Related papers: Probabilistic Inference Modulo Theories
Causal inference has shown potential in enhancing the predictive accuracy, fairness, robustness, and explainability of Natural Language Processing (NLP) models by capturing causal relationships among variables. The emergence of generative…
Recent advances in neural symbolic learning, such as DeepProbLog, extend probabilistic logic programs with neural predicates. Like graphical models, these probabilistic logic programs define a probability distribution over possible worlds,…
Large language models (LLMs) have achieved impressive human-like performance across various reasoning tasks. However, their mastery of underlying inferential rules still falls short of human capabilities. To investigate this, we propose a…
Recent work on loglinear models in probabilistic constraint logic programming is applied to first-order probabilistic reasoning. Probabilities are defined directly on the proofs of atomic formulae, and by marginalisation on the atomic…
Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…
Scaling inference compute in large language models (LLMs) through repeated sampling consistently increases the coverage (fraction of problems solved) as the number of samples increases. We conjecture that this observed improvement is…
Temporal logic inference is the process of extracting formal descriptions of system behaviors from data in the form of temporal logic formulas. The existing temporal logic inference methods mostly neglect uncertainties in the data, which…
Standard approaches to probabilistic reasoning require that one possesses an explicit model of the distribution in question. But, the empirical learning of models of probability distributions from partial observations is a problem for which…
Probabilistic logic programs are logic programs in which some of the facts are annotated with probabilities. Several classical probabilistic inference tasks (such as MAP and computing marginals) have not yet received a lot of attention for…
This paper discusses the semantics and proof theory of Nilsson's probabilistic logic, outlining both the benefits of its well-defined model theory and the drawbacks of its proof theory. Within Nilsson's semantic framework, we derive a set…
The combination of higher-order theories and fuzzy logic can be useful in decision-making tasks that involve reasoning across abstract functions and predicates, where exact matches are often rare or unnecessary. Developing efficient…
Probabilistic programs provide an expressive representation language for generative models. Given a probabilistic program, we are interested in the task of posterior inference: estimating a latent variable given a set of observed variables.…
In deduction modulo, a theory is not represented by a set of axioms but by a congruence on propositions modulo which the inference rules of standard deductive systems---such as for instance natural deduction---are applied. Therefore, the…
Spatial generalized linear mixed models (SGLMMs) are popular and flexible models for non-Gaussian spatial data. They are useful for spatial interpolations as well as for fitting regression models that account for spatial dependence, and are…
Complex continuous or mixed joint distributions (e.g., P(Y | z_1, z_2, ..., z_N)) generally lack closed-form solutions, often necessitating approximations such as MCMC. This paper proposes Indeterminate Probability Theory (IPT), which makes…
Large Language Models (LLMs) have demonstrated remarkable capabilities across various applications, fundamentally reshaping the landscape of natural language processing (NLP) research. However, recent evaluation frameworks often rely on the…
We present a propositional logic to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and complete axiomatization…
Large language models (LLMs) have achieved significant performance gains via scaling up model sizes and/or data. However, recent evidence suggests diminishing returns from such approaches, motivating scaling the computation spent at…
We enable aProbLog---a probabilistic logical programming approach---to reason in presence of uncertain probabilities represented as Beta-distributed random variables. We achieve the same performance of state-of-the-art algorithms for highly…
Propositional representation services such as truth maintenance systems offer powerful support for incremental, interleaved, problem-model construction and evaluation. Probabilistic inference systems, in contrast, have lagged behind in…