Streamlining Input/Output Logics with Sequent Calculi

TL;DR

This paper introduces sequent calculi for input/output logics, providing a unified proof system that simplifies semantics, complexity analysis, and embeddings into modal logics, thus advancing reasoning about norms and causal relations.

Contribution

It develops proof-search-oriented sequent calculi for I/O logics, linking derivability to original logics and offering new semantics, complexity bounds, and embeddings.

Findings

Established natural syntactic link between derivability and original I/O logics

Provided new, simple semantics for I/O logics

Achieved complexity bounds and embeddings into modal logics

Abstract

Input/Output (I/O) logic is a general framework for reasoning about conditional norms and/or causal relations. We streamline Bochman's causal I/O logics via proof-search-oriented sequent calculi. Our calculi establish a natural syntactic link between the derivability in these logics and in the original I/O logics. As a consequence of our results, we obtain new, simple semantics for all these logics, complexity bounds, embeddings into normal modal logics, and efficient deduction methods. Our work encompasses many scattered results and provides uniform solutions to various unresolved problems.