Interpretation, coordination and conformity, in Ondrej Majer, Ahti-Veikko Pietarinen & Tero Tulenheimo (eds): Logic and
Games: Foundational Perspectives, Springer, to appear.
Abstract - MIMS Eprint 2005.32 (pdf)
The aim of this note is to investigate a very general problem of (radical) interpretation in terms of a simple coordination game: the conformity game. We show how, within our mathematical framework, the solution concept for the conformity game does indeed provide an algorithmic procedure facilitating triangulation, in the sense of Davidson.
KEYWORDS Rationality, Strategic interaction, Focal points, Radical Interpretation, Selection of multiple Nash-equilibria.
- An inductionless, default based account of machine learning (With E. Datteri and G. Tamburrini ) in L. Magnani (ed.) Model-Based Reasoning in Science and Engineering, College Publications, 2006, pp. 379-399 (ISBN 1-904987-23-0)
It has been suggested that AI investigations of mechanical learning undermine sweeping anti-inductivist views in the theory of knowledge and the philosophy of science. In particular, it is claimed that some mechanical learning systems perform epistemically justified inductive generalization and prediction. Contrary to this view, it is argued that no trace of such epistemic justification is to be found within a rather representative class of mechanical learning agents. An alternative deductive analysis of mechanical learning from examples is outlined.
First drawing on behaviour-based robotics, we examine relatively simple autonomous robots that learn from experience, insofar as they acquire new sensorimotor capabilities and generalize from observation. Analysis of a representative behaviour-based architecture reveals that even these rudimentary learning mechanisms embody crucial assumptions about their environment. In this context, the epistemic problem of induction is not ?solved?. Rather it is reformulated as the problem of assessing whether projections based on such background assumptions are reasonable to believe.
This epistemic problem is more informatively addressed by reference to the symbolically richer, ID3-style learning algorithms. Pervasive overfitting of training data jeopardizes the idea that epistemically justified induction is at work there: overfitting reminds one that good approximation to the target concept or rule on training data is not, in itself, diagnostic of good approximation over the whole instance space of that concept or rule. Once again, both ID3 learning and successful post-pruning of overfitting trees rely on the conjectural representativeness of concept instance collections.
Having found no trace of epistemically justified induction, an alternative deductivist account is outlined, drawing on some families of non-monotonic consequence relations, and emphasizing deductive trial and error-elimination processes in autonomous learning mechanisms. These processes interleave default-based introduction of projective hypotheses from observed samples, retraction of falsified hypotheses, and heuristic selection of new background assumptions for more effective learning.
KEYWORDS:Induction, machine learning, behavior-based robotics, non-monotonic consequence relations, artificial intelligence.
- Maximum Entropy Inference for Geographical Information Systems
(With Maria Vittoria Masserotti and Chiara Renso). in in G.Bordogna and G. Psaila (eds.) Flexible Databases supporting Imprecision and Uncertainty, Studies in Fuzziness and Soft Computing, Vol. 203 Springer, 2006.
The paper considers the problem of characterizing an inference process for reasoning under uncertainty in Geographic Information Systems (GIS). By focusing on a representative case study we outline the crucial aspects of the management of uncertainty in GIS. This enables us to argue, on methodological rather than practical grounds, in favour of the Maximum Entropy (ME) inference process. Specifically, we show how this constitutes a theoretically well-founded solution to the problems that arise naturally in GIS facing imperfect information. We also put forward how, as a consequence of the encouraging developments on computational techniques for reasoning under maximum entropy, the latter must be considered as a most crucial approach to uncertainty management in various fields of GIS science.
- Rationality as conformity (With J B Paris ), Synthese (Knowledge, Rationality and Action), Volume 144, Issue 2, 2005, Pages 249 - 285.
Abstract - MIMS Eprint 2005.31 (pdf) - Journal version (subscription required).
We argue in favour of identifying one aspect of rational choice with the tendency to conform to the choice you expect another like-minded, but non-communicating, agent to make and study this idea in the very basic case where the choice is from a non-empty subset $K$ of $2^A$ and no further structure or knowledge of $A$ is assumed.
KEYWORDS: Rationality; Common Sense; Coordination Games; Uncertainty; Principle of Charity; Social Choice Theory; Reasons.
- A note on Bridges from Classical to Nonmonotonic Logic,
Logic and Philosophy of Science, Vol.3, No.2.
Abstract - Preprint
Review and critical note on the newly published book by David Makinson, Bridges from Classical to Nonmonotonic Logic, King's College Text in Computing, volume 5, 2005 ISBN 1-904987-00-1. Published February 2005. Paperback.
- Imperfect information management in GIS: A logico-mathematical approach (With Maria Vittoria Masserotti and Chiara Renso). Technical Report 2004-TR-10, 2004-03-09, Institute for the Sciences and Technology of Information (ISTI-CNR), Pisa, Italy.
- Review of Bridges from Classical to Nonmonotonic Logic, by David Makinson, Bulletin of Symbolic Logic, 12, 3, 2006, pp. 499-502. (MIMS Eprint 2006.71)
- Philosophy of Probability, English translation of B. de Finetti's: Filosofia della Probabilitą, forthcoming in Kluwer's Synthese Library.
