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Tim French

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Published work

6 published item(s)

preprint2026arXiv

Causal Reinforcement Learning for Complex Card Games: A Magic The Gathering Benchmark

Causal reinforcement learning (RL) lacks benchmarks for complex systems that combine sequential decision making, hidden information, large masked action spaces, and explicit causal structure. We introduce MTG-Causal-RL, a Gymnasium benchmark built on Magic: The Gathering with a 3,077-dimensional partial observation, a 478-action masked discrete action space, five competitive Standard archetypes, three reward schemes, and a hand-specified Structural Causal Model (SCM) over strategic variables. Every episode exposes causal variables, SCM-predicted intervention effects, and per-factor credit traces, making causal credit assignment, leave-one-out cross-archetype transfer, and policy auditability first-class metrics. We adapt a panel of reference baselines: random, heuristic, masked PPO, a causal-world-model PPO variant, and an architecture-matched scalar control. We propose Causal Graph-Factored Advantage PPO (CGFA-PPO) as a reference causal agent that uses SCM parents of win probability as factor-aligned critic targets with an intervention-calibration loss. All comparisons use paired seeds, paired-bootstrap confidence intervals, and Holm-Bonferroni correction within pre-registered families. Masked PPO and CGFA-PPO reach competitive in-distribution win rates and exceed the random baseline; per-factor calibration trajectories and leave-one-out transfer gaps expose diagnostic structure that scalar win rate alone cannot. We release the benchmark, reference-baseline results, and full evaluation protocol openly. By coupling a strategically rich, partially observed domain with an explicit causal interface and statistical protocol, MTG-Causal-RL gives causal-RL, world-model, and LLM-agent research a shared testbed for questions current benchmarks cannot pose together: causal credit assignment under masked action spaces, structural transfer across archetypes, and SCM-grounded policy auditability.

preprint2026arXiv

PODiff: Latent Diffusion in Proper Orthogonal Decomposition Space for Scientific Super-Resolution

Probabilistic super-resolution of high-dimensional spatial fields using diffusion models is often computationally prohibitive due to the cost of operating directly in pixel space. We propose PODiff, a structured conditional generative framework that performs diffusion in a fixed, variance-ordered Proper Orthogonal Decomposition (POD) coefficient space, exploiting the orthogonality of POD modes to impose an interpretable, variance-ordered latent geometry. This design enables efficient ensemble generation, preserves dominant spatial structure, and yields spatially interpretable, well-calibrated uncertainty at substantially lower computational cost. We evaluate PODiff on sea surface temperature downscaling over the West Australian coast and on a controlled advection-diffusion benchmark. PODiff achieves reconstruction accuracy comparable to pixel-space diffusion while requiring significantly less memory and producing more reliable uncertainty estimates than deterministic and Monte Carlo Dropout baselines.

preprint2016arXiv

Finding Minimum and Maximum Termination Time of Timed Automata Models with Cyclic Behaviour

The paper presents a novel algorithm for computing best and worst case execution times (BCET/WCET) of timed automata models with cyclic behaviour. The algorithms can work on any arbitrary diagonal-free TA and can handle more cases than previously existing algorithms for BCET/WCET computations, as it can handle cycles in TA and decide whether they lead to an infinite WCET. We show soundness of the proposed algorithm and study its complexity. To our knowledge, this is the first model checking algorithm that addresses comprehensively the BCET/WCET problem of systems with cyclic behaviour. Behrmann et al. provide an algorithm for computing the minimum cost/time of reaching a goal state in priced timed automata (PTA). The algorithm has been implemented in the well-known model checking tool UPPAAL to compute the minimum time for termination of an automaton. However, we show that in certain circumstances, when infinite cycles exist, the algorithm implemented in UPPAAL may not terminate, and we provide examples which UPPAAL fails to verify.

preprint2014arXiv

A composable language for action models

Action models are semantic structures similar to Kripke models that represent a change in knowledge in an epistemic setting. Whereas the language of action model logic embeds the semantic structure of an action model directly within the language, this paper introduces a language that represents action models using syntactic operators inspired by relational actions. This language admits an intuitive description of the action models it represents, and we show in several settings that it is sufficient to represent any action model up to a given modal depth and to represent the results of action model synthesis, and give a sound and complete axiomatisation in some of these settings.

preprint2013arXiv

Knowledge, Awareness, and Bisimulation

We compare different epistemic notions in the presence of awareness of propositional variables: the logics of implicit knowledge (in which explicit knowledge is definable), explicit knowledge, and speculative knowledge. Different notions of bisimulation are suitable for these logics. We provide correspondence between bisimulation and modal equivalence on image-finite models for these logics. The logic of speculative knowledge is equally expressive as the logic of explicit knowledge, and the logic of implicit knowledge is more expressive than both. We also provide axiomatizations for the three logics -- only the one for speculative knowledge is novel. Then we move to the study of dynamics by recalling action models incorporating awareness. We show that any conceivable change of knowledge or awareness can be modelled in this setting, we give a complete axiomatization for the dynamic logic of implicit knowledge. The dynamic versions of all three logics are, surprising, equally expressive.

preprint2013arXiv

Specifying Robustness

This paper proposes a new logic RoCTL* to model robustness in concurrent systems. RoCTL* extends CTL* with the addition of Obligatory and Robustly operators, which quantify over failure-free paths and paths with one more failure respectively. We present a number of examples of problems to which RoCTL* can be applied. The core result of this paper is to show that RoCTL* is expressively equivalent to CTL* but is non-elementarily more succinct. We present a translation from RoCTL* into CTL* that preserves truth but may result in non-elementary growth in the length of the translated formula as each nested Robustly operator may result in an extra exponential blowup. However, we show that this translation is optimal in the sense that any equivalence preserving translation will require an extra exponential growth per nested Robustly. We also compare RoCTL* to Quantified CTL* (QCTL*) and hybrid logics.