A tableau methodology for deontic conditional logics

TL;DR

This paper introduces a tableau-based theorem proving approach for a fragment of deontic conditional logics, utilizing possible world semantics and label formalism to facilitate proof construction.

Contribution

It adapts the KEM label formalism and KE+ tableau system to deontic conditional logics, providing a new proof methodology for this logical fragment.

Findings

The method effectively handles boolean combinations of conditional statements.

It offers a refutation and proof approach for deontic conditionals.

Lays groundwork for algorithmic reasoning in deontic logic applications.

Abstract

In this paper we present a theorem proving methodology for a restricted but significant fragment of the conditional language made up of (boolean combinations of) conditional statements with unnested antecedents. The method is based on the possible world semantics for conditional logics. The KEM label formalism, designed to account for the semantics of normal modal logics, is easily adapted to the semantics of conditional logics by simply indexing labels with formulas. The inference rules are provided by the propositional system KE+ - a tableau-like analytic proof system devised to be used both as a refutation and a direct method of proof - enlarged with suitable elimination rules for the conditional connective. The theorem proving methodology we are going to present can be viewed as a first step towards developing an appropriate algorithmic framework for several conditional logics for (defeasible) conditional obligation.