To me the semantic continuum of phrasal verbs means the progression from what we might call non-phrasal verb constructions to full-blown phrasal verbs:
1. As I came in to the room, Mary looked up.
2. As a child, I always looked up to my older sister.
3a. I’ll look you up when I am next in town.
3b. I had to look up ‘continuum’ in my dictionary.
In #1, the words ‘look’ and ‘up’ retain their literal meanings. I doubt if anybody would consider the underlined words to be an example of a phrasal verb.
In #2, the words have taken on a metaphorical meaning. The ‘Oxford Advanced Learner’s Dictionary (2000) considers ‘look up to’ (= admire/respect) to be a phrasal verb.
In #3a and b, we have moved some way from the literal meanings of ‘look’ and ‘up’. These are what I have called ‘full-blown’ phrasal verbs.
This continuum is similar to that of Celce-Murcia and Larsen-Freeman (1999): Literal, Aspectual and Idiomatic Phrasal Verbs
Some writers class such constructions as ‘look at’ (= turn your eyes towards) and go in(to) (= enter) as phrasal verbs. If you agree with such a classification, then you would presumably have a new category 2; and 3a and b would become 4a and b.
Some writers, e.g. Carter and McCarthy (2006), class as prepositional verbs those which “consist of a verb and a preposition which are closely linked with each other’. Their examples include such verbs as ‘deal’ with, which Sinclair (1990) considers to be a phrasal verb. These would presumably come immediately after my #1.
Another personal view is that of Phil White: "The whole issue of multi-word verbs is, however, fraught, and there seems to me to be a continuum between phrasals, prepositional verbs and verb + preposition combinations, with the borderlines subject to blurring."
Carter, Ronald & McCarty, Michael (2006) Cambridge Grammar of English, Cambridge: CUP
Celce-Murcia, Marianne and Larsen- Freeman, Diane (1999) The Grammar Book, Second Edition, Boston, Mass: Heinle & Heinle.
Sinclair, John [Editor-in-Chief] (1990) Collins Cobuild English Grammar, London: HarperCollins
Wehmeier, Sally [Editor] (2000); Oxford Advanced Learner’s Dictionary: Oxford: OUP
White, Phil: Posting on: wordwizard.com - View topic - Separating prepositions from verbs
References to a continuum of opaqueness in: http://acl.ldc.upenn.edu/W/W03/W03-1810.pdf
The gradability of idiomaticity in: Verbal idioms in focus - towards the continuum of idiomatic expressions. (Linguistics). - Studia Anglica Posnaniensia: international review of English Studies | HighBeam Research - FREE trial