Tense in a vectorial model for the conceptualization of time

Resumen

In this work we assume that the human mind cannot perceive time directly and thus resorts to a metaphor of space in order to conceptualize it (Casasanto & Boroditsky, 2008; Gentner et al., 2002; Merrit et al., 2010). We argue that time, which is conceptualized in terms of a path image schema, is needed along with spatial coordinates in order to locate a proposition in a possible world so that it can receive a truth-value. In other words, both time and space are needed to evaluate a proposition. The human mind codifies the temporal properties of a proposition by means of three systems, which are based upon Reichenbach's (1947) temporal variables, namely speech time, evaluation time and utterance time: tense, which locates an event or situation  along the temporal path image schema (past, present or future); aspect, which represents the speaker's viewpoint of the event or situation conveyed in the utterance (perfectivity and progressivity, among others); and lexical aspect or aktionsart, which encodes the temporal properties of the event or situation itself (i.e. whether it is bound, unbound, or punctual). Specifically, we provide a mathematical model that represents the information codified by these three systems by means of a Euclidean vector (a geometric entity characterized by a magnitude, which in our case is a number times an abstract temporal unit) in a four-dimensional-like mental representation, namely an R3 +ˆt mental representation: a three dimensional space (R3 ) defined by three versors (a vector whose magnitude equals one unit and defines a line), xˆ, yˆ and zˆ plus a fourth versor ˆt that defines the temporal path image schema along which the proposition must be placed in order to receive a truth value. Ultimately, this work aims to offer a novel account of tense using theoretical tools from cognitive linguistics and formal logic, as well as mathematical formalisms, which will allow us to carry out the computational implementation of the model in NLP systems.