Necessity and relative contingency

Studia Logica 85 (3):395 - 410 (2007)
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.
Keywords Philosophy   Computational Linguistics   Mathematical Logic and Foundations   Logic
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References found in this work BETA
Lloyd Humberstone (2002). The Modal Logic of Agreement and Noncontingency. Notre Dame Journal of Formal Logic 43 (2):95-127.
Steven T. Kuhn (1995). Minimal Non-Contingency Logic. Notre Dame Journal of Formal Logic 36 (2):230-234.
I. L. Humberstone (1995). The Logic of Non-Contingency. Notre Dame Journal of Formal Logic 36 (2):214-229.

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