A contra-classical logic is a logic that, over the same language as that of classical logic, validates arguments that are not classically valid. In this paper I investigate whether there is a single, non-trivial logic that exhibits many features of already known contra-classical logics. I show that Mortensen’s three-valued connexive logic _M3V_ is one such logic and, furthermore, that following the example in building _M3V_, that is, putting a suitable conditional on top of the \(\{\sim, \wedge, \vee \}\) -fragment of (...) _LP_, one can get a logic exhibiting even more contra-classical features. (shrink)

In this paper, we apply relating semantics to the widely discussed problem of free choice between permitted actions or situations in normative systems. Leaving aside contexts in which the free choice principle is obviously unacceptable or uncontroversially valid, we concentrate on free choice for explicit permissions. In order to construct a formal representation of explicit permissions, we introduce a special constant, $\texttt {permit}$, which is analogous to the constant $\texttt {violation}$ used in the Andersonian–Kangerian approach to deontic logic with respect (...) to prohibition and obligation. Consequently, we define a permission operator on the basis of the $\texttt {permit}$ constant and a relation of legitimization. The general idea is that $P \varphi $ is true if and only if $\texttt {permit}$ is true, which means that a permission is actually issued and $\varphi $ is legitimized by $\texttt {permit}$. The intuitive notion of legitimization is formally represented by an operator of relating implication: a non-classical implication that is semantically defined by adding a constraint to the classical meaning of implication to the effect that arguments are related by a special relation. The properties of this relation are based on an informal, intuitive meaning of legitimization and determine the properties of the permission operator. We show that the resulting permission operator possesses the free choice property and avoids certain unwanted consequences that follow from alternative approaches. (shrink)