Rationality as conformity, Doctoral dissertation: School of Mathematics, The University of Manchester, (Successfully examined on 22 June 2005.)
Outline -- Full text (pdf)
Rationality-as-conformity begins with the idea that a ``rational", ``commonsensical",
``natural", or simply ``logical" choice is one which corresponds to the choice other
similar agents would come up with in similar situations. Our aim is to model the
choice processes leading to this sort of conformity. Consider the following example.
[Supermarket shelf arrangement.] There are numerous ways in which a supermarket manager might choose to arrange the shelves in her store, for example by alphabetical order of product name, by product size or weight, by price, by the package's colours, and so on indefinitely (not to mention the astronomic number of random orderings!). However when stepping into a new supermarket (i.e. one we have never visited before, and about which nothing is known to us, apart from the fact it is a supermarket) we expect to find teas close to coffees, pastas close to rices, nappies near to toilet rolls. At least we argue that it would surely seem natural to hold expectations of this sort. In fact, if after ten minutes searching we finally located the sugar among the washing powders, we might well be inclined to question the store manager's rationality! After all, we see this as a situation where, for mutual convenience, the store manager and ourselves are trying to conform on the selection of a common world, i.e. shelf arrangement.
Although this is the sort of situation we intend to model within our framework, it is not hard to see how rapidly the complications would arise, if we were to work with this informal problem. For instance it could be put forward that in fact there is no choice process to be modelled, but rather the appropriate use of common knowledge. The objection here would be that that there are in fact rules or conventions (arising in all probability from marketing research) that regulate what a ``rational" shelf arrangement is. [Surely there seems to be some cold-blooded form of logicality when it comes to shelving sweets right at the eyes-height of an invariantly bored child queueing at the till!] Hence, the objection would conclude, those rules or conventions are all that a ``rational" customer would have to learn to shop conveniently. This would surely work if there was something as a ``universal shelving rule" around. Yet, needless to say, this is utterly unreasonable. Therefore it is not hard to see that this possible objection just begs the question for ``the new customer" would still have to figure out which shelving convention the supermarket manager is in fact adopting.
The next objection then, might be to notice that supermarket managers might indeed fill up the store with signs and maps indicating to the unlearned customer where is what. An account of ``rational shelving" pursuing this line, however, would seem to be easily exposed to two sorts of shortcomings. Firstly, this rule would require an enormous amount of computational effort to be learnt. And surely the vast majority of this effort could in fact be spared if the manager would adopt the same rule she thinks the customer would utilize in the same situation. Secondly, what if the customer doesn't happen speak the language(s) chosen by the manager for the sings? What if the manager and the customer didn't in fact share any language at all?
In this thesis we shall consider an idealised and mathematically abstract situation where communication or knowledge of such rules and conventions are not available to the agents. Since it is assumed that agents' ultimate goal is that of conforming to the expectations of their peers, we shall refer to the overall approach as Rationality-as-conformity.
Rationality (or common sense - we shall not make a distinction among these terms) is, in its full generality an extremely complex and widely debated subject. Yet within the scope of our simple mathematical formulation we shall be able to provide what amounts to a characterization or definition of what it means to choose rationally. The hope is that such investigations will ultimately provide a way of viewing and understanding these notions in a much more general real world context.
- Rational coordination without communication, Department of Computer Science, The University of Liverpool, 18/10/2005 (pdf file of the presentation)
- Razionalitą come conformitą, Dipartimento di scienze fisiche, Universitį Federico II, Napoli 13/01/2005
- Relazioni di conseguenza non-monotoniche e agenti adattativi, Dipartimento di scienze fisiche, Universitį Federico II, Napoli Italy 12/01/2005
- Razionalitą come conformitą, Dipartimento di Scienze Matematiche e Informatiche, Universitį di Siena, Italy 11/01/2005
- Interpretation, Coordination and Conformity, Human-Machine Communication Department of the Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur (LIMSI), Orsay, France, 16 November 2004.
- A logical model of rationality as conformity, 1st World Congress on Universal Logic, Montreaux, Swizerland: March 31 - April 3 - 2005
- Razionalitą come conformitą, XXII meeting of the Italian Association for Logic and Applications (AILA), Pisa, Italy 14/02/2005
- An inductionless, default based account of machine learning,(with E. Datteri and G. Tamburrini) Model-Based Reasoning in Science and Engineering: Abduction, Visualization, Simulation Pavia, Italy, December 16-18, 2004.
- Conformity and Interpretation, Prague International Colloquium on Logic, Games and Philosophy, Prague, Czech Republic, October 2004.
- Machine learning from examples: A non inductivist analysis, (with E. Datteri and G. Tamburrini), Philosophy: problems, aims, responsibilities, Warwick, UK, September 2004
- Rationality as Conformity, (with J.B. Paris), Logic Colloquium 2004, Torino, Italy, July 2004.
- Rationality as Conformity, (with J.B. Paris), Degrees of Belief, Konstanz, Germany, July 2004.
- Rationality constraints on BDI logics Symposium on Logic in Games and Multiagent Systems, University of Liverpool, UK, December, 2002.