Predication via Finite-State Methods

Commonly reduced to set membership in a straightforward way, predication can be analyzed in terms of labelled transitions between states, modelling cognitive processes constitutive of linguistic meaning. Requiring the set of transitions to be finite leads to a finite-state approach to predication, which we can refine by letting the set vary over larger and larger finite sets. Variations in these finite sets supports open-endedness in individual-level, stage-level and kind-level predication alike. One form of open-endedness is variable adicity, the raison d’ˆetre of events in Davidson 1967. A second form of open-endedness arises from the choice of temporal propositions, changes in which determine a notion of time. We analyze open-endedness uniformly through model-theoretic notions of satisfaction formulated within institutions in the sense of Goguen and Burstall 1992. Models take the form of strings, as in the Büchi-Elgot-Trakhtenbrot theorem equating Monadic Second-Order Logic with regular languages, or of finite frames, understood as finite automata.