Humble Connexivity

Andreas Kapsner

DOI: http://dx.doi.org/10.12775/LLP.2019.001

Abstract


In this paper, I review the motivation of connexive and strongly connexive logics, and I investigate the question why it is so hard to achieve those properties in a logic with a well motivated semantic theory. My answer is that strong connexivity, and even just weak connexivity, is too stringent a requirement. I introduce the notion of humble connexivity, which in essence is the idea to restrict the connexive requirements to possible antecedents. I show that this restriction can be well motivated, while it still leaves us with a set of requirements that are far from trivial. In fact, formalizing the idea of humble connexivity is not as straightforward as one might expect, and I offer three different proposals. I examine some well known logics to determine whether they are humbly connexive or not, and I end with a more wide-focused view on the logical landscape seen through the lens of humble connexivity.


formalizing the idea of humble connexivity is not as straightforward as one might expect, and
I offer three different proposals. I examine some well known logics to determine whether they
are humbly connexive or not, and I end with a more wide-focused view on the logical landscape
seen through the lens of humble connexivity.

Keywords


connexive logic; strong connexivity; unsatisfiability; paraconsistency; conditional logic; modal logic

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References


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