Semantic graph parser based on Categorial grammars

Related tags

Deep Learninglambekseq
Overview

Lambekseq

semgraph

"Everyone who failed Greek or Latin hates it."


This package is for proving theorems in Categorial grammars (CG) and constructing semantic graphs, i.e., semgraphs on top of that.

Three CG calculuses are supported here (see below). A "proof" is simply a set of atom links, abstracting away from derivaiton details.

Requirements

Add the path to the package to PYTHONPATH. None of the below packages is needed to use the theorem proving facility.

Semantic graphs derive from digraph:

For graph visualization we use

Background

This package is used for the author's PhD thesis in progress.

Categorial grammars:

Semantic graphs:

Theorem Proving

To prove a theorem, use atomlink module. For example, using Lambek Calculus to prove np np\s -> s.

>>> import lambekseq.atomlink as al

>>> con, *pres = 's np np\\s'.split()
>>> con, pres, parser, _ = al.searchLinks(al.LambekProof, con, pres)
>>> al.printLinks(con, pres, parser)

This outputs

----------
s_0 <= np_1 np_2\s_3

(np_1, np_2), (s_0, s_3)

Total: 1

You can run atomlink in command line. The following finds proofs for the theorems in input, using abbreviation definitions in abbr.json and Contintuized CCG.

$ python atomlink.py -i input -a abbr.json -c ccg --earlyCollapse

Theorem s qp vp/s qp vp (the first item is the conclusion, the rest the premises) is thus proved as follows:

<class 'lambekseq.cntccg.Cntccg'>
----------
s_0 <= (s_1^np_2)!s_3 (np_4\s_5)/s_6 (s_7^np_8)!s_9 np_10\s_11

(np_10, np_8), (np_2, np_4), (s_0, s_3), (s_1, s_5), (s_11, s_7), (s_6, s_9)

Total: 1

When using Lambek/Displacement/CCG calculus, you can also inspect the proof tree that yields atom links:

>>> con, *pres = 's', 'np', '(np\\s)/np', 'np'
>>> con, pres, parser, _ = al.searchLinks(al.LambekProof, con, pres)
>>> parser.buildTree()
>>> parser.printTree()
(np_1, np_2), (np_4, np_5), (s_0, s_3)
........ s_3 -> s_0
........ np_1 -> np_2
.... np_1 np_2\s_3 -> s_0
.... np_5 -> np_4
 np_1 (np_2\s_3)/np_4 np_5 -> s_0

You can export the tree to Bussproofs code for Latex display:

bussproof

>>> print(parser.bussproof)
...
\begin{prooftree}
\EnableBpAbbreviations
        \AXC{s$_{3}$ $\to$ s$_{0}$}
        \AXC{np$_{1}$ $\to$ np$_{2}$}
    \BIC{np$_{1}$\enskip{}np$_{2}$\textbackslash s$_{3}$ $\to$ s$_{0}$}
    \AXC{np$_{5}$ $\to$ np$_{4}$}
\BIC{np$_{1}$\enskip{}(np$_{2}$\textbackslash s$_{3}$)/np$_{4}$\enskip{}np$_{5}$ $\to$ s$_{0}$}
\end{prooftree}

Run python atomlink.py --help for details.

Semantic Parsing

Use semcomp module for semantic parsing. You need to define graph schemata for parts of speech as in schema.json.

>>> from lambekseq.semcomp import SemComp
>>> SemComp.load_lexicon(abbr_path='abbr.json',
                         vocab_path='schema.json')
>>> ex = 'a boy walked a dog'
>>> pos = 'ind n vt ind n'
>>> sc = SemComp(zip(ex.split(), pos.split()), calc='dsp')
>>> sc.unify('s')

Use graphviz's Source to display the semgraphs constructed from the input:

>>> from graphviz import Source
>>> Source(sc.semantics[0].dot_styled)

This outputs
a boy walked a dog

You can inspect the syntax behind this parse:

>>> sc.syntax[0].insight.con, sc.syntax[0].insight.pres
('s_0', ['np_1/n_2', 'n_3', '(np_4\\s_5)/np_6', 'np_7/n_8', 'n_9'])

>>> sc.syntax[0].links
['(n_2, n_3)', '(n_8, n_9)', '(np_1, np_4)', '(np_6, np_7)', '(s_0, s_5)']

See demo/demo.ipynb for more examples.

You can export semgraphs to tikz code that can be visually edited by TikZit.

a boy walked a dog

>>> print(sc.semantics[0].tikz)
\begin{tikzpicture}
\begin{pgfonlayer}{nodelayer}
        \node [style=node] (i1) at (-1.88,2.13) {};
        \node [style=none] (g2u0) at (-2.99,3.07) {};
        \node [style=node] (i0) at (0.99,-2.68) {};
        \node [style=none] (g5u0) at (1.09,-4.13) {};
        \node [style=node] (g3a0) at (0.74,0.43) {};
        \node [style=none] (g3u0) at (2.05,1.19) {};
        \node [style=none] (0) at (-3.04,2.89) {boy};
        \node [style=none] (1) at (0.61,-4.00) {dog};
        \node [style=none] (2) at (-0.66,0.72) {ag};
        \node [style=none] (3) at (0.63,-0.77) {th};
        \node [style=none] (4) at (2.42,1.09) {walked};
\end{pgfonlayer}
\begin{pgfonlayer}{edgelayer}
        \draw [style=arrow] (i1) to (g2u0.center);
        \draw [style=arrow] (i0) to (g5u0.center);
        \draw [style=arrow] (g3a0) to (i1);
        \draw [style=arrow] (g3a0) to (i0);
        \draw [style=arrow] (g3a0) to (g3u0.center);
\end{pgfonlayer}
\end{tikzpicture}
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