Based on: https://arxiv.org/abs/2202.00293

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We will here present a precise mathematical definition of classical propositional logic without atoms, present a semantics for it, a sequent calculus and prove the completeness theorem using a very general abstract version of this theorem (Beziau 2001).

- J.-Y. Béziau, “Sequents and bivaluations”, Logique et Analyse, 44 (2001), pp.373-394.
- K. Gödel, “Eine Eigenschaft der Realisierungen des Aussagenkalküls”, Ergebnisse eines mathematischen Kolloquiums, 2 (1929/30), pp.20-21.
- B. Russell, “Logical Atomism”, in J. H. Muirhead (ed.), Contemporary British Philosophers, London: Allen and Unwin, 1924, pp.356–383.
- R. Suszko (with S. L. Bloom and D. J. Brown) “A note on abstract logics”, Bulletin de l’Académie Polonaise des Sciences, 18 (1970), pp. 109-110.
- L. Wittgenstein, “Logisch-Philosophische Abhandlung”, Annalen der Naturphilosophie, 14 (1921).

The presented results are based on a joint work with Rostyslav Bodnar and Taras Bodnar.

]]>In this work, we focus on the Jackiw-Teitelboim gravity in classical limit, and use Peierls bracket (which is a linear response like computation of observables’ bracket) to compute the algebra of a large class of diffeomorphism invariant observables. With this algebra, we can reproduce some recent results in Jackiw-Teitelboim gravity including: traversable wormhole, scrambling effect, and $SL(2)$ charges. We can also use it to clarify the question of when the creation of an excitation deep in the bulk increases or decreases the boundary energy, which is of crucial importance for the “typical state” version of the firewall paradox.

In the talk, I will first give a brief introduction of Peierls bracket, and then use the Peierls bracket to study the brackets between diffeomorphism invariant observables in Jackiw-Teitelboim gravity. I will then give two applications of this algebra: reproducing the scrambling effect, and studying the energy change after creating an excitation in the bulk.

Work based on https://arxiv.org/pdf/2108.04841.pdf

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