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I am trying to construct a first-order logic representation of the following sentence. My general approach for constructing the representation is to parse the sentence into a phrase structure tree using a context-free grammar with features.

One of those features is an expression in lambda-calculus, which allows the composition the sentences semantics from the nodes of the phrase structure tree.

Sentence

I am not the alien here. 

S -> NP LV NP

NP -> Det N | N

N -> 'I' | 'alien'

Det -> 'the'

LV -> Neg Copula | Copula

Neg -> 'not'

Copula -> 'am'

I am stuck on how to parse the word "here". Formally, 'here' is a deictic locative predicate (source).

I understand, from the linke English.SE answer, that a first-order logic representation of "I am the alien here" could be (here(I) & alien(I)). Which one should receive the negation in "I am not the alien here"?

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  • Can you clarify whether you're looking for a phrase structure tree, or a representation in first-order logic? In terms of the former, i'd generally treat 'here' as a VP-level adjunct, scoping below negation, but above the predicate. Also, i don't think the phrase-structural rules you give are broadly correct, as they assign the copular sentence a ternery branching structure. There's evidence that the copular+pred behave as a constituent to exclusion of the subject. See, e.g. clefting options: It is I who is not the alien here.
    – P Elliott
    Commented Oct 7, 2013 at 8:54
  • One consequence of the phrase structural rules you've given is that's impossible to have 'here' scoping over both the copular and the predicate without also scoping over the negation. You want the copular and the predicate to be a constituent to the exclusion of negation.
    – P Elliott
    Commented Oct 7, 2013 at 8:59
  • @PElliott updated as to your first comment. As to the second, I agree completely. What would a reasonably alternate set of rules be to give 'here' scope over both but not the negation?
    – mac389
    Commented Oct 7, 2013 at 21:02

3 Answers 3

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Below you can see how I would do it. I didn't use triangles to be clearer.

I follow Carnie (2012), just instead of a TP, a tense phrase, I used an IP, an inflectional phrase (see Tallerman 2005). Supposedly the IP structure is the structure that all finite verbs have and all finite verbs have an inflection as far as European languages are concerned.

'Here' is out of the scope of the inflection phrase since it's an adjunct; this type of information is not required by the theta roles of the verb. Also, since 'here' is not under the scope of any of the core arguments and you can't have oblique arguments in a sentence like "X be X", it must be an adjunct and therefore lie outside the scope of the IP.

You can generate the tree using this:

[S[IP [DP [D' [NP [N' [N I]]]]] [I' [I am] [NegP [Neg' [Neg not]] [DP [D'[D the][NP[N' [N alien]]]]]]]][DP[D'[D[AdvP[AdvP'[AdvP[here]]]]]

Notice: no triangles were used to improve clarity

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  • The questioner states clearly: "I am trying to construct a first-order logic representation of the following sentence", not a phrase structure tree. Additionally, there're a couple of things i find odd about this tree. You have a head D directly dominating a phrasal node AdvP which is counter to standard X'-theory. Also, AdvP isn't headed - again, counter to standard X'-theory.
    – P Elliott
    Commented Jan 4, 2014 at 20:45
  • "I am trying to construct a first-order logic representation of the following sentence", then rewrite rules for a phrase structure tree follow. To me the question seemed to be "I am stuck on how to parse the word "here"" - from a syntactic perspective. Could you give me a quotation for your second claim? You are certainly right about the first one, I had changed the tree on the go without noticing: The D dominating AdvP shouldn't be there.
    – Muffin
    Commented Jan 4, 2014 at 21:09
  • What kind of node would u have then for 'here'?
    – Muffin
    Commented Jan 4, 2014 at 21:15
  • Would you have DP-D'-D-here?
    – Muffin
    Commented Jan 4, 2014 at 21:22
  • I wouldn't analyse here as a determiner, no, i'd have it as an adverb. It doesn't have the distribution of a determiner, e.g. you can't say here dog is sleeping. As for my second claim, i could find a direct quotation, but the point is very simple: If you have an XP node, it must dominate both an X' AND an X node. In other words, every phrase must have a head.
    – P Elliott
    Commented Jan 4, 2014 at 22:23
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Maybe not exactly the answer, but here is the syntactic structure for this sentence:

I am not the alien here.
[S [NP I] [V [VP am] [NP not the alien here]]]

Which should give you this tree:

enter image description here

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In Davidsonian first-order logic, the semantic representation would be

∃e.not(e) & alien'(e,I) & here(e)

where e is the eventuality of being an alien.

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    Why are you treating negation as a predicate? What does not(e) mean? Could you provide a reference for the logical system you're presupposing here? I'm not familiar with it at all.
    – P Elliott
    Commented Oct 6, 2013 at 21:25
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    @PElliott I think the best reference is Jerry Hobbs' "Discourse and Inference" link. Within the Minimalist Program, an almost identical approach is elaborated in link. In Hobbs' notation, ∀e1.not(e1)≡∃e2.not'(e2,e1)∧Rexists(e2). It's generally based on Davidson's account of action sentences. Pietroski discusses at length the advantages of what he calls "conjunctivism".
    – Atamiri
    Commented Oct 6, 2013 at 22:49
  • @PElliott You're welcome. I'd recommend googling for "neo-Davidsonian semantics" as there alternative approaches to how thematic relations are represented.
    – Atamiri
    Commented Oct 7, 2013 at 0:10
  • Yes, i'm familiar with neo-Davidsonian formulae, just not the logical system you use here,. It seems very odd to me to treat the predicate alien as a two place relation between an eventuality and an individual.
    – P Elliott
    Commented Oct 7, 2013 at 16:52
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    @PElliott Exactly. This treatment is universal. Semantically, there's only one predicate in the sentence. Note that there are languages without copula. In unification-based grammars, there'd be only one (flat) feature structure: [SEM 'alient(SUBJ)', SUBJ "I"] (likewise, there'd be only two nodes in a dependency-based (deep) syntax tree)
    – Atamiri
    Commented Oct 7, 2013 at 17:28

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