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`

.

`=^`

`<=`

`=>`

eye observership u / \ =^ / \ l <= eye => r origin ------- evolution

`_:x`

blank nodes in triples and quads`?x`

quickvars in rules and queries`var:x`

variables in proofsThe **EYE stack** comprises the following Software and Machines:

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

- Select rule
`P => C`

- Prove
`P & ˜C`

(backward chaining) and if it fails backtrack to 1. - If
`P & ˜C`

assert`C`

(forward chaining) and remove brake - If
`C = answer(A)`

and tactic limited-answer stop, else backtrack to 2. - If brake or tactic linear-select stop, else start again at 1.

- 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: Notation3 Builtin Functions

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

- 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, beetle, dp, diamond-property, gcc, hanoi, lee, socrates, witch, zebra
- markovian networks: mmln
- mathematical reasoning: ackermann, fibonacci, padovan, pi, polygon, tak
- neural networks: fcm, fgcm
- quantum computation: dqc
- universal machines: turing, usm
- workflow composers: gps, map, resto, restpath, twf

- 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
- N3 editor: Notation3 Editor