., 'Probabilistic logics and probabilistic networks', Springer 2010).

This project will:
(i) develop the formal apparatus of inductive logic as underpinned by the emerging probabilistic epistemology,
(ii) investigate whether the resulting logic does indeed survive the traditional philosophical critiques of inductive logic, and
(iii) develop computational methods, based on probabilistic networks, for performing inference in the resulting inductive logic.

Who will benefit from this research?

This is principally a philosophical and theoretical project, whose direct beneficiaries will be academic philosophers, logicians and computer scientists.

However, there are many more potential beneficiaries in the long term. A viable inductive logic would be of immense interest to engineers who produce decision support systems for reasoning in the presence of complex structure and uncertainty. Such systems are used by scientists (e.g., bioinformaticians, computational linguists) but also by medics (e.g., diagnostic / prgnostic systems) and by the public at large (e.g., automated troubleshooters, translation tools).

How will they benefit from this research?

Philosophers will benefit from the research at the end of the project by having a greater understanding as to whether recent developments in epistemology can be applied to yield an inductive logic that avoids the broad range of problems that beset previous inductive logics.

Logicians will benefit at the end of the project by having a greater understanding of probabilistic logics and of decision methods for those logics.

Computer scientists will benefit at the end of the project by having a greater understanding of a range of computational methods for reasoning under uncertainty.

Should the project demonstrate that a viable inductive logic can be produced (i.e., one that survives philosophical critiques and can be meshed with tractable computational methods), then in the long term (3-20 years) the research of this project can benefit scientists, medics and the general public via the development of more effective decision support systems.

Improved medical decision support systems will clearly impact on the nation's health, as decision support systems are already used widely in frontline services (e.g., NHS Direct, ambulance prioritisation systems) as well as behind the scenes in diagnostic and prognostic tools and in the advancement of medical science.

Improved decision support systems will also impact on the nation's wealth, as decision support systems are widely used in finance (e.g., automated trading, economic forecasting, loan authorisation) as well as manufacturing (e.g., quality control systems, logistics, troubleshooting) and other areas.