Abstract
The paper introduces a contingential language extended with a propositional constant τ axiomatized in a system named KΔτ , which receives a semantical analysis via relational models. A definition of the necessity operator in terms of Δ and τ allows proving (i) that KΔτ is equivalent to a modal system named K□τ (ii) that both KΔτ and K□τ are tableau-decidable and complete with respect to the defined relational semantics (iii) that the modal τ -free fragment of KΔτ is exactly the deontic system KD. In §4 it is proved that the modal τ -free fragment of a system KΔτw weaker than KΔτ is exactly the minimal normal system K.
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Pizzi, C. Necessity and Relative Contingency. Stud Logica 85, 395–410 (2007). https://doi.org/10.1007/s11225-007-9044-y
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DOI: https://doi.org/10.1007/s11225-007-9044-y