UK Arts and Humanities Research Council project 201215.
Investigators: Teddy Groves (PhD student), Juergen Landes (RA), Jon Williamson (PI)
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 1950s70s, 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 1980s90s, 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).
Visitors:
We are keen to welcome visitors who want to work on inductive logic at the University of Kent.
 10 February 2014 – 30 April 2014: Christian Wallmann
 29 March 2013 – 31 March 2013: Kevin Korb
 15 November 2012 – 28 February 2013: Soroush Rad
 15 September 2012 – 16 November 2012: Martin Adamcik
 1214 September 2012: Jeff Paris, Alena Vencovska, George Wilmers.
PublicationsJon Williamson: Lectures on inductive logic, Oxford University Press, 2017. Teddy Groves: Let’s Reappraise Carnapian Inductive Logic! PhD thesis, University of Kent, 2015. Journal special issue: Combining probability and logic, Journal of Applied Logic 14. March 2016. Editorial: Journal special issue: Maximum Entropy Applied to Inductive Logic and Reasoning, Entropy journal. Jim Hawthorne, Juergen Landes, Christian Wallmann & Jon Williamson: The Principal Principle implies the Principle of Indifference, British Journal for the Philosophy of Science. 68:123–131, 2017. doi: 10.1093/bjps/axv030. Juergen Landes & Jon Williamson: Objective Bayesian nets from consistent datasets, in Adom Giffin & Kevin H. Knuth (eds), Proceedings of the 35th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Potsdam NY. American Institute of Physics Conference Proceedings 1757, 2016. doi: 10.1063/1.4959048 Teddy Groves: Lakatos’ criticism of Carnap’s inductive logic was mistaken, Journal of Applied Logic 14:321, 2016. doi: 10.1016/j.jal.2015.09.014 Teddy Groves: An application of Carnapian inductive logic to an argument in the philosophy of statistics, Journal of Applied Logic 12(3): 302318, 2014. doi: 10.1016/j.jal.2014.05.002 Juergen Landes & Jon Williamson: Justifying Objective Bayesianism on Predicate Languages, Entropy 17: 24592543, 2015; doi: 10.3390/e17042459. Objective Bayesianism says that the strengths of one’s beliefs ought to be probabilities, calibrated to physical probabilities insofar as one has evidence of them, and otherwise sufficiently equivocal. These norms of belief are often explicated using the maximum entropy principle. In this paper we investigate the extent to which one can provide a unified justification of the objective Bayesian norms in the case in which the background language is a firstorder predicate language, with a view to applying the resulting formalism to inductive logic. We show that the maximum entropy principle can be motivated largely in terms of minimising worstcase expected loss. Jürgen Landes & Jon Williamson: Objective Bayesianism and the Maximum Entropy Principle, Entropy 15(9): 35283591, 2013. . . doi:10.3390/e15093528
Jon Williamson: From Bayesian epistemology to inductive logic, Journal of Applied Logic 11: 468486, 2013. doi: 10.1016/j.jal.2013.03.006
Jon Williamson: Inductive logic, The Reasoner 6(11):1767, 2012. Michael Wilde & Jon Williamson: Bayesianism and information, in L. Floridi (ed.), The Routledge Handbook of Philosophy of Information. In press.
Jürgen Landes: Probabilism, Entropies and Strictly Proper Scoring Rules, International Journal of Approximate Reasoning 63:121, 2015. . doi:10.1016/j.ijar.2015.05.007 Accuracy arguments are the en vogue route in epistemic justifications of probabilism and further norms governing rational belief. These arguments often depend on the fact that the employed inaccuracy measure is strictly proper. I argue controversially that it is illadvised to assume that the employed inaccuracy measures are strictly proper and that strictly proper statistical scoring rules are a more natural class of measures of inaccuracy. Building on work in belief elicitation I show how strictly proper statistical scoring rules can be used to give an epistemic justification of probabilism. An agent’s evidence does not play any role in these justifications of probabilism. Principles demanding the maximisation of a generalised entropy depend on the agent’s evidence. In the second part of the paper I show how to simultaneously justify probabilism and such a principle. I also investigate scoring rules which have traditionally been linked with entropies. Jürgen Landes: MinMax Decision Rules for Choice under Complete Uncertainty: Axiomatic Characterizations for Preferences over Utility Intervals, International Journal of Approximate Reasoning 55: 13011317, 2014. . doi 10.1016/j.ijar.2013.10.008
Jon Williamson: Deliberation, Judgement and the Nature of Evidence, Economics and Philosophy 31(1): 2765, 2015. doi: 10.1017/S026626711400039X
Jon Williamson: How uncertain do we need to be? Erkenntnis 79(6):12491271, 2014. Published version:. Local version: . Video: doi 10.1007/s1067001395166.
