you need to add a prime at the end of the context name, and delete it from the file name:

Needs["MATHPROG`LOGICPROGRAMMING`", "D:\\Mathematica\\Mathematica \
Programer II\\MATHPROG`LOGICPROGRAMMING.m"]

Also, are you sure your context in the .m file is in all capital letters like that? -- make sure to match the case of the Begin[...] in the .m file.

The first argument of Needs is not the path, but the context. You can give the path as second argument. Something like this:

Needs["MATHPROG`LOGICPROGRAMMING", "D:\\Mathematica\\Mathematica \
Programer II\\MATHPROG`LOGICPROGRAMMING.m`"]

but you will probably have to retype the context and path. You can use Get with the path only.