A Reduction of Input/Output Logics to SAT

2025-08-22

AI Summary

This work addresses the challenge of automated reasoning for conditional norms in input/output (I/O) logic. We propose a novel SAT-based reduction framework that, unlike conventional approaches requiring truth assignments to normative statements, systematically encodes I/O conditional inference problems into propositional logic formulas solvable by off-the-shelf SAT solvers. Based on this framework, we implement rio, a prototype symbolic reasoning system supporting multiple I/O logics—including basic, simple-minded, and through variants. Experimental evaluation demonstrates that rio achieves both strong expressive power and competitive computational efficiency, successfully verifying several canonical normative examples. To our knowledge, this is the first scalable, formally verifiable automation framework for non-truth-functional normative reasoning.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Deontic logics are formalisms for reasoning over norms, obligations, permissions and prohibitions. Input/Output (I/O) Logics are a particular family of so-called norm-based deontic logics that formalize conditional norms outside of the underlying object logic language, where conditional norms do not carry a truth-value themselves. In this paper, an automation approach for I/O logics is presented that makes use of suitable reductions to (sequences of) propositional satisfiability problems. A prototypical implementation, named rio (reasoner for input/output logics), of the proposed procedures is presented and applied to illustrative examples.

Problem

• Automating reasoning for conditional deontic logics
• Reducing I/O logic problems to SAT sequences
• Implementing computational procedures for norm-based reasoning

Innovation

• Reduces I/O logic to SAT
• Automates reasoning via satisfiability
• Implements prototype named rio