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

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

Alignment-based conformance checking over probabilistic events

Conformance checking techniques allow us to evaluate how well some exhibited behaviour, represented by a trace of monitored events, conforms to a specified process model. Modern monitoring and activity recognition technologies, such as those relying on sensors, the IoT, statistics and AI, can produce a wealth of relevant event data. However, this data is typically characterised by noise and uncertainty, in contrast to the assumption of a deterministic event log required by conformance checking algorithms. In this paper, we extend alignment-based conformance checking to function under a probabilistic event log. We introduce a weighted trace model and weighted alignment cost function, and a custom threshold parameter that controls the level of confidence on the event data vs. the process model. The resulting algorithm considers activities of lower but sufficiently high probability that better align with the process model. We explain the algorithm and its motivation both from formal and intuitive perspectives, and demonstrate its functionality in comparison with deterministic alignment using real-life datasets