Birthday

A RDF Surfaces implementation trying to implement the birthday app with deontic rules.

Expriment 1. Minimal Deontic rules

Minimal deontic logic : "Sartor G (2006) Fundamental legal concepts: a formal and teleological characterisation. Artif Intell Law 14(1–2):101–142"

• [1] Prohibition action(X) = Duty NOT ( action(X) )
• [2] Permission action(X) = NOT (Prohibition action(X))
• [3] IF Duty action(X) THEN Permission action(X)
• [4] IF Duty action(X) AND Duty action(Y) THEN Duty action(X AND Y)

But, from [1] should follow:

[5] Prohibition NOT action(X) = Duty action(X) .

And, from [2] should follow:

[6] NOT (Permission action(X)) = Prohibition action(X)

And from [5] & [6] should follow:

[7] Prohibition action(X) = NOT (Permission action(X)) = Duty NOT( action(X) )

The challenge is here to model and implement [5], [6] and [7].

In this project we also assume :

[8] Duty( action(X) & NOT action(X)) is false

[9] Prohibition( action(X) & NOT action(X)) is false

But, do not include such a rule for Permissions. One could have a permission to call and not call your mother. But, not a duty to call and not call your mother.

This logic is quite unsatisfactory:

• [8] with [1] gives the conclusion that Prohibition(T) = false
• [9] with [1] gives the conclusion that Duty(T) = false

Experiment 2 Standard Deontic Rules

An attempt with a Notation3 implementation of deonitic rules using Standard Deontic Rules : https://plato.stanford.edu/entries/logic-deontic/

We implement a fragment of standard deontic logic using derived rules that don't contain any negations:

• [1] : p => Duty(p)
• [2] : Duty(p) => Prem(p)

and derived

• [3] : Perm(p) & Proh(p) => false
• [4] : Duty(p) & Proh(p) => false
• [5] : p & Proh(p) => false
• [6] : Duty(p & q) => Duty(p) & Duty(q)
• [7] : Perm(p & q) => Perm(p) & Perm(q)
• [8] : Proh(p & q) => Proh(p) v Proh(q) (not implemented: standard Notation3 doesn't have disjunctions in the conclusion)

Policy

A policy is on a target (a URL) and defined what actions are allowed on a target. E.g. the following policy says that in Room101 it is allowed to talk loudy.

@prefix : <http://example.org/ns#> .
@prefix log: <http://www.w3.org/2000/10/swap/log#> .

:Room101 
    a :PolicyTarget .

() log:onPermissionSurface {
    :Room101 :action :TalkLoudly 
} .

Demo

• ./bin/test.sh all - query all policies and display what is allowed
• ./bin/test.sh policies/policy1.n3s - query just one policy
• ./bin/test.sh policies/policy1.n3s show - show all inferred deontic surfaces for one policy
• ./bin/combine.sh policy* - combine policies to check for inconsistencies
• ./bin/combine.sh -s policy* - combine policies to check for inconsistencies (show generated surfaces)