# A Neutral Temporal Deontic STIT Logic

## TL;DR

This paper introduces TDS, a neutral multi-agent temporal deontic STIT logic based on atemporal utilitarian logic, with soundness, completeness, and transformation to utilitarian frames, addressing issues with binary utility functions.

## Contribution

It presents the first neutral temporal deontic STIT logic, TDS, with soundness, completeness, and a method to transform neutral frames into utilitarian temporal frames.

## Key findings

- TDS is sound and complete with respect to relational frames.
- Neutral frames can be transformed into utilitarian temporal frames.
- Binary utility functions pose problems in temporal settings.

## Abstract

In this work we answer a long standing request for temporal embeddings of deontic STIT logics by introducing the multi-agent STIT logic TDS. The logic is based upon atemporal utilitarian STIT logic. Yet, the logic presented here will be neutral: instead of committing ourselves to utilitarian theories, we prove the logic TDS sound and complete with respect to relational frames not employing any utilitarian function. We demonstrate how these neutral frames can be transformed into utilitarian temporal frames, while preserving validity. Last, we discuss problems that arise from employing binary utility functions in a temporal setting.