Disclaimer 1: This question asks for a genealogical approach to philosophy, top-down, yet philosophy, in it's natural order of evolution, is learned down-top. Here we will have to perform some detective work, unless you want to hear as an answer: logic, epistemology, Descartes and Greece...
Disclaimer 2: Terms can be borrowed between fields. When that happens they do take on other meanings and significance. Borrowed terms will then be specialized according to the field they are now used in. For example it's quite common to use terms from geography, origami, army, etc. fields in philosophy. These borrowed terms are generally used in a figurative way but may take on a specific or specialized meaning depending on the field in question and the author. It's also common that some well know philosophical terms need a redefinition for a specific author, time period, language, ...
Disclaimer 3: This questions asks for a longer answer; unfortunately at this time I can only give some directions or a starting point.
Given the scope, the nature and the specific understanding of some terms like "ontology" in the semantic web I'd say that its terms are likely a derivative of the continental branch of philosophy, semiotics seem to be the one to blame here. If the direction seems interesting I may try to elaborate a little more.
While the link to semiotics in particular and structuralism in general seemed promising, I cannot find any historical link or correlation between them. These two projects don't even seem to share any "spirit of the time". Structuralism came under attack in the 60s when in parallel some of the foundations for the semantic network model was explored, and by the 90s structuralism was clearly abandoned.
I was not able to track the exact genesis of the semantic web but it seems linked to western culture and is probably rooted in some cognitive and multidisciplinary study like Artificial Intelligence.
Reading more about web semantics also brings two different visions for it, one far away of any philosophical concern and quite practical in its scope, the other one might be interpreted as more philosophical. Unfortunately most of the papers I read lean towards the practical direction, which concentrates on how to make the web more useful.
Even the term "ontology" is often replaced by the more ambiguous term "vocabulary", ambiguous because while vocabulary is more practical and understandable it also removes the idea of a specific knowledge linked to a being to just be a set of terms. And while an ontology tends or implies to be exhaustive, that's not a requirement for a vocabulary.
So on one hand a semantic web is just a tool to improve the web by making it more useful. On the other hand the semantic web, and that's how I understood it at first, was a project to organize, understand and access human knowledge. In this sense and only in this sense you can draw a parallel with structuralism. Both structuralism and the semantic web share some premise or axiom.
First you need to have a system and underneath this system a structure which can be extracted and studied even when not visible. This structure is in fact understood as the reason for existence of the studied system. Every element inside the system is then apprehended and understood as where it sits in the structure.
We may have another parallel, with some reserve, in the way the semantic web handles triple. Regarding linguistic Saussure said "there are only differences with no positive terms". You can see that in the way the semantic web structures its content where you differentiate form term to term: animal -> feline -> cat and where each terms declines its meaning based on its relative position in opposition to other terms.
Even if there's no historical relation or correlation between these two fields (and the semantic web currently seems more like a project than a field), they do share some premises, and given the fact that structuralism is a well known flaw, I am tempted to believe that the same applies to the semantic web. But as long as the semantic web is used in this practical project to make the web better and doesn't start a crusade pretending that the structure it's based on is objective and real, we should be fine...