Necessity and Relative Contingency

Author: Pizzi Claudio  

Publisher: Springer Publishing Company

ISSN: 0039-3215

Source: Studia Logica, Vol.85, Iss.3, 2007-04, pp. : 395-410

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Abstract

The paper introduces a contingential language extended with a propositional constant τ axiomatized in a system named K∆τ , which receives a semantical analysis via relational models. A definition of the necessity operator in terms of ∆ and τ allows proving (i) that K∆τ is equivalent to a modal system named K□τ (ii) that both K∆τ and K□τ are tableau-decidable and complete with respect to the defined relational semantics (iii) that the modal τ -free fragment of K∆τ is exactly the deontic system KD. In §4 it is proved that the modal τ -free fragment of a system K∆τw weaker than K∆τ is exactly the minimal normal system K.