Connexive Conditional Logic. Part I

Abstract

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.

Superconnexivity Reconsidered

“…In fact, this is even the case in some of the systems following the recipe suggested by Wansing in [21] that validates BT1 and BT2 by tweaking the falsity condition for various kinds of conditional, even with very weak ones (cf. [13,23]). See, for example, the main system discussed in [9] as well as the system cCL in [23].…”

An Easy Road to Multi-contra-classicality

“…Omori Unpublished typescript) that a number of well-known and new paraconsistent and relevant logics can be obtained also by changing appropriately the falsity condition for some connectives while leaving the FDE -like truth and falsity conditions for the remaining ones, in most cases even negation, fixed. 2 More recently, Wansing and Unterhuber ( 2019 ) modified the falsity condition of Chellas’ basic conditional logic CK and they obtained a (weakly) connexive logic. Even more recently, Omori and Wansing ( 2019 ) have put forward a systematization of connexive logics based on certain controlled modifications in the conditional’s truth and falsity conditions, showing that, in general, changing the truth condition has led only to weak connexivity (Boethius’ Theses hold only in rule form, if at all), whereas changing the falsity condition has led to hyper-connexivity (i.e.…”

Modal Boolean Connexive Logics: Semantics and Tableau Approach

“…In the literature one could distinguish three approaches to the connexivity. The first one consists of proposals of specific logical systems designed for a given intended aims, such as [12], where connexive systems of conditionals are investigated. In the second approach, such as [7] and [8], some additional conditions are proposed to distinguish the well behaving connexive logics.…”