Tenses haven't been introduced yet here but from my short memory tenses are particles at the end of verbs. Be thankful tenses will probably be covered towards the end. If you listen to Korean a lot you should be able to notice the changes when people talk about the past or future a lot. Time traveling kdramas help!
Could be both.
봅시다 : Propositive mood, present tense, formal & polite style
봐요 : Propositive mood, present tense, casual & polite style
Also, Declarative mood, present tense, casual & polite style
With -요 verb ending, the ways to distinguish the propositive/advisory mood, in writing, are either by context (not in this case) or by using tag expressions s.a. 어때요? (What about?); -(으)ㄹ까요? (Shall we?); (으)시겠어요/-(으)ㄹ래요? (Would you mind?) etc.
Maybe DLG could provide us some examples. That would be very useful in daily interactions.
My understanding is that subjects like that are often assumed or derived from context in Korean. Depending on the context you could probably translate this as "He/she looks after a different dog today", "You look after a different dog today", or a number of other possibilities.
Ok thanks! But why does it have a topic particle? I do not understand how it is a topic in this sentence. As I understand (the translation) it is just an indication of when the action takes places it could be yesterday, tomorrow whatever (conjuging tense accordingly of course). Just confused on why it is not a simple indication of time but a topic.
There is a slight difference when the topic particle is added. It gives a sense of contrast is in play.
오늘 다른 개를 봐요 = Let's look after another dog today. (A simple proposition /statement, with no condition attached)
오늘은 다른 개를 봐요 = For today, let's look after another dog (but tomorrow/but after today ...)
The use of the topic particle "은" sends out the unsaid and contrasting condition "today, yes but ..." .
"은" offers "today" as a theme for discussion/negotiation.
Context (in writing) and intonation (in speech) play a big role in identifying the "mode" of the sentence (whether declarative, interrogative, imperative, propositive or exclamatory).
Unfortunately since we are restricted to a single-sentence example, it is difficult to compare hence make a distinction between declarative vs propositive in this case.
Propositive is supposed to be more even-toned while declarative, fallen tone at the end of the sentence.
Propositive: 봐요 -> bwa - yo (Let's look after)
Declarative: 봐요 -> buo'yo (I or we look after)
[Speaking as a non expert]
Both are grammatically correct. In usage however there are differences.
The 해요체 (봐요) style is friendly while remaining polite while 해라체 (보자) may sound a bit terse. 해라체 is considered an impersonal style, stripped of any form of humility and politeness and usually directed at a non-specific audience.
Using this style in a suggestion could make the speaker sound somewhat removed (It's worth noting here that 해라체 is used in indirect quotation), and even a bit patronizing, if directed at specific friend(s) or even acquaintance(s).
It's fine if used as a soliloquy (talking to oneself).