Self-referential order

Modeling Uncertain Self-Referential Semantics with Infinite-Order Probabilities

The notion of a “second-order probability” (a probability distribution defined over a space of probability distributions), while not exactly commonplace, has become less obscure in recent decades due to the advent of imprecise probability theory as developed by Peter Walley [1] and others [2]. It is straightforward to generalize the notion further to thirdorder probabilities and so forth; and t...

Transformations between Self-Referential Sets

Self-Referential Definition of Orthogonality

There has for longer been an interest in finding equivalent conditions which define inner product spaces, and the respective literature is considerable, see for instance Amir, which lists 350 such results. Here, in this tradition, an alternative definition of orthogonality is presented which does not make use of any inner product. This definition, in the spirit of the recently developed non-wel...

Differential electrophysiological response during rest, self-referential, and non-self-referential tasks in human posteromedial cortex.

The electrophysiological basis for higher brain activity during rest and internally directed cognition within the human default mode network (DMN) remains largely unknown. Here we use intracranial recordings in the human posteromedial cortex (PMC), a core node within the DMN, during conditions of cued rest, autobiographical judgments, and arithmetic processing. We found a heterogeneous profile ...

Completely Self-referential Optimal Reinforcement Learners

We present the first class of mathematically rigorous, general, fully self-referential, self-improving, optimal reinforcement learning systems. Such a system rewrites any part of its own code as soon as it has found a proof that the rewrite is useful, where the problemdependent utility function and the hardware and the entire initial code are described by axioms encoded in an initial proof sear...