Triadic temporal representations and deformations (2023)

Abstract: Triadic representations that temporally order events and states are described, consisting of strings and sets of strings of bounded but refinable granularities. The strings are compressed according to J.A. Wheeler’s dictum it-from-bit, with bits given by statives and non-statives alike. A choice of vocabulary and constraints expressed in that vocabulary shape representations of cause-and-effect with deformations characteristic, Mumford posits, of patterns at various levels of cognitive processing. These deformations point to an ongoing process of learning, formulated as grammatical inference of finite automata, structured around Goguen and Burstall’s institutions.

## introduction what does a string s that is assigned a probability by a language model describe? over a range of uses, s is uttered at time s to describe an event occurrence at time e. @xcite suggests that s is connected to e by a reference time r, traversing three corners language (s), agent (r), and world (e) of a triangle that is arguably congruent with the well-known symbol-thought-referent triangle from @xcite , page 11. reichenbach derives nine fundamental forms, including the simple past (1) and present perfect (2), by positioning r relative to s and to e (@xmath0.