Abstract Logical investigations of the notion of secrecy are typically concentrated on tools for deducing whether private information is well hidden from unauthorized, direct, or indirect access attempts. This paper proposes a multi-agent, normal multi-modal logic to capture salient features of secrecy’s intentions. Specifically, we focus on the intentions, beliefs and knowledge of secret keepers and, more generally, of all the actors involved in secret-keeping scenarios. In particular, we investigate intentions underlying the keeping of a true secret, namely a secret concerning information known (and so true) by the secret keeper. The resulting characterization of intending to keep a true secret provides valuable insights into conditions ensuring or undermining secrecy depending on agents’ attitudes and links between secrets and their surrounding context. We present the proposed logical system’s soundness, completeness and decidability results. Furthermore, we outline some theorems with potential applications to several fields, e.g. computer science and the social sciences.

Abstract In this paper, we introduce the concept of a (lattice) skew Hilbert algebra as a natural generalization of Hilbert algebras. This notion allows a unified treatment of several structures of prominent importance for mathematical logic, e.g. (generalized) orthomodular lattices, and MV-algebras, which admit a natural notion of implication. In fact, it turns out that skew Hilbert algebras play a similar role for (strongly) sectionally pseudocomplemented posets as Hilbert algebras do for relatively pseudocomplemented ones. We will discuss basic properties of closed, dense and weakly dense elements of skew Hilbert algebras and their applications, and we will provide some basic results on their structure theory.

Abstract In this paper, we consider a generalization of the notion of orthomodularity for posets to the concept of the generalized orthomodularity property (GO-property) by considering the $LU$-operators. This seemingly mild generalization of orthomodular posets and its order theoretical analysis yield rather strong application to effect algebras and orthomodular structures. Also, for several classes of orthoalgebras, the GO-property yields a completely order-theoretical characterization of the coherence law, and, in turn, of proper orthoalgebras.