In this framework, you can think about a morpheme as being a tuple of features. Like you said, it is sort of akin to a type system, where passing the wrong type to a function won't work. A morpheme will select for a feature or set of features from whatever its merged with, and won't merge with something it doesn't agree with.
I think using a language which doesn't care much about word order will be illustrative here, so let's use Latin:
puella vidit canem
The girl sees the dog
We can break this down into:
puell - a vid - et can - em
girl - NOM.S.FEM sees - S.3 dog - ACC.S.FEM
So 'puella' is the tuple of features [+NOM, +S, +FEM], 'videt' is [+PRES, +ACTIVE, +S, +3], etc.
Here, we want to do a Merge with 'puella' and 'videt': we say that 'puella' selects for the features +NOM, +3, +S (nominative, third person, and singular) in its verb, but doesn't care about the others. It can still agree with its verb if the verb is passive or in the past tense. But if a verb is conjugated in a way that violates the features it selects for (eg the verb is conjugated as first person plural), 'puella' won't merge with it.
As you said, a phrase level structure will have the features of its constituent parts bubble up to it. So once we've done the first Merge with 'puella' and 'videt', our structure is now selecting for a noun phrase that has the feature +ACC. Because 'canem' meets this requirement, we can get the final Merge necessary for our finished sentence.
{ { puella, videt }, canem }
Note that this account still works if we change the order of the sentence to any configuration, we just need to reorder the merges.
Thanks, that's really neat (and since I know Latin, the analysis made perfect sense to me).
I suppose that you could, for example, account for the different conjugations and declensions by saying that they are also features of noun and verb stems that have to agree with endings that want to bind with them, right? Like "vid-" and "-et" is not just "sees - S.3" but also something like "see [+2conj]" and "S.3 [+2conj]" allowing them to bind with each other, where "-at" might be "S.3 [+1conj]" so it could bind with "am-" being "love [+1conj]", while "-et" doesn't bind with "am-" (except when interpreted as a different lexical item that adds [+subjunctive] to a [+1conj] stem?).
My next question is whether there are tools to facilitate writing parsers with this framework because it makes me want to write a Latin parser and see how well it does (and maybe how many formal syntactic ambiguities exist in Latin texts that we might not even notice most of the time).
Yep, but, as soon as you exit very simple phrases subject/action/object, the approach may become complex to apply in practice, a couple (known) latin (tricky) examples (JFYI):
Unfortunately that's true, which is why linguistics is a field of study with its own journals, rather than something that can be summarized neatly in the space of an HN comment :P
Speaking to your examples: "mala mala mala sunt bona" isn't particularly difficult to analyze this way, you just need to realize that the "mala"s are different words (kind of like the famous English "Buffalo buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo" sentence). If I remember the proverb correctly, it means "apples (mala) are good (sunt bona) for a painful jaw (mala mala)".
You need an analysis that allows adjectives to Merge with nouns iff they match case, gender and number, so that allows us to create a noun phrase "mala mala" in the instrumental ablative. Then you need a way to have the case, gender and number of subject bubble to the top of the phrase it will make with an auxiliary so that the adjective after the auxiliary is feature restricted to that case, gender and number. Once the elements of the auxiliary verb phrase have Merged, you get:
{{ mala, sunt }, bona }
Finally you have a rule that allows auxiliary verb phrases to Merge with noun phrases headed by an ablative. If you want the first "mala" to be the subject, then re-Merge it with the whole sentence so far, which in effect moves it to the top of the tree, leaving a trace in its original position.
I'm not sure what the second example means. My best guess is that it's the dative singular of 'sol', a matching masculine dative singular of 'solus' and a genitive singular of 'solum', so something like "for the only sun of the land". If that's correct, you need our previously used rule for Merging adjectives iff they match the noun in case, gender and number. Then you can add an additional rule that genitive nouns can be Merged with noun phrases (without any feature selection needing to take place) to form a new noun phrase.
Hopefully that shows that Merge and feature selection as mechanisms can be used outside of toy models, to actually account for real data.
Your translations/guesses are correct, "mala mala mala sunt bona" is afaik an invented phrase, not entirely unlike "I Vitelli dei romani sono belli" (which is bilingual Latin/Italian, meaning in italian "The calves of the Romans are beautiful" but meaning in latin "Go, Vitellio at the sound of the Roman war god") to trick/have some fun of Latin students, while "Soli soli soli" was a phrase sometimes inscribed on sundials.
Anyway, yes, the Merge and feature can work just fine outside of "toy models" the note was about about they soon becoming complex.
I think using a language which doesn't care much about word order will be illustrative here, so let's use Latin:
puella vidit canem
The girl sees the dog
We can break this down into:
puell - a vid - et can - em
girl - NOM.S.FEM sees - S.3 dog - ACC.S.FEM
So 'puella' is the tuple of features [+NOM, +S, +FEM], 'videt' is [+PRES, +ACTIVE, +S, +3], etc.
Here, we want to do a Merge with 'puella' and 'videt': we say that 'puella' selects for the features +NOM, +3, +S (nominative, third person, and singular) in its verb, but doesn't care about the others. It can still agree with its verb if the verb is passive or in the past tense. But if a verb is conjugated in a way that violates the features it selects for (eg the verb is conjugated as first person plural), 'puella' won't merge with it.
As you said, a phrase level structure will have the features of its constituent parts bubble up to it. So once we've done the first Merge with 'puella' and 'videt', our structure is now selecting for a noun phrase that has the feature +ACC. Because 'canem' meets this requirement, we can get the final Merge necessary for our finished sentence.
{ { puella, videt }, canem }
Note that this account still works if we change the order of the sentence to any configuration, we just need to reorder the merges.