A Simple Sequent Calculus for Weak Full Grounding

This paper investigates the logic of grounding, a non-causal explanatory relation. While the study of this field is flourishing, it is still in its early stages. This paper contributes to the literature by presenting GLWG G LWG , a novel sequent calculus for weak full grounding. While it provides a sequent-style presentation of the existing axiomatic system LWG LWG proposed by Adam Lovett, our calculus is balanced and avoids the ad-hoc rules contained in LWG LWG . An important fact shown in this paper is that if a sequent Γ ⇒ Δ Γ ⇒ Δ is derivable in GLWG G LWG , then any variable occurring positively (or negatively) in Γ Γ also occurs positively (or negatively) in Δ Δ . This highlights a deep connection between grounding and variable inclusion. This property, in particular, suggests a similarity to Rohan French’s sequent calculus for analytic containment, GAC G AC . Indeed, we demonstrate that GLWG G LWG is the negation dual of GAC G AC . The paper concludes by proving the equivalence between GLWG G LWG and LWG LWG .