Stratified Counterpossible Logic
For logicians and philosophers, this provides a novel framework to handle counterpossibles without vacuism, addressing a known problem in modal logic.
The paper introduces two logic systems, SCP and SCP1, that use a stratified world structure to distinguish metaphysical impossibility from logical contradiction, ensuring counterpossibles with impossible antecedents are non-trivially evaluated. The systems are proven sound, complete, and decidable.
This paper presents two logic systems, SCP and its extension SCP1, to distinguish between different types of impossibility. The semantics use a stratified structure that partitions worlds into logic-normal worlds (N) and anti-logic worlds (I). By defining a metaphysical accessibility relation within N, the systems separate metaphysical impossibility from logical contradiction. This allows for logical reasoning to be maintained even when dealing with metaphysical impossibilities. To address the challenge of vacuism, SCP1 implements a non-empty constraint on the selection function, ensuring that counterpossibles with impossible antecedents are not trivially true but depend on the connection between the antecedent and the consequent. We provide proofs for the soundness, completeness, and decidability of both systems. Finally, we indicate the possibility of applying this stratified approach to other modal domains, such as deontic or epistemic logic.