I had checked out and read Silvia Luraghi’s On the Meaning of Prepositions and Cases: The Expression of Semantic Roles in Ancient Greek (Studies in Language Companion Series), a book that I continue to dream of owning at some point.
Her discussion of the semantics of the cases and prepositions is very helpful. Its diachronic focusing mainly on Homer through the Classical period, but she does have some discussion of Koine and Byzantine Greek as well.
She uses what are called, “mental maps” for describing semantics.
The meaning of grammatical forms is included in a ‘conceptual space’, in which it can be described as a semantic map, or mental map (se Croft 2001:92-98; Haspelmath, forthcoming). Conceptual space is universally available to human cognition, while a mental map is the portion of conceptual space which constitutes the meaning of a certain form in a certain language. The mental map of a highly polysemous form, such as a case or preposition, involves a number of neighboring concepts. The use of mental maps for the representation of meaning has the advantage that these concepts are not listed randomly, but according to their closeness and, as far as possible, to the direction of semantic spread.
The use of mental maps requires an in-depth understanding of the(presumably universal) organization of conceptual space, which in turn can be understood only in the light of accurate descriptions of a large amount of different languages. Such a task has not yet been accomplished: consequently, descriptions of conceptual space for the time being remain tentative. To my view, such limitation does not mean that one should give up the use of mental maps, because it is only by trying to understand how different meanings of a certain language-specific form relate to each other that one can reach an understanding of the structure of conceptual space. However, one must be careful in one’s assumptions about this matter (page 16).
In discussing the individual prepositions, she regular compares and contrasts similar ones. For example, here are her conclusions about ἐκ along side here conclusions about ἀπό:
In Figure 7, I give a mental map of ek; it can be compared with the mental map of apo which will be given in Figure 9 (page 106).
In Figure 9 I give a mental map of the meaning of apo.
having analyzed the use and the semantic evolution of both ek and apo, we can now finish the discussion started in 3.2. the two prepositions have quite distinct meanings in homer, where the more specific meaning of ek appears to make it more suitable for various types of extension outside the spatial domain: so ek is found in Time and sometimes in Cause expressions, it is the standard way to denote Origin, and its occurrences in Agent expressions is also significant. On the spatial plane too, the two prepositions appear to overlap only partially, since landmarks that can be conceived as containers normally take ek.
Starting with Herodotus, we find a process of convergence between ek and apo. In Herodotus, convergence owes to the extension of the possible uses of apo, which acquires temporal value, can be found with city names and in the expression of Origin, and sometimes for Agent. Later on, in Attic prose, some of the peculiarities of ek also disappear, as demonstrated by its use in Cause expressions, similar to those in which only apo formerly occurred. Comparison of the two prepositions shows that they ended up with much the same meaning, although semantic extension followed different paths. in particular, it can shown that the causal meaning of the two particles originated in different ways: for apo, Cause was a semantic extension of the spatial meaning, while in the case of ek the meaning extended first to time, and then to Cause. the difference between the two processes is apparent in Homer, who has concrete landmarks in Cause expressions with apo, and abstract ones (mostly states of affairs) with ek. Extension to Agent, on the other hand, seems to follow the same path, from Source to Origin, to Agent, in fact Agent expressions with apo start to occur only when Origin expressions also appear.
Anyway, that’s bit of a taste of the book. Its quite good and I enjoyed reading it. Hopefully I’ll have a copy to make reference to more easily (I scanned only a couple pages with charts).