In information security, ignorance is not bliss. It is always stated that hiding the protocols (let the other be ignorant about it) does not increase the security of organizations. However, there are cases that ignorance creates protocols. In this paper, we propose distributed contingency logic, a proper extension of contingency (ignorance) logic. Intuitively, a formula is distributed contingen...

A formula is contingent if it is possibly true and possibly false. A formula is noncontingent if it is not contingent, i.e., if it is necessarily true or necessarily false. In an epistemic setting, ‘a formula is contingent’ means that you are ignorant about its value, whereas ‘a formula is non-contingent’ means that you know whether it is true. Although non-contingency is definable in terms of ...

This note proposes various axiomatizations of contingency logic under neighborhood semantics. In particular, by defining a suitable canonical neighborhood function, we give sound and complete axiomatizations of monotone contingency logic and regular contingency logic, thereby answering two open questions raised by Bakhtiari, van Ditmarsch, and Hansen. The canonical function is inspired by a fun...

Hilbert-style axiomatic systems are presented for versions of the modal logics KΣ, where Σ ⊆ {D,4,5}, with non-contingency as the sole modal primitive. The classes of frames characterized by the axioms of these systems are shown to be first-order definable, though not equal to the classes of serial, transitive, or euclidean frames. The canonical frame of the non-contingency logic of any logic c...

Our paper continues, on the one hand, the study of modal logics that have arithmetical semantics, and on the other, the investigation of decidability (or “non-contingency”) logics. We present Hilbert-style axiomatic system for the non-contingency logic of the Gödel-Löb provability logic GL, in other words, for the logic that is complete under the interpretation of a formula BA as ‘a sentence A ...

We investigate an alternative language for equilibrium logic that is based on the concept of positive and negative contingency. Beyond these two concepts our language has the modal operators of necessity and impossibility and the Boolean operators of conjunction and disjunction. Neither negation nor implication are available. Our language is just as expressive as the standard language of equili...

We introduce a notion of bisimulation for contingency logic interpreted on neighbourhood structures, characterise this logic as bisimulationinvariant fragment of modal logic and of first-order logic, and compare it with existing notions in the literature.

This paper combines a non-contingency logic with an epistemic logic by means of fusions and products of modal systems. Some consequences of these interplays are pointed out.