Except the general definition of foliation, bedding and cleavage, what are the other clues for defining these structures in the field? Or what is the philosophy of foliation?
You are asking to define foliation, bedding and cleavage in the field, completely neglecting the predominant features that enable one to positively recognize those structures in the field. It is like asking someone to explain, what is an egg? (to recognize it) without mentioning about its shell. One will say, egg is an object that is part of the reproductive process of chicken. Will that answer enable someone who has never seen an egg to recognize that positively?
The philosophy is that bedding is due to deposition and all other foliations are due to mineral alignment in deformed rocks. Bedding is recognized by material changes (e.g. sandstone-shale or limestone-marl) and by any structures that we think are produced by or during sedimentary processes (ripples, cross-stratification, grading, desiccation cracks, fossil accumulations, trace fossils etc. etc.). Slaty cleavage, which forms at the onset of metamorphism as the first foliation associated with tectonic strain, is recognized as subparallel splitting surfaces n o t associated with material change across them but exhibiting systematic relationships with bedding surfaces and folds. In greenschist facies and higher-grade metamorphic rocks, foliations (e.g. schistosity and gneissic layering) are typically the only parallel fabric present (sometimes several generations). They are most easily recognized from the type of rock in which they occur. Has this been what you were asking for?
The book by Passchier & trouw, or the textbook by Fossen are indeed good general descriptions and definitions. Note that foliations (defined as mineral alignments or fabrics) do not actually require metamorphism to develop - they can form during deformation of completely unlithified sediments (see attachment).