Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Computational Grounding of Responsibility Attribution and Anticipation in LTLf

Giuseppe De Giacomo, Emiliano Lorini, Timothy Parker, Gianmarco Parretti

TL;DR

This paper studies different variants of responsibility in a strategic setting based on LTLf and shows a connection with notions in reactive synthesis, including synthesis of winning, dominant, and best-effort strategies.

Abstract

Responsibility is one of the key notions in machine ethics and in the area of autonomous systems. It is a multi-faceted notion involving counterfactual reasoning about actions and strategies. In this paper, we study different variants of responsibility in a strategic setting based on LTLf. We show a connection with notions in reactive synthesis, including synthesis of winning, dominant, and best-effort strategies. This connection provides the building blocks for a computational grounding of responsibility including complexity characterizations and sound, complete, and optimal algorithms for attributing and anticipating responsibility.

Computational Grounding of Responsibility Attribution and Anticipation in LTLf

TL;DR

This paper studies different variants of responsibility in a strategic setting based on LTLf and shows a connection with notions in reactive synthesis, including synthesis of winning, dominant, and best-effort strategies.

Abstract

Responsibility is one of the key notions in machine ethics and in the area of autonomous systems. It is a multi-faceted notion involving counterfactual reasoning about actions and strategies. In this paper, we study different variants of responsibility in a strategic setting based on LTLf. We show a connection with notions in reactive synthesis, including synthesis of winning, dominant, and best-effort strategies. This connection provides the building blocks for a computational grounding of responsibility including complexity characterizations and sound, complete, and optimal algorithms for attributing and anticipating responsibility.

Paper Structure

This paper contains 12 sections, 15 theorems, 2 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Responsibility
  4. Attribution against Environment Strategies.
  5. Attribution on Histories.
  6. Active Responsibility
  7. Responsibility and Strategy Properties
  8. Checking Techniques
  9. Conclusions
  10. Supplementary Material
  11. Hardness Proofs
  12. Proof of Theorems \ref{['thm:pass-and-dom']}, \ref{['thm:pass-and-dom-2']}, and \ref{['thm:responsibility-checking-thm']}

Key Result

Theorem 1

Figures (3)

  • Figure 1: dfa$\mathcal{A}_{\mathcal{Y} \neq \mathcal{Y}'}$. Final states are in bold. $y = y'$ (resp. $y \neq y'$) denotes equal (resp. distinct) assignments of atoms in $\mathcal{Y}$ and $\mathcal{Y}'$. Similarly for $x = x'$ (resp. $x \neq x'$).
  • Figure 2: dfa$\mathcal{A}_{\mathcal{E}_h}$ of ltl$_f$ environment specification $\mathcal{E}_h$ that captures environment strategies $\sigma_{env}$ such that history $h = (Y_0 \cup X_0) \cdots (Y_n \cup X_n)$ is consistent with $\sigma_{env}$.
  • Figure 2: dfa$\mathcal{A}_{\mathcal{E}_h}$ of ltl$_f$ environment specification $\mathcal{E}_h$ that captures environment strategies $\sigma_{env}$ such that history $h = (Y_0 \cup X_0) \cdots (Y_n \cup X_n)$ is consistent with $\sigma_{env}$.

Theorems & Definitions (28)

  • Definition 1: Passive Responsibility Attribution, PRAttr
  • Definition 2: Inexcusable Passive Responsibility Attribution, IPRAttr
  • Definition 3: (Inexcusable) Passive Responsibility Attribution on History, IPRAttr$(h)$/PRAttr$(h)$
  • Definition 4: (Inexcusable) Passive Responsibility Anticipation, IPRAnt/PRAnt
  • Definition 5: Active Responsibility Attribution and Anticipation, ARA
  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • Theorem 5
  • ...and 18 more