To advance an algebraical-computational view of knowledge representation we examine the domain of space as an abstract relational system with wide cross domain applicability with regard to relational properties generally. It is no accident that any coherent system of relations is understood as a 'space' of such relations. Jackendoff's work shows this. We have good grounds for considering spatial relations a universal ‘modular’ faculty of human cognition.
Just to set the stage for our paper and raise issues we need to address, we will first address certain fairly recent work done on the cognition of space by Levinson, Herskovits, and Talmy, and discuss their data and ours from languages like Italian, Burmese, Haka Chin, and Tongan and show that relativist conclusions follow directly from neo-behaviorist failure to be abstract enough in dealing with conceptual-relational structure.
Then we will introduce basic concepts of LOCUS, PLACE, MOTION, PATH and DIRECTION and will provide definitions of spatial prepositions like ‘at’, ‘on’ and‘in’, as well as discuss in detail prepositions like ‘to’, ‘towards’, ‘from’, ‘away from’, and ‘via’. We will conclude our work by indicating a minimal universal content of the domain of space that will eventually become the axiomatizable component of the system from which the linguistic expressions derive as theorems of that same system.