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fixed error pointed out by Todd
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Alec Rhea
Alec Rhea
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Sentential, propositional, first order and higher logics from a category theoreticcategorical perspective

Is there a standard reference for understanding sentential, propositional, first and higher order logics from a categorical perspective?

I'm close to knowing enough $1$/$2$/internal category theory to tackle the Joyal-Tierney Galois theorem for toposes and the Borceux-Janelidze generalization for internal precategories to give some idea of my knowledge base. I've heard that category theory can model all of these logics as the internal logic of an appropriate (possibly higher) category, and I was looking for a reference that builds up logic from this perspective for someone who has never explicitly read a logic textbook.

For the record I have "A Course in Mathematical Logic" by Bell and Machover ordered and in the mail; I fully intend to take the classical route up through logic as well, but I was curious about any categorical cheat codes along the way.

It seems (naively) like type theory might be the answer here, and I would be open to suggestions in that direction, but I am currently unfamiliar with the inner workings (or general moral) of type theory.

Sentential, propositional, first order and higher logics from a category theoretic perspective

Is there a standard reference for understanding sentential, propositional, first and higher order logics from a categorical perspective?

I'm close to knowing enough $1$/$2$/internal category theory to tackle the Joyal-Tierney Galois theorem for toposes and the Borceux-Janelidze generalization for internal precategories to give some idea of my knowledge base. I've heard that category theory can model all of these logics as the internal logic of an appropriate (possibly higher) category, and I was looking for a reference that builds up logic from this perspective for someone who has never explicitly read a logic textbook.

For the record I have "A Course in Mathematical Logic" by Bell and Machover ordered and in the mail; I fully intend to take the classical route up through logic as well, but I was curious about any categorical cheat codes along the way.

It seems (naively) like type theory might be the answer here, and I would be open to suggestions in that direction, but I am currently unfamiliar with the inner workings (or general moral) of type theory.

Sentential, first order and higher logics from a categorical perspective

Is there a standard reference for understanding sentential, first and higher order logics from a categorical perspective?

I'm close to knowing enough $1$/$2$/internal category theory to tackle the Joyal-Tierney Galois theorem for toposes and the Borceux-Janelidze generalization for internal precategories to give some idea of my knowledge base. I've heard that category theory can model all of these logics as the internal logic of an appropriate (possibly higher) category, and I was looking for a reference that builds up logic from this perspective for someone who has never explicitly read a logic textbook.

For the record I have "A Course in Mathematical Logic" by Bell and Machover ordered and in the mail; I fully intend to take the classical route up through logic as well, but I was curious about any categorical cheat codes along the way.

It seems (naively) like type theory might be the answer here, and I would be open to suggestions in that direction, but I am currently unfamiliar with the inner workings (or general moral) of type theory.

Source Link
Alec Rhea
Alec Rhea
  • 10.1k
  • 3
  • 30
  • 88

Sentential, propositional, first order and higher logics from a category theoretic perspective

Is there a standard reference for understanding sentential, propositional, first and higher order logics from a categorical perspective?

I'm close to knowing enough $1$/$2$/internal category theory to tackle the Joyal-Tierney Galois theorem for toposes and the Borceux-Janelidze generalization for internal precategories to give some idea of my knowledge base. I've heard that category theory can model all of these logics as the internal logic of an appropriate (possibly higher) category, and I was looking for a reference that builds up logic from this perspective for someone who has never explicitly read a logic textbook.

For the record I have "A Course in Mathematical Logic" by Bell and Machover ordered and in the mail; I fully intend to take the classical route up through logic as well, but I was curious about any categorical cheat codes along the way.

It seems (naively) like type theory might be the answer here, and I would be open to suggestions in that direction, but I am currently unfamiliar with the inner workings (or general moral) of type theory.