This paper introduces an extension of logic programming based on multi-dimensional logics, called MLP. In a multi-dimensional logic the values of elements vary depending on more than one dimension, such as time and space. The resulting logic programming language is suitable for modelling objects which involve implicit and/or explicit temporal and spatial dependencies. The execution of programs of the language is based on a resolution-type proof procedure called MSLD-resolution (for multi-dimensional SLD-resolution). The paper also establishes the declarative semantics of multi-dimensional logic programs, based on an extension of Herbrand models. In particular, it is shown that MLP programs satisfy the minimum model semantics. A novel multidimensional interface to MLP is also outlined; it can be used as a powerful development tool with the advantage of non-determinism inherent in logic programming.
Orgun, M. A., & Du, W. (1997). Multi-dimensional logic programming: Theoretical foundations. Theoretical Computer Science, 185(2), 319–345. https://doi.org/10.1016/S0304-3975(97)00048-0