A meta-probabilistic-programming language for bisimulation of probabilistic and non-well-founded type systems

• URL: http://arxiv.org/abs/2203.15970v1
• Date: Wed, 30 Mar 2022 01:07:37 GMT
• Title: A meta-probabilistic-programming language for bisimulation of probabilistic and non-well-founded type systems
• Authors: Jonathan Warrell, Alexey Potapov, Adam Vandervorst, Ben Goertzel
• Abstract summary: We introduce a formal meta-language for probabilistic programming, capable of expressing both programs and the type systems in which they are embedded. We draw on the frameworks of cubical type theory and dependent typed metagraphs to formalize our approach.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a formal meta-language for probabilistic programming, capable of expressing both programs and the type systems in which they are embedded. We are motivated here by the desire to allow an AGI to learn not only relevant knowledge (programs/proofs), but also appropriate ways of reasoning (logics/type systems). We draw on the frameworks of cubical type theory and dependent typed metagraphs to formalize our approach. In doing so, we show that specific constructions within the meta-language can be related via bisimulation (implying path equivalence) to the type systems they correspond. In doing so, our approach provides a convenient means of deriving synthetic denotational semantics for various type systems. Particularly, we derive bisimulations for pure type systems (PTS), and probabilistic dependent type systems (PDTS). We discuss further the relationship of PTS to non-well-founded set theory.

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