From objective Bayesian epistemology
to inductive logic

UK Arts and Humanities Research Council project 2012-15

Teddy Groves (PhD student), Juergen Landes (RA), Jon Williamson (PI)

INTRODUCTION

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 critiques 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 2011).

EVENTS & TALKS

Conference: progic 2015: The Seventh Workshop on Combining Probability and Logic. Special focus: formal epistemology and inductive logic. University of Kent, Canterbury, UK, 20-22 April 2015.

Workshop: Inductive logic and confirmation in science. University of Kent, Paris Campus, France, 17-18 October 2013.

Workshop: Bristol-Kent workshop on scoring rules. London, 10 June 2013.

Teddy Groves: In what sense is Carnapian inductive logic objective? PhDs in Logic V, Munich, 8-10 April 2013.

Jon Williamson: Inductive Logic for Automated Decision Making. Artificial Intelligence and Simulation of Behaviour, 3-5 April 2013.

Juergen Landes: An objective Bayesian's bedtime story. Mathematics Department, Manchester, 13 March 2013.

Jon Williamson: Classical inductive logic. Reasoning Club conference, VUB, Belgium, 17-19 September 2012.

Teddy Groves: What does Shackel show about Bertrand's paradox? Reasoning Club conference, VUB, Belgium, 17-19 September 2012.

Workshop: Inductive logic. University of Kent, Canterbury, UK, 12-13 September 2012.

12th September - Keynes Seminar room 6
12.30pm lunch at the Gulbenkian cafe
1.30-2.00 Jon Williamson - Welcome and introduction
2.00-3.00 Jeff Paris - Guessing the World
3.00-3.30 coffee
3.30-4.30 Juergen Landes - How Objective Bayesianism met Dung-Style Argumentation
4.30-5.30 George Wilmers - The Social Entropy Process: Can it be Justified Axiomatically as a Natural Generalisation of the Maximum Entropy Inference Process?
13th September - Cornwallis Seminar room 12
9.30-10.30 Jon Williamson - How uncertain do we need to be?
10.30-11.30 Teddy Groves - What does Shackel show about Bertrand's paradox?
11.30-12.00 coffee
12.00-1pm Alena Vencovska - Probability Functions respecting the structure of information in Inductive Logic (as they arise when considering non-unary predicates)

Juergen Landes: Inductive logic, 12-13 September, The Reasoner 6(11):172, 2012.

PUBLICATIONS

Jon Williamson: Inductive logic, The Reasoner 6(11):176-7, 2012.

Juergen Landes: Inductive logic, 12-13 September, The Reasoner 6(11):172, 2012.

Jon Williamson: From Bayesian epistemology to inductive logic, Journal of Applied Logic, to appear.

Inductive logic admits a variety of semantics (Haenni et al., 2011, Part 1). This paper develops semantics based on the norms of Bayesian epistemology (Williamson, 2010, Chapter 7). §1 introduces the semantics and then, in §2, the paper explores methods for drawing inferences in the resulting logic and compares the methods of this paper with the methods of Barnett and Paris (2008). §3 then evaluates this Bayesian inductive logic in the light of four traditional critiques of inductive logic, arguing (i) that it is language independent in a key sense, (ii) that it admits connections with the Principle of Indifference but these connections do not lead to paradox, (iii) that it can capture the phenomenon of learning from experience, and (iv) that while the logic advocates scepticism with regard to some universal hypotheses, such scepticism is not problematic from the point of view of scientific theorising.

VISITORS

We are keen to welcome visitors who want to work on inductive logic at the University of Kent.

29 March 2013 - 31 March 2013: Kevin Korb
15 November 2012 - 28 February 2013: Soroush Rad
15 September 2012 - 16 November 2012: Martin Adamcik
12-14 September 2012: Jeff Paris, Alena Vencovska, George Wilmers.

ACKNOWLEDGEMENTS

We are very grateful to the UK Arts and Humanities Research Council for funding this research.