Setting the bar for cognitive agency: Or,how minimally autonomous can an autonomous agent be?

Embodied cognition comes in many variants. Yet, in most if not all of these variants the notion of agency, or more precisely autonomous agency, occupies center stage. However, whereas in its original context of application autonomy applies strictly to the human sphere, cognitive theory must needs generalize this concept so as to render it applicable to a much wider range of entities and processes. Theorists of embodied cognition must therefore strive to articulate a valid sense of minimal autonomy applicable to animals and, arguably, to artificial agents as well. In this paper I discuss two major attempts to articulate a conception of minimal autonomy which I describe, respectively, as the adaptive-behavior approach (ABA) and the systemic-constructivist approach (SCA). The differences between these two leading views on minimal autonomy reveal fundamental disagreements not only with respect to the nature of autonomous agency but also with respect to embodiment and the relevance of biological life to the making of mental life.     

Finite basis problems and results for quasivarieties

Let be a finite collection of finite algebras of finite signature such that SP( ) has meet semi-distributive congruence lattices. We prove that there exists a finite collection ₁ of finite algebras of the same signature, , such that SP( ₁) is finitely axiomatizable.We show also that if , then SP( ₁) is finitely axiomatizable. We offer new proofs of two important finite basis theorems of D. Pigozzi and R. Willard. Our actual results are somewhat more general than this abstract indicates.While working on this paper, the first author was partially supported by the Hungarian National Foundation for Scientific Research (OTKA) grant no. T37877 and the second author was supported by the US National Science Foundation grant no. DMS-0245622.Special issue of Studia Logica: Algebraic Theory of Quasivarieties Presented by M. E. Adams, K. V. Adaricheva, W. Dziobiak, and A. V. Kravchenko     

The road to two theorems of logic

Work on how to axiomatize the subtheories of a first-order theory in which only a proper subset of their extra-logical vocabulary is being used led to a theorem on recursive axiomatizability and to an interpolation theorem for first-order logic. There were some fortuitous events and several logicians played a helpful role.