In this paper, first some propositional conditional logics based on Belnap and Dunn's useful four-valued logic of first-degree entailment are introduced semantically, which are then turned into systems of weakly and unrestrictedly connexive conditional logic. The general frame semantics for these logics makes use of a set of allowable (or admissible) extension/antiextension pairs. Next, sound and complete tableau calculi for these logics are presented. Moreover, an expansion of the basic conditional connexive logics by a constructive implication is considered, which gives an opportunity to discuss recent related work, motivated by the combination of indicative and counterfactual conditionals. Tableau calculi for the basic constructive connexive conditional logics are defined and shown to be sound and complete with respect to their semantics. This semantics has to ensure a persistence property with respect to the preorder that is used to interpret the constructive implication.

We investigate a lattice of conditional logics described by a Kripke type semantics, which was suggested by Chellas and Segerberg -Chellas-Segerberg (CS) semantics -plus 30 further principles. We (i) present a non-trivial frame-based completeness result, (ii) a translation procedure which gives one corresponding trivial frame conditions for arbitrary formula schemata, and (iii) nontrivial frame conditions in CS semantics which correspond to the 30 principles.

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What are ceteris paribus (cp) laws? Which disciplines appeal to cp laws and which semantics, metaphysical underpinning, and epistemological dimensions do cp law statements have? Firstly, we give a short overview of the recent discussion on cp laws, which addresses these questions. Secondly, we suggest that given the rich and diverse literature on cp laws a broad conception of cp laws should be endorsed which takes into account the different ways in which laws can be nonuniversal (by being ''non-strict'', ''inexact'', ''exception-ridden'', ''idealized'' and so forth). Finally, we provide an overview of the special issue on that basis and describe the individual contributions to the special issue according to the issues they address: (a) the range of applications of cp laws as well as the (b) semantics, (c) metaphysics, and (d) epistemology pertaining to cp law statements.Both authors-Alexander Reutlinger and Matthias Unterhuber have contributed equally to this paper.