Related papers: Inference of Abstraction for Grounded Predicate Lo…

An increasing number of scientific experiments support the view of perception as Bayesian inference, which is rooted in Helmholtz's view of perception as unconscious inference. Recent study of logic presents a view of logical reasoning as…

This paper synthesizes a series of formal proofs to construct a unified theory on the logical limits of the Symbol Grounding Problem. We distinguish between internal meaning (sense), which formal systems can possess via axioms, and external…

This paper introduces a novel type theory and logic for probabilistic reasoning. Its logic is quantitative, with fuzzy predicates. It includes normalisation and conditioning of states. This conditioning uses a key aspect that distinguishes…

Analyzing a distributed computation is a hard problem in general due to the combinatorial explosion in the size of the state-space with the number of processes in the system. By abstracting the computation, unnecessary explorations can be…

This paper provides a definitive, unifying framework for the Symbol Grounding Problem (SGP) by reformulating it within Algorithmic Information Theory (AIT). We demonstrate that the grounding of meaning is a process fundamentally constrained…

The extent to which neural networks are able to acquire and represent symbolic rules remains a key topic of research and debate. Much current work focuses on the impressive capabilities of large language models, as well as their often…

The computational burden of probabilistic inference remains a hurdle for applying probabilistic programming languages to practical problems of interest. In this work, we provide a semantic and algorithmic foundation for efficient exact…

This paper introduces Logical Credal Networks, an expressive probabilistic logic that generalizes many prior models that combine logic and probability. Given imprecise information represented by probability bounds and conditional…

Precedential constraint is one foundation of case-based reasoning in AI and Law. It generally assumes that the underlying set of precedents must be consistent. To relax this assumption, a generalized notion of the reason model has been…

Predicate abstraction provides a powerful tool for verifying properties of infinite-state systems using a combination of a decision procedure for a subset of first-order logic and symbolic methods originally developed for finite-state model…

Probabilistic logic programming is a major part of statistical relational artificial intelligence, where approaches from logic and probability are brought together to reason about and learn from relational domains in a setting of…

While probability theory is normally applied to external environments, there has been some recent interest in probabilistic modeling of the outputs of computations that are too expensive to run. Since mathematical logic is a powerful tool…

Abstract reasoning, i.e., inferring complicated patterns from given observations, is a central building block of artificial general intelligence. While humans find the answer by either eliminating wrong candidates or first constructing the…

At its core, abstraction is the process of generalizing from specific instances to broader concepts or models, with the primary objective of reducing complexity while preserving properties essential to the intended purpose. It is…

We develop the theory and practice of an approach to modelling and probabilistic inference in causal networks that is suitable when application-specific or analysis-specific constraints should inform such inference or when little or no data…

Abstraction is key to human and artificial intelligence as it allows one to see common structure in otherwise distinct objects or situations and as such it is a key element for generality in AI. Anti-unification (or generalization) is…

Probability theory as extended logic is completed such that essentially any probability may be determined. This is done by considering propositional logic (as opposed to predicate logic) as syntactically suffcient and imposing a symmetry…

The rapid advancement of embodied intelligence and world models has intensified efforts to integrate physical laws into AI systems, yet physical perception and symbolic physics reasoning have developed along separate trajectories without a…

We describe a representation and a set of inference methods that combine logic programming techniques with probabilistic network representations for uncertainty (influence diagrams). The techniques emphasize the dynamic construction and…

Efficiently navigating complex environments requires agents to internalize the underlying logic of their world, yet standard world modelling methods often struggle with sample inefficiency, lack of transparency, and poor scalability. We…