Improving self-control by practicing logical reasoning

We tested the hypothesis that practicing logical reasoning can improve self-control. In an experimental training study (N = 49 undergraduates), for one week participants engaged in daily mental exercises with or without the requirement to practice logical reasoning. Participants in the logic group showed improvements in self-control, as revealed by anagram performance after a depleting self-control task. The benefits of the intervention were short-lived; participants in the two groups performed similarly just one week after the intervention had ended. We discuss the findings with respect to the strength model of self-control and consider possible benefits of regular cognitive challenges in education.

Logical omniscience as infeasibility

Logical theories for representing knowledge are often plagued by the so-called Logical Omniscience Problem. The problem stems from the clash between the desire to model rational agents, which should be capable of simple logical inferences, and the fact that any logical inference, however complex, almost inevitably consists of inference steps that are simple enough. This contradiction points to the fruitlessness of trying to solve the Logical Omniscience Problem qualitatively if the rationality of agents is to be maintained. We provide a quantitative solution to the problem compatible with the two important facets of the reasoning agent: rationality and resource boundedness. More precisely, we provide a test for the logical omniscience problem in a given formal theory of knowledge. The quantitative measures we use are inspired by the complexity theory. We illustrate our framework with a number of examples ranging from the traditional implicit representation of knowledge in modal logic to the language of justification logic, which is capable of spelling out the internal inference process. We use these examples to divide representations of knowledge into logically omniscient and not logically omniscient, thus trying to determine how much information about the reasoning process needs to be present in a theory to avoid logical omniscience.