Jürgen Landes: Review of Michael Strevens’ Tychomancy: Inferring Probability from Causal Structure, International Studies in the Philosophy of Science 28(4): 446448, 2014. . doi: 10.1080/02698595.2014.979675 Jon Williamson: Review of Reliable Reasoning by Gilbert Harman and Sanjeev Kulkarni, Mind 121:10731076, doi 10.1093/mind/fzt006, 2013. Jürgen Landes: Review of Evolution and Rationality: Decisions, Cooperation and Strategic Behaviour by Samir Okasha and Ken Binmore, Philosophical Quarterly, 2014; doi: 10.1093/pq/pqt040. . Jürgen Landes: Inductive logic, 1213 September, The Reasoner 6(11): 172, 2012. George Darby & Jürgen Landes: There Is More to a Paradox Than Credence, Thought 3(2): 99109, 2014. doi:10.1002/tht3.117

Events and TalksTeddy Groves – Revisiting Lakatos’s criticism of Carnapian inductive logic, CLMPS, University of Helsinki, 38 August 2015. Jürgen Landes: Objective Bayesian nets from consistent data sets. 35th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Clarkson University, 19 24 July 2015. Jürgen Landes: Objective Bayesian Nets – from consistent data sets. British Society for the Philosophy of Science. Manchester, UK, 2 – 3 July 2015. Jürgen Landes: Objective Bayesian Nets – from consistent data sets. Computability in Europe. Bucharest, Romania, 29 June – 3 July 2015. Jon Williamson – Epistemic consequentialism and the principle of indifference, Epistemic Consequentialism: problems and prospects, Kent, 2526 June 2015. Teddy Groves – Response to Jon Williamson, Epistemic Consequentialism: problems and prospects, Kent, 2526 June 2015. Teddy Groves – Accuracy arguments for probabilism, Formal Epistemology, Bristol, 15 June 2015. Jon Williamson – Objective vs Subjective Bayesianism, The Odds for Bayesianism, Vienna, 2830 May 2015. Teddy Groves – Problems with Accuracy Arguments for Probabilism, The Odds for Bayesianism, Vienna, 2830 May 2015. Jürgen Landes: A course on Bayesian Epistemology. Lund, 1822 May 2015. Conference: progic 2015: The Seventh Workshop on Combining Probability and Logic. Special focus: formal epistemology and inductive logic. Following the Spring School on Combining Probability and Logic. University of Kent, Canterbury, UK, 2024 April 2015. Teddy Groves: A problem for objective Bayesian inductive logic. Progic 2015. University of Kent, Canterbury, UK, 2224 April 2015. Jürgen Landes: Maximum entropy and inductive logic. Spring School on Combining Probability and Logic. University of Kent, Canterbury, UK, 2021 April 2015. Jon Williamson: Classical, Carnapian and objective Bayesian inductive logics. Spring School on Combining Probability and Logic. University of Kent, Canterbury, UK, 2021 April 2015. Teddy Groves – Objective Bayesian epistemology and inductive logic, Reasoning Club, Manchester, 3031 March 2015. Jon Williamson: Classical inductive logic, Carnap’s programme and the objective Bayesian approach. Perspectives on Inductive Logic, Irvine, 1920 March 2015. Jürgen Landes: Evidence aggregation, decision making, hierarchy, CHiP. Theoretical Reasoning seminar, Kent, 28 January 2015. Jon Williamson: The Principal Principle implies the Principle of Indifference. Objective Probability and Conditional Reasoning seminar, Institute of Philosophy, London, 18 November 2014. Jürgen Landes: How an Objective Bayesian Integrates Data. Inductive Logic and Confirmation in Science II, Utah, 2425 October 2014. Jon Williamson: The Principal Principle implies the Principle of Indifference. Knowledge in a Digital World, Canterbury, 1617 October 2014. Jürgen Landes: How an Objective Bayesian Integrates Data. Knowledge in a Digital World, Canterbury, 1617 October 2014. Teddy Groves: Was Carnapian inductive logic degenerate? Theoretical Reasoning seminar, Kent, 8 October 2014. Jon Williamson: The Principal Principle implies the Principle of Indifference. Munich Centre for Mathematical Philosophy, 8 October 2014. Jürgen Landes: Philosophy: rational belief formation. Erasmus lectures at the Munich Centre for Mathematical Philosophy, 1418 July 