1,720,977 research outputs found
Content and Depth Revisited
Full text linkIn this paper I will compare depth relevance to what has come to be called depth hyperformalism. Ordinary formality, is typically taken to require closure under uniform substitutions. Depth hyperformality requires closure under depth substitutions—not-necessarily-uniform substitutions that are allowed to vary with depth. As it turns out, all depth hyperformal logics are depth relevant but not vice-versa.
So we’re left to ask the following question: for the particular projects Ross Brady is engaged in, should it be depth relevance or depth hyperformalism that should set the pace? More to the point, I’ll be interested in the following two claims:
Logics of meaning containment are necessarily depth hyperformal.
Logics of meaning containment are necessarily depth relevant.
The first entails the second. Brady seems to endorse the second. I’ll argue in this paper that he should also endorse the first
Putting the Stars in their Places
Full text linkThis paper presents a new semantics for the weak relevant logic DW that makes the role of the infamous Routley star more explicable. Central to this rewriting is combining aspects of both the American and Australian plan for understanding negations in relevance logics
Putting the Stars in their Places
No full textThis paper presents a new semantics for the weak relevant logic DW that makes the role of the infamous Routley star more explicable. Central to this rewriting is combining aspects of both the American and Australian plan for understanding negations in relevance logics
Strong Depth Relevance
No full textRelevant logics infamously have the property that they only validate a conditional when some propositional variable is shared between its antecedent and consequent. This property has been strengthened in a variety of ways over the last half-century. Two of the more famous of these strengthenings are the strong variable sharing property and the depth relevance property. In this paper I demonstrate that an appropriate class of relevant logics has a property that might naturally be characterized as the supremum of these two properties. I also show how to use this fact to demonstrate that these logics seem to be constructive in previously unknown ways
Depth Relevance and Hyperformalism
No full textFormal symptoms of relevance usually concern the propositional variables shared between the antecedent and the consequent of provable conditionals. Among the most famous results about such symptoms are Belnap’s early results showing that for sublogics of the strong relevant logic R, provable conditionals share a signed variable between antecedent and consequent. For logics weaker than R stronger variable sharing results are available. In 1984, Ross Brady gave one well-known example of such a result. As a corollary to the main result of the paper, we give a very simple proof of a related but strictly stronger result
Semantics for Second Order Relevant Logics
No full textHere's the thing: when you look at it from just the right angle, it's entirely obvious how semantics for second-order relevant logics ought to go. Or at least, if you've understood how semantics for first-order relevant logics ought to go, there are perspectives like this. What's more is that from any such angle, the metatheory that needs doing can be summed up in one line: everything is just as in the first-order case, but with more indices.
Of course, it's no small matter finding the magical angle from which everything becomes obvious. And even having found this perspective, one cannot assume one's audience will find things as obvious as oneself. All that to say this: if the results in the paper below strike you as obvious, pay attention to the perspective that makes that possible. And if they don't, feel free to ignore this preamble in its entirety
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