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Weak Permission is not Well-Founded, Grounded and Stable

Guido Governatori

TL;DR

It is shown that it is not possible to capture weak permission in the presence of deontic conflicts under the well-founded, grounded and (sceptical) stable semantics.

Abstract

We consider the notion of weak permission as the failure to conclude that the opposite obligation. We investigate the issue from the point of non-monotonic reasoning, specifically logic programming and structured argumentation, and we show that it is not possible to capture weak permission in the presence of deontic conflicts under the well-founded, grounded and (sceptical) stable semantics.

Weak Permission is not Well-Founded, Grounded and Stable

TL;DR

It is shown that it is not possible to capture weak permission in the presence of deontic conflicts under the well-founded, grounded and (sceptical) stable semantics.

Abstract

We consider the notion of weak permission as the failure to conclude that the opposite obligation. We investigate the issue from the point of non-monotonic reasoning, specifically logic programming and structured argumentation, and we show that it is not possible to capture weak permission in the presence of deontic conflicts under the well-founded, grounded and (sceptical) stable semantics.

Paper Structure

This paper contains 4 sections, 2 theorems, 19 equations.

Table of Contents

  1. Introduction
  2. Logic Programming and Weak Permission
  3. Argumentation and Weak Permission
  4. Summary and Conclusions

Key Result

Theorem 1

Let $P$ be a conflicted deontic program, and let $l$ be a conflicted literal. Then $\mathop{\mathsf{perm}}\nolimits_w(l)$ and $\mathop{\mathsf{perm}}\nolimits_w(\neg l)$ are not conclusions of the program under well-founded and stable semantics.

Theorems & Definitions (17)

  • definition 1: Program
  • definition 2: Deontic Program
  • definition 3
  • definition 4
  • definition 5: Logic Programming Semantics
  • definition 6: Conflicted Deontic Program
  • Theorem 1
  • proof
  • definition 7
  • definition 8
  • ...and 7 more