This paper presents a unified perspective on a range of probabilistic updating methods ranging from conditionalization to imaging techniques. We focus in particular on an imaging method that we call non-Bayesian, because it changes a prior probability in a belief function, in the sense of Dempster-Shafer theory of evidence. We show the effect of combining that non-Bayesian imaging with the so called pignistic transformation, a method that allows to recover a probability from a belief function. Finally, we leverage the results obtained to present a kind of extension of Lewis’s celebrated triviality result to relate Bayesian and non-Bayesian imaging methods. The main methodological path we will follow is algebraic and, thanks to it, we will employ recently introduced modal algebraic models for conditionals and counterfactuals to shed further light on the Bayesian and the non-Bayesian approaches to imaging.
Large Language Models have transformed automated code generation across general programming domains. In the specialized field of operations research, however, translating natural language problem descriptions into executable optimization solver code remains difficult due to strict syntactic requirements. Existing methods relying on static retrieval or one-shot generation frequently fail to align human intent with rigid solver APIs, resulting in hallucinated constraints and execution errors. To address this, we introduce CHORUS++, an agentic framework that replaces fragile one-shot generation with a loop of hierarchical retrieval, multi-layer validation, and iterative self-correction. Our results show that this approach allows open-source models, such as Llama-3.3 (70B), to achieve an accuracy of 78.89 × despite extensive documentation changes. By closing the feedback loop between generation and execution, CHORUS++ provides a scalable, privacy-preserving method for utilizing advanced optimization technologies without reliance on costly proprietary models.
Lifted inference exploits indistinguishabilities in probabilistic graphical models by using a representative for indistinguishable objects, thereby speeding up query answering while maintaining exact answers. In this article, we show how lifting can be applied to efficiently compute causal effects in relational domains. More specifically, we introduce parametric causal factor graphs (PCFGs) to incorporate causal knowledge in lifted models and give a formal semantics of interventions therein. We further present the Lifted Causal Inference (LCI) algorithm to compute causal effects on a lifted level, thereby drastically speeding up causal inference compared to propositional inference, e.g., in causal Bayesian networks. In addition, we present partially directed parametric causal factor graphs (PD-PCFGs) as a generalisation of PCFGs to handle partial causal knowledge and extend LCI to perform lifted causal inference in a PD-PCFG, thereby extending the applicability of lifted causal inference to a broader range of models requiring less prior knowledge about causal relationships.
Least general generalization is the problem of finding the most specific term that can generate all given terms via substitutions. It is also known as anti-unification and is considered a dual of the most general unification. It is known that both the least general generalization problem and the unification problem can be solved in polynomial time; however the latter becomes NP-hard when commutative function symbols are allowed. In this paper, we study the complexity of the least general generalization problem with commutative functions, formulated as a minimization problem. In particular, we show that this problem is NP-hard even if both input and output terms are restricted so that each variable occurs only once. We also show that this restricted variant can be solved in polynomial time if both the maximum arity and the number of input terms are bounded by constants. For the general terms, we present exponential-time algorithms for finding the most specific term in some restricted cases and in the general case.
