The role of falsification in the development of cognitive architectures: insights from a Lakatosian analysis

It has been suggested that the enterprise of developing mechanistic theories of the human cognitive architecture is flawed because the theories produced are not directly falsifiable. Newell attempted to sidestep this criticism by arguing for a Lakatosian model of scientific progress in which cognitive architectures should be understood as theories that develop over time. However, Newell’s own candidate cognitive architecture adhered only loosely to Lakatosian principles. This paper reconsiders the role of falsification and the potential utility of Lakatosian principles in the development of cognitive architectures. It is argued that a lack of direct falsifiability need not undermine the scientific development of a cognitive architecture if broadly Lakatosian principles are adopted. Moreover, it is demonstrated that the Lakatosian concepts of positive and negative heuristics for theory development and of general heuristic power offer methods for guiding the development of an architecture and for evaluating the contribution and potential of an architecture’s research program

Adaptive logic characterizations of input/output logic

We translate unconstrained and constrained input/output logics as introduced by Makinson and van der Torre to modal logics, using adaptive logics for the constrained case. The resulting reformulation has some additional benefits. First, we obtain a proof-theoretic (dynamic) characterization of input/output logics. Second, we demonstrate that our framework naturally gives rise to useful variants and allows to express important notions that go beyond the expressive means of input/output logics, such as violations and sanctions

The Tracy--Widom limit for the largest eigenvalues of singular complex Wishart matrices

This paper extends the work of El Karoui [Ann. Probab. 35 (2007) 663--714] which finds the Tracy--Widom limit for the largest eigenvalue of a nonsingular $p$-dimensional complex Wishart matrix $W_{\mathbb{C}}(\Omega_p,n)$ to the case of several of the largest eigenvalues of the possibly singular $(n<p)$ matrix $W_{\mathbb{C}}(\Omega_p,n).$ As a byproduct, we extend all results of Baik, Ben Arous and Peche [Ann. Probab. 33 (2005) 1643--1697] to the singular Wishart matrix case. We apply our findings to obtain a 95% confidence set for the number of common risk factors in excess stock returns.Comment: Published in at http://dx.doi.org/10.1214/07-AAP454 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Learning-Assisted Automated Reasoning with Flyspeck

The considerable mathematical knowledge encoded by the Flyspeck project is combined with external automated theorem provers (ATPs) and machine-learning premise selection methods trained on the proofs, producing an AI system capable of answering a wide range of mathematical queries automatically. The performance of this architecture is evaluated in a bootstrapping scenario emulating the development of Flyspeck from axioms to the last theorem, each time using only the previous theorems and proofs. It is shown that 39% of the 14185 theorems could be proved in a push-button mode (without any high-level advice and user interaction) in 30 seconds of real time on a fourteen-CPU workstation. The necessary work involves: (i) an implementation of sound translations of the HOL Light logic to ATP formalisms: untyped first-order, polymorphic typed first-order, and typed higher-order, (ii) export of the dependency information from HOL Light and ATP proofs for the machine learners, and (iii) choice of suitable representations and methods for learning from previous proofs, and their integration as advisors with HOL Light. This work is described and discussed here, and an initial analysis of the body of proofs that were found fully automatically is provided

Are Unemployment and Out of the Labor Force Behaviorally Distinct Labor Force States?

This paper formulates and tests the hypothesis that the categories unemployed and out of the labor force are behaviorally distinct labor force states. Our empirical results indicate that they are. In the empirically relevant range the exit rate from unemployment to employment exceeds the exit rate from out of the labor force to employment. This evidence is shown to be consistent with a simple job search model of productive unemployment with log concave wage offer distributions. We prove that if unemployed workers receive job offers more frequently than workers out of the labor force, and if wage offer distributions are log concave, the exit rate from unemployment to employment exceeds the exit rate from out of the labor force to employment.

How to define and test explanations in populations

Solving applied social, economic, psychological, health care and public health problems can require an understanding of facts or phenomena related to populations of interest.  Therefore, it can be useful to test whether an explanation of a phenomenon holds in a population.  However, different definitions for the phrase “explain in a population” lead to different interpretations and methods of testing.  In this paper, I present two definitions:  The first is based on the number of members in the population that conform to the explanation’s implications; the second is based on the total magnitude of explanation-consistent effects in the population.  I show that claims based on either definition can be tested using random coefficient models, but claims based on the second definition can also be tested using the more common, and simpler, population-level regression models.   Consequently, this paper provides an understanding of the type of explanatory claims these common methods can test

Asymptotics of the principal components estimator of large factor models with weak factors and i.i.d. Gaussian noise.

We consider large factor models where factors' explanatory power does not strongly dominate the explanatory power of the idiosyncratic terms asymptotically. We find the first and second order asymptotics of the principal components estimator of such a weak factors as the dimensionality of the data and the number of observations tend to infinity proportionally. The principal components estimator is inconsistent but asymptotically normal