In the study of cognitive processes, limitations on computational resources (computing time and memory space) are usually considered to be beyond the scope of a theory of competence, and to be exclusively relevant to the study of performance. Starting from considerations derived from the theory of computational complexity, in this paper I argue that there are good reasons for claiming that some aspects of resource limitations pertain to the domain of a theory of competence.

Why should moral philosophers, moral psychologists, and machine ethicists care about computational complexity? Debates on whether artificial intelligence (AI) can or should be used to solve problems in ethical domains have mainly been driven by what AI can or cannot do in terms of human capacities. In this paper, we tackle the problem from the other end by exploring what kind of moral machines are possible based on what computational systems can or cannot do. To do so, we analyze normative (...) ethics through the lens of computational complexity. First, we introduce computational complexity for the uninitiated reader and discuss how the complexity of ethical problems can be framed within Marr’s three levels of analysis. We then study a range of ethical problems based on consequentialism, deontology, and virtue ethics, with the aim of elucidating the complexity associated with the problems themselves (e.g., due to combinatorics, uncertainty, strategic dynamics), the computational methods employed (e.g., probability, logic, learning), and the available resources (e.g., time, knowledge, learning). The results indicate that most problems the normative frameworks pose lead to tractability issues in every category analyzed. Our investigation also provides several insights about the computational nature of normative ethics, including the differences between rule- and outcome-based moral strategies, and the implementation-variance with regard to moral resources. We then discuss the consequences complexity results have for the prospect of moral machines in virtue of the trade-off between optimality and efficiency. Finally, we elucidate how computational complexity can be used to inform both philosophical and cognitive-psychological research on human morality by advancing the moral tractability thesis. (shrink)

Four articles in this issue of topiCS (volume 4, issue 1) argue against a computational approach in cognitive science in favor of a dynamical approach. I concur that the computational approach faces some considerable explanatory challenges. Yet the dynamicists’ proposal that cognition is self-organized seems to only go so far in addressing these challenges. Take, for instance, the hypothesis that cognitive behavior emerges when brain and body (re-)configure to satisfy task and environmental constraints. It is known that for certain systems (...) of constraints, no procedure can exist (whether modular, local, centralized, or self-organized) that reliably finds the right configuration in a realistic amount of time. Hence, the dynamical approach still faces the challenge of explaining how self-organized constraint satisfaction can be achieved by human brains and bodies in real time. In this commentary, I propose a methodology that dynamicists can use to try to address this challenge. (shrink)

This paper has a twofold scope. The first one is to clarify and put in evidence the isomorphic character of two theories developed in quite different fields: on one side, threshold logic, on the other side, simple games. One of the main purposes in both theories is to determine when a simple game is representable as a weighted game, which allows a very compact and easily comprehensible representation. Deep results were found in threshold logic in the sixties and seventies for (...) this problem. However, game theory has taken the lead and some new results have been obtained for the problem in the past two decades. The second and main goal of this paper is to provide some new results on this problem and propose several open questions and conjectures for future research. The results we obtain depend on two significant parameters of the game: the number of types of equivalent players and the number of types of shift-minimal winning coalitions. (shrink)

Leech et al. present a connectionist algorithm as a model of (the development) of analogizing, but they do not specify the algorithm's associated computational-level theory, nor its computational complexity. We argue that doing so may be essential for connectionist cognitive models to have full explanatory power and transparency, as well as for assessing their scalability to real-world input domains.

Despite its strengths, Leech et al.'s model fails to address the important benefits that derive from self-explanation and task feedback in analogical reasoning development. These components encourage explicit, self-reflective processes that do not necessarily link to knowledge accretion. We wonder, therefore, what mechanisms can be included within a connectionist framework to model self-reflective involvement and its beneficial consequences.

Leech et al.'s model proposes representing relations as primed transformations rather than as structured representations (explicit representations of relations and their roles dynamically bound to fillers). However, this renders the model unable to explain several developmental trends (including relational integration and all changes not attributable to growth in relational knowledge). We suggest looking to an alternative computational model that learns structured representations from examples.