Simplicity, scientific inference and econometric modelling

Economic Schools;Econometric Models;Economic Methodology

On the relative proof complexity of deep inference via atomic flows

We consider the proof complexity of the minimal complete fragment, KS, of standard deep inference systems for propositional logic. To examine the size of proofs we employ atomic flows, diagrams that trace structural changes through a proof but ignore logical information. As results we obtain a polynomial simulation of versions of Resolution, along with some extensions. We also show that these systems, as well as bounded-depth Frege systems, cannot polynomially simulate KS, by giving polynomial-size proofs of certain variants of the propositional pigeonhole principle in KS.Comment: 27 pages, 2 figures, full version of conference pape

Epistemological Foundations for Neuroeconomics

Neuroeconomics is an emerging field crossing neuroscientific data, the use of brain-imaging tools, experimental and behavioral economics, and an attempt at a better understanding of the cognitive assumptions that underlie theoretical predictive economic models. In this paper the authors try two things: 1) To assess the epistemological biases that affect Neuroeconomics as it is currently done. A number of significant experiments are discussed in that perspective. 2) To imagine an original way - apart from what is already being done - to run experiments in brain-imaging that are relevant to the discussion of rationality assumptions at the core of economic theory.Neuroeconomics, Rationality Assumptions, Abduction

Relating Church-Style and Curry-Style Subtyping

Type theories with higher-order subtyping or singleton types are examples of systems where computation rules for variables are affected by type information in the context. A complication for these systems is that bounds declared in the context do not interact well with the logical relation proof of completeness or termination. This paper proposes a natural modification to the type syntax for F-Omega-Sub, adding variable's bound to the variable type constructor, thereby separating the computational behavior of the variable from the context. The algorithm for subtyping in F-Omega-Sub can then be given on types without context or kind information. As a consequence, the metatheory follows the general approach for type systems without computational information in the context, including a simple logical relation definition without Kripke-style indexing by context. This new presentation of the system is shown to be equivalent to the traditional presentation without bounds on the variable type constructor.Comment: In Proceedings ITRS 2010, arXiv:1101.410

Mind change efficient learning

This paper studies efficient learning with respect to mind changes. Our starting point is the idea that a learner that is efficient with respect to mind changes minimizes mind changes not only globally in the entire learning problem, but also locally in subproblems after receiving some evidence. Formalizing this idea leads to the notion of uniform mind change optimality. We characterize the structure of language classes that can be identified with at most α mind changes by some learner (not necessarily effective): A language class L is identifiable with α mind changes iff the accumulation order of L is at most α. Accumulation order is a classic concept from point-set topology. To aid the construction of learning algorithms, we show that the characteristic property of uniformly mind change optimal learners is that they output conjectures (languages) with maximal accumulation order. We illustrate the theory by describing mind change optimal learners for various problems such as identifying linear subspaces and one-variable patterns