We discuss a number of distance functions encountered in the theory of computation, including metrics, ultra-metrics, quasi-metrics, generalized ultra-metrics, partial metrics, d-ultra-metrics and generalized metrics. We consider their properties, associated fixed-point theorems and some general applications they have within the theory of computation. We consider in detail the applications of generalized distance functions in giving a uniform treatment of several important semantics for logic programs, including acceptable programs and natural generalizations of them, and also the supported model and the stable model in the context of locally stratified extended disjunctive logic programs and databases.

10adenotational semantics10afixed-point theorems10ageneralized distance functions10aLogic Programming10astable model10asupported model10atopology10aultra-metrics1 aSeda, Anthony, K.1 aHitzler, Pascal uhttp://dx.doi.org/10.1093/comjnl/bxm10800479nam a2200133 4500008004100000022001800041245005600059210005600115260003100171300000800202100002000210700002200230856009300252 2010 eng d a978143982961500aMathematical Aspects of Logic Programming Semantics0 aMathematical Aspects of Logic Programming Semantics bChapman and Hall/CRC Press a3041 aHitzler, Pascal1 aSeda, Anthony, K. uhttps://daselab.cs.ksu.edu/publications/mathematical-aspects-logic-programming-semantics