Relevant logics are a family of non-classical logics characterized by the behavior of their implication connectives. Unlike some other non-classical logics, such as intuitionistic logic, there are multiple philosophical views motivating relevant logics. Further, different views seem to motivate different logics. In this article, we survey five major views motivating the adoption of relevant logics: Use Criterion, sufficiency, meaning containment, theory construction, and truthmaking. We highlight the philosophical differences as well as the different logics they support. We end with some (...) questions for future research. (shrink)

In this paper, we examine a number of relevant logics’ variable sharing properties from the perspective of theories of topic or subject-matter. We take cues from Franz Berto’s recent work on topic to show an alignment between families of variable sharing properties and responses to the topic transparency of relevant implication and negation. We then introduce and defend novel variable sharing properties stronger than strong depth relevance—which we call cn-relevance and lossless cn-relevance—showing that the properties are satisfied by the weak (...) relevant logics and , respectively. We argue that such properties address a sort of semantic lossiness of strong depth relevance. (shrink)

In this article, we present a definition of a hyperintensionality appropriate to relevant logics. We then show that relevant logics are hyperintensional in this sense, drawing consequences for other non-classical logics, including HYPE and some substructural logics. We further prove results concerning extensionality in relevant logics. We close by discussing related concepts for classifying formula contexts and potential applications of these results.

Jc Beall has made several contributions to the theory of restricted quantification in relevant logics. This paper examines these contributions and proposes an alternative account of restricted universals. The alternative is not, however, a theory of relevant restricted universals in any real sense. It is, however, a theory of restricted universals phrased in the most plausible general quantificational theory for relevant logics—Kit Fine’s stratified semantics. The motivation both for choosing this semantic framework and for choosing the particular theory of restricted (...) quantification we use is because they are the best way of dealing with these topics from Beall’s theory-building theory picture of logic, establishing a second point of contact with Beall’s work. (shrink)

The purpose of this introduction is to give a rough overview of the discussion of the formalization of arguments, focusing on deductive arguments. The discussion is structured around four important junctions: i) the notion of support, which captures the relation between the conclusion and premises of an argument, ii) the choice of a formal language into which the argument is translated in order to make it amenable to evaluation via formal methods, iii) the question of quality criteria for such formalizations, (...) and finally iv) the choice of the underlying logic. This introductory discussion is supplemented by a brief description of the genesis of the special issue, acknowledgements, and summaries of each article. (shrink)

In classically based modal logic, there are three common conceptions of necessity, the universal conception, the equivalence relation conception, and the axiomatic conception. They provide distinct presentations of the modal logic S5, all of which coincide in the basic modal language. We explore these different conceptions in the context of the relevant logic R, demonstrating where they come apart. This reveals that there are many options for being an S5-ish extension of R. It further reveals a divide between the universal (...) conception of necessity on the one hand, and the axiomatic conception on the other: The latter is consistent with motivations for relevant logics while the former is not. For the committed relevant logician, necessity cannot be the truth in all possible worlds. (shrink)

Entailment is an interesting sigmatoid: It should mean one thing, but it means another, just for starters. When used in Mathematics, it is usually with the sense of saying that something is definitely true. That would be the use in Classical Logic then. When used in Logic, it became something else. Now it was about how the logical system, which can be any nonclassical one, could be making a proposition become true or false. The major issue we found in 2000, (...) when learning from the own nonclassicists what they do, was that they talk about Nonclassical Logic, therefore a way of thinking that is not Cartesian, yet they stick to the notion of entailment we use in Mathematics, and therefore to the Classical Logic ways. We here discuss exactly this. (shrink)