76 research outputs found
Object-Level Reasoning with Logics Encoded in HOL Light
We present a generic framework that facilitates object level reasoning with
logics that are encoded within the Higher Order Logic theorem proving
environment of HOL Light. This involves proving statements in any logic using
intuitive forward and backward chaining in a sequent calculus style. It is made
possible by automated machinery that take care of the necessary structural
reasoning and term matching automatically. Our framework can also handle type
theoretic correspondences of proofs, effectively allowing the type checking and
construction of computational processes via proof. We demonstrate our
implementation using a simple propositional logic and its Curry-Howard
correspondence to the lambda-calculus, and argue its use with linear logic and
its various correspondences to session types.Comment: In Proceedings LFMTP 2020, arXiv:2101.0283
Formalising the Foundations of Discrete Reinforcement Learning in Isabelle/HOL
We present a formalisation of finite Markov decision processes with rewards
in the Isabelle theorem prover. We focus on the foundations required for
dynamic programming and the use of reinforcement learning agents over such
processes. In particular, we derive the Bellman equation from first principles
(in both scalar and vector form), derive a vector calculation that produces the
expected value of any policy p, and go on to prove the existence of a
universally optimal policy where there is a discounting factor less than one.
Lastly, we prove that the value iteration and the policy iteration algorithms
work in finite time, producing an epsilon-optimal and a fully optimal policy
respectively
Linear resources in Isabelle/HOL
We present a formal framework for process composition based on actions that are specified by their input and output resources. The correctness of these compositions is verified by translating them into deductions in intuitionistic linear logic. As part of the verification we derive simple conditions on the compositions which ensure well-formedness of the corresponding deduction when satisfied. We mechanise the whole framework, including a deep embedding of ILL, in the proof assistant Isabelle/HOL. Beyond the increased confidence in our proofs, this allows us to automatically generate executable code for our verified definitions. We demonstrate our approach by formalising part of the simulation game Factorio and modelling a manufacturing process in it. Our framework guarantees that this model is free of bottlenecks
Formalising Geometric Axioms for Minkowski Spacetime and Without-Loss-of-Generality Theorems
This contribution reports on the continued formalisation of an axiomatic
system for Minkowski spacetime (as used in the study of Special Relativity)
which is closer in spirit to Hilbert's axiomatic approach to Euclidean geometry
than to the vector space approach employed by Minkowski. We present a brief
overview of the axioms as well as of a formalisation of theorems relating to
linear order. Proofs and excerpts of Isabelle/Isar scripts are discussed, with
a focus on the use of symmetry and reasoning "without loss of generality".Comment: In Proceedings ADG 2021, arXiv:2112.1477
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