In this paper we study a new operator of strong modality ⊞, related to the non-contingency operator ∆. We then provide soundness and completeness theorems for the minimal logic of the ⊞-operator.

We offer tableaux systems for logics of essence and accident and logics of non-contingency, showing their soundness and completeness for Kripke semantics. We also show an interesting parallel between these logics based on the semantic insensitivity of the two non-normal operators by which these logics are expressed.

The logic of change formulated by K. Świętorzecka, has its motivation coming from the Aristotelian theory of substantial change which is undrstood as a transformation consisting in the disappearing and becoming of individual substances. The transition: becoming/disapearing (and conversely) is expressed in by the primitive operator C, to be read: it changes that …, and it is mapped by the progressively expanding language. We are interested in attributive changes of individual substances. We consider a formalism with two non-normal and not (...) mutually definable operators of possible and necessary change, inspired by Aristotelian distinction of accidental and essential attributes. From we adopt the idea that temporal concepts are defined via change operators, and the idea of an expanding language. In what follows, We axiomatise our new logic and describe its semantics, giving the proof of its completeness. We compare our formalism with selected modal logics. (shrink)