🇬🇧 English to First-Order Logic 💫

Parsing English text and interpreting it as first-order logic formulas can be done in accordance to Montague grammar using Stanza.

Consider the following examples of interpretations á la Montague grammar:

Text	Category	Constituents	Interpretation
Nemo is a fish	S	NP VP	∃x₀[(fish(x₀) ∧ is(x₀,"Nemo"))]
Nemo	NP	NNP	λP → P("Nemo")
is a fish	VP	VBZ NP	λx → ∃x₀[fish(x₀) ∧ is(x₀,x)]
is	VBZ		λx → is(x)
a fish	NP	DT NN	λQ λx → ∃x₀[fish(x₀) ∧ Q(x₀,x)]
a	DT		λP λQ λx → ∃x₀[P(x₀) ∧ Q(x₀,x)]
fish	NN		λx → fish(x)

Parser

We can use Stanza's constituency parser to acquire the constituents of the provided text. The resulting grammar tree can be used for interpretation. See /parser for more information about the parser.

Interpreter

The interpreter implements interpretation rules in accordance to Montague grammar. See GRAMMAR.md for an account of the currently available categories and interpretation rules. See /interpreter for more information about the interpreter.

Examples

Interpreting examples/parser/nemo-is-a-fish.json gives the following output:

Nemo is a fish.

ROOT
|
`- S
   |
   +- NP
   |  |
   |  `- NNP
   |     |
   |     `- Nemo
   |
   `- VP
      |
      +- VBZ
      |  |
      |  `- is
      |
      `- NP
         |
         +- DT
         |  |
         |  `- a
         |
         `- NN
            |
            `- fish

∃x₀[(fish(x₀) ∧ is(x₀,"Nemo"))]

Interpreting examples/parser/no-fish-walks.json gives the following output:

No fish walks.

ROOT
|
`- S
   |
   +- NP
   |  |
   |  +- DT
   |  |  |
   |  |  `- No
   |  |
   |  `- NN
   |     |
   |     `- fish
   |
   `- VP
      |
      `- VBZ
         |
         `- walks

∀x₀[(fish(x₀) → ¬(walks(x₀)))]

Building

Install all prerequisites and build the project using install.sh.

Running

Run the full program (parser and interpreter) with run.sh path/to/json/file.

Using the container

Build the image with docker build -t english2logic:latest .. (Takes around 40 minutes.)

Then run a container using docker run -it -v .:/english2logic english2logic. You can skip the -v if you want to run the container in isolation.