How to read the symbol © within a text

I'm working on the copy for an album's liner notes, and text with the following structure is to appear:

All songs © 2016 [publishing company X] and [publishing company Y], except tracks 3, 4, and 8 © 2016 [publishing company X].

My instinct is to put a period at the end of this phrase, as it looks and reads like a sentence even though it lacks a predicate. Is this because the © symbol stands for "are copyright" in this case? Is this a sentence?

It is a sentence (with some implied words), but the part of speech that the symbol is fulfilling in the sentence is open to the interpretation of the reader. It is most likely functioning as a verb or noun.

The symbol represents the word "copyright," which can fulfill 3 different parts of speech:

copyright.

[ˈkäpēˌrīt]

As a NOUN:

1. the exclusive legal right, given to an originator or an assignee to print, publish, perform, film, or record literary, artistic, or musical material, and to authorize others to do the same:

   Example: "he issued a writ for breach of copyright" ·

   Also: a particular literary, artistic, or musical work that is covered by copyright.

As an ADJECTIVE:

1. protected by copyright:

   Example: "permission to reproduce photographs and other copyright material"

As a VERB:

1. secure copyright for (material).

(Source: Oxford Dictionaries).

So we see that the symbol can fulfill multiple parts of speech in the sentence in question, with several possible readings of the sentence:

1. "All songs [are] copyright(s) [of]... [publishing company X] and [publishing company Y]" (adjective or noun).

Where "©" is a noun clarifying the songs as "musical work that is covered by copyright." It can also be read as an adjective stating that the songs have the quality of being protected by copyright.

2. "All songs [are] copyright(ed) [by]... [publishing company X] and [publishing company Y]" (verb).

or

3. "All songs [were] copyright(ed) [in] 2016" (verb).

Where "©" is a verb describing the action taken by the publishing companies and/or in the year 2016 to protect the songs by copyright.

Finally, it's possible that the sentence might read (although the reader would have to read many more implied words into the sentence):

4. "All songs['] copyright(s) [were acquired in] 2016 [by] [publishing company X] and [publishing company Y]" (noun).

Where "©" is a noun referring to the legal rights held on the songs by the publishing companies and acquired in the year 2016.