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https://github.com/comfreek/basic-ontology-language

An experimental ontology language formalized in Coq with many semantics
https://github.com/comfreek/basic-ontology-language

coq-formalization formal-languages formal-methods ontologies semantics

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An experimental ontology language formalized in Coq with many semantics

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# Basic Ontology Language: an experimental ontology language in Coq with many semantics

The **B**asic **O**ntology **L**anguage (BOL) is a toy language for designing ontologies made-up for educational purposes in a course on [knowledge representation and processing (WuV)](https://kwarc.info/courses/wuv/) by [Michael Kohlhase](https://kwarc.info/people/mkohlhase/) and [Florian Rabe](https://kwarc.info/people/frabe/).

This repository formalizes BOL and gives
- a deductive semantics for BOL given by a derivation calculus
- a semantics BOL -> FOL
- a semantics BOL -> SQL
- a semantics FOL -> [TPTP](http://www.tptp.org/) (an interface language to feed FOL automatic theorem provers)

Sample BOL ontology as a Coq definition (and using a lot of notations):

```coq
Definition sampleOntology : bolOntology :=
SIGNATURE
CON "professor" ;;
CON "lecturer" ;;
CON "course" ;;
REL "teaches" ;;
REL "responsible for" ;;

IND "FR" ;;
IND "WuV" ;;
END
THEORY
"FR" <."teaches" u "responsible for".> "WuV" ;;
"lecturer" == "professor" ;;
END.

Definition sampleQuery: bolQuery := (sampleOntology, "WuV" IS-A "course").

Definition bolQueryToTPTP := tptpQueryToString ∘ folQueryToTPTP ∘ bolQueryToFol.
Compute (bolQueryToTPTP sampleQuery).
```

Here, we see a semantics construction from BOL to FOL, to TPTP, and finally to a string.
The output is:

```
= "fof(0, axiom, ects(wuv, s(s(s(s(s(z))))))).
fof(1, axiom, hard(wuv, false)).
fof(2, axiom, course(wuv)).
fof(3, axiom, taughtat(wuv, fau)).
fof(4, axiom, lecturer(fr)).
fof(5, axiom, ?[Z] : ((teaches(fr, Z)) & (taughtat(Z, fau)))).
fof(6, axiom, ![X] : ((lecturer(X)) => (![Y] : ((teaches(X, Y)) => (course(Y)))))).

fof(query, conjecture, course(wuv))."

: string
```

This TPTP document can then be fed, for instance, to the [Vampire](https://vprover.github.io/) automatic theorem prover.

## Building and Usage

Install Coq and run

```
coqc utils.v -R . bol
coqc bol.v -R . bol
coqc bolcalc.v -R . bol
coqc fol.v -R . bol
coqc sql.v -R . bol

coqc boltofol.v -R . bol
coqc foltotptp.v -R . bol
coqc boltosql.v -R . bol

coqc main.v -R . bol
```

Copyable one-liner for PowerShell:

```
coqc utils.v -R . bol;coqc bol.v -R . bol;coqc bolcalc.v -R . bol;coqc fol.v -R . bol;coqc sql.v -R . bol;coqc boltofol.v -R . bol;coqc foltotptp.v -R . bol;coqc boltosql.v -R . bol;coqc main.v -R . bol;
```

Then you can seamlessly open `main.v` in CoqIDE (or other Coq IDEs) and step through it!

*TODO:* improve build system.