# Euler Yet another proof Engine - EYE

EYE is a reasoning engine supporting the Semantic Web layers. It performs forward and backward chaining along Euler paths. Via N3 it is interoperable with Cwm.
Forward chaining is applied for rules using `=>` in N3 and backward chaining is applied for rules using `<=` in N3 which one can imagine as built-ins. Euler paths are roughly "don't step in your own steps" which is inspired by what Leonhard Euler discovered in 1736 for the Königsberg Bridge Problem. EYE sees the rule `P => C` as `P & ˜C => C`.

## Architecture and design

The EYE stack comprises the following Software and Machines:

This is what the basic EAM (Euler Abstract Machine) does in a nutshell:

1. Select rule `P => C`
2. Prove `P & ˜C` (backward chaining) and if it fails backtrack to 1.
3. If `P & ˜C` assert `C` (forward chaining) and remove brake
4. If `C = answer(A)` and tactic limited-answer stop, else backtrack to 2.
5. If brake or tactic linear-select stop, else start again at 1.

## EYE Unifying Logic

- Design Issues of Tim Berners-Lee: The Semantic Web as a language of logic
- PhD thesis of Dörthe Arndt: Notation3 as the Unifying Logic for the Semantic Web
- Proposed built-ins of w3c N3: Vocabulary Definitions

## EYE Reasoning

Running the Semantic Web Databus and Proofbus from Tim Berners-Lee which is like a world wide welding machine transforming data into proofs:

### Examples and Test Cases

- bayesian networks: ccd, nbbn, swet
- control systems: cs
- description logic: bmt, dt, edt, entail, gedcom, graph, h2o, RDF plus OWL (source)
- ershovian compilation: preduction
- extensible imaging: lldm
- logic programming: 4color, de, dp, dpe, gcc, hanoi, lee, socrates, witch, zebra
- markovian networks: mmln
- mathematical reasoning: complex, equation, fibonacci, padovan, pi, polygon, polynomial, prime, tak
- neural networks: fcm, fgcm
- quantum computation: dqc
- universal machines: turing, usm
- workflow composers: gps, map, resto, restpath, twf

## See also

- EYE paper: Drawing Conclusions from Linked Data on the Web: The EYE Reasoner
- EYE tutorial: Semantic Web Reasoning With EYE
- EYE talk: EYE looking through N3 glasses
- N3 talk: Notation3 Logic: A Practical Introduction