2014. Jürgen Landes: Strictly Proper Scoring Rules and the Probability Norm, British Society for Philosophy of Science, 1011 July 2014. Teddy Groves: Accuracy arguments in the context of Carnapian inductive logic, British Society for Philosophy of Science, 1011 July 2014. Jürgen Landes: Scoring rules, entropies and indifference, Reasoning Club conference, 2324 June 2014. Teddy Groves: Accuracy arguments for probabilism in the context of Carnapian inductive logic, 4th LSE Graduate Conference in Philosophy of Probability, 67 June 2014. Jon Williamson: Induction. Erasmus lectures at Boğaziçi University Philosophy Department, 2630 May 2014. CANCELLED. Jon Williamson: Inductive logic for automated decision making. Italian Association for Logic, Pisa, 1417 April 2014. Jeff Paris & Jon Williamson: Workshop on Pure Inductive Logic. 5th Indian School on Logic and its Applications, Tezpur University, 617 January 2014. Jon Williamson: Inductive Logic for Automated Decision Making. Cognitive Science Institute, Osnabrück, 4 December 2013. Jon Williamson: Aggregating degrees of belief. Theoretical Reasoning Seminar, Kent, 7 November 2013. Jürgen Landes: Comparing Epistemic and Statistical Scoring Rules. Theoretical Reasoning Seminar, Kent, 24 October 2013. Workshop: Inductive logic and confirmation in science. University of Kent, Paris Campus, France, 1718 October 2013. Teddy Groves: An application of Carnapian inductive logic to philosophy of statistics. progic 2013, The Sixth Workshop on Combining Probability and Logic: Combining probability and logic to solve philosophical problems, Munich, 1718 September 2013. Juergen Landes & Jon Williamson: Objective Bayesian Epistemology for Inductive Logic on Predicate Languages. progic 2013, The Sixth Workshop on Combining Probability and Logic: Combining probability and logic to solve philosophical problems, Munich, 1718 September 2013. Jon Williamson: Inductive Logic for Automated Decision Making. British Logic Colloquium, 57 September 2013. Teddy Groves: An application of Carnapian inductive logic to philosophy of statistics. Second Reasoning Club Conference, Scuola Normale Superiore, Pisa, 1719 June 2013. Jürgen Landes: Objective Bayesianism and the maximum entropy principle. Second Reasoning Club Conference, Scuola Normale Superiore, Pisa, 1719 June 2013. Teddy Groves: An application of Carnapian inductive logic to philosophy of statistics. Theoretical Reasoning Seminar, Kent, 13 June 2013. Workshop: BristolKent workshop on scoring rules. London, 10 June 2013.
Teddy Groves: In what sense is Carnapian inductive logic objective? PhDs in Logic V, Munich, 810 April 2013. Teddy Groves: In what sense is Carnapian inductive logic objective? Theoretical Reasoning Seminar, Kent, 4 April 2013. Jon Williamson: Inductive Logic for Automated Decision Making. Artificial Intelligence and Simulation of Behaviour, 35 April 2013. Teddy Groves: In what sense is Carnapian inductive logic objective? Advanced Topics in Reasoning, Kent, 26 March 2013. Jürgen Landes: The OBEIL project and YOU. Advanced Topics in Reasoning, Kent, 26 March 2013. Jürgen Landes: Coordination Problems and You. Theoretical Reasoning Seminar, Kent, 21 March 2013. Jürgen Landes: An objective Bayesian’s bedtime story. Mathematics Department, Manchester, 13 March 2013. Jürgen Landes: Proper scoring rules. Philosophy Department Seminar, Kent, 22 January 2013. Jürgen Landes: Mechanism design and you. Philosophy Department MA seminar, Kent, 5 December 2012. Soroush Rad: Updating. Theoretical Reasoning Seminar, Kent, 15 November 2012. Martin Adamcik: Aggregating evidence bases. Theoretical Reasoning Seminar, Kent, 4 October 2012. Jon Williamson: Classical inductive logic. Reasoning Club conference, VUB, Belgium, 1719 September 2012. Teddy Groves: What does Shackel show about Bertrand’s paradox? Reasoning Club conference, VUB, Belgium, 1719 September 2012. Workshop: Inductive logic. University of Kent, Canterbury, UK, 1213 September 2012.

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