New Framework Merges Graded Linear Logic with Differential Operators

A new differential version of graded linear logic indexes exponential connectives with a monoid of differential operators and is modeled using distribution theory. Read more: getnews.me/new-framework-merges-gra... #gradedlogic #differentiallogic

Logic Syllabus - OeisWiki

Logic Syllabus

This page serves as a focal node for a collection of related resources.

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Differential Logic • Overview
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Differential Propositional Calculus • 22 A One‑Dimensional Universe (cont.) The first order differential extension of $latex \mathcal{X}&fg=000000$ is $latex \mathrm{E}\mathcal{X} = \{ x_1, \mathrm{d}x_1 \} = \{ A, \mathrm{d}A \…

Differential Propositional Calculus • 22
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Differential Propositional Calculus • 21
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Differential Propositional Calculus • 20
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Differential Propositional Calculus • 19
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Differential Propositional Calculus • 18 The Extended Universe of Discourse The extended basis $latex \mathrm{E}\mathcal{A}&fg=000000$ of a universe of discourse $latex [\mathcal{A}]&fg=000000$ is formed by taking the initial basi…

Differential Propositional Calculus • 18
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Differential Propositional Calculus • 17
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Differential Propositional Calculus • 16
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Differential Extension of Propositional Calculus —

This much preparation is enough to begin introducing my subject, if I excuse myself from giving full arguments for my definitional choices until a later stage.

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Differential Propositional Calculus • 14 Differential Extensions Table 11 summarizes the notations needed to describe the first order differential extensions of propositional calculi in a systematic manner. $latex \text{Table 11. Dif…

Differential Propositional Calculus • 14
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Differential Propositional Calculus • 13
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Note. Please see the blog post linked above for the proper formats of the notations used below, as they depend on many typographical distinctions lost in the following transcript.

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Differential Propositional Calculus • 12 Special Classes of Propositions (concl.) Last and literally least in extent, we examine the family of singular propositions in a 3‑dimensional universe of discourse. In our model of propositi…

Differential Propositional Calculus • 12
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Special Classes of Propositions (concl.)

Last and literally least in extent, we examine the family of singular propositions in a 3‑dimensional universe of discourse.

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Differential Propositional Calculus • 11
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Special Classes of Propositions —

Next we take up the family of positive propositions, tracing the rule of their formation in the case of a 3‑dimensional universe of discourse.

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Differential Propositional Calculus • 9
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Special Classes of Propositions —

The full set of propositions f : A → B contains a number of smaller classes deserving of special attention.

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Differential Propositional Calculus • 8
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Before moving on, let's unpack some of the assumptions, conventions, and implications involved in the array of concepts and notations introduced above.

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