TLDR: A new framework called Capacity Logic Programs (CaLPs) extends Probabilistic Logic Programs (PLPs) to better handle epistemic uncertainty, which arises from incomplete knowledge. By integrating belief functions, CaLPs can represent uncertainty using interval probabilities, offering a more flexible and robust way to reason in AI applications like computer vision and autonomous systems. The paper details the theoretical foundations and outlines how existing PLP systems can be adapted for CaLPs.
In the realm of Artificial Intelligence, particularly in areas like computer vision and autonomous systems, dealing with uncertainty is a critical challenge. Traditional Probabilistic Logic Programming (PLP) has been a leading approach for reasoning under uncertainty, with well-known implementations like ProbLog and cplint/PITA. However, these systems typically rely on ‘point-probabilities,’ which assume a precise degree of knowledge about a distribution. This can be problematic when that knowledge isn’t fully available, leading to what is known as ‘epistemic uncertainty.’
Epistemic uncertainty arises from a lack of complete information or evidence. For instance, imagine trying to determine the probability of picking a blue ball from an urn when you know 30% are red, 10% are blue, and 60% are either blue or yellow. While the red balls are straightforward, the blue and yellow balls present a challenge. You can say at least 10% of balls are blue, and at most 70% (10% blue + 60% blue/yellow). This range, rather than a single point, is where belief functions come into play.
Belief functions offer a more generalized approach to probability, allowing for the expression of epistemic uncertainty through ‘interval probabilities.’ They are non-additive, meaning the belief assigned to the union of disjoint events isn’t necessarily the sum of their individual beliefs, which is a key difference from traditional probabilities. This framework, rooted in Dempster-Shafer theory, separates uncertainty inherent in an event (aleatory uncertainty) from uncertainty due to limited evidence (epistemic uncertainty).
Consider a more complex scenario, such as an unmanned aerial vehicle (UAV) using a visual model to classify objects on a roadway. While the visual model provides confidence scores, these scores might not always translate directly into true probabilities, especially when dealing with hierarchical classifications (e.g., an object being a ‘Passenger Vehicle’ which could then be a ‘Chevy’ or ‘Fiat’). Belief functions can assign uncertainty mass to sets of possibilities (like {blue, yellow} balls) rather than just single outcomes, making them ideal for such situations where information is incomplete or ambiguous.
This is where the new framework, Capacity Logic Programs (CaLPs), comes into play. CaLPs extend the existing Distribution Semantics for Probabilistic Logic Programs to seamlessly integrate belief functions. The paper, titled “Integrating Belief Domains into Probabilistic Logic Programs”, demonstrates that CaLPs form a ‘normalized capacity,’ which is an analog to a probability measure but designed for belief functions. It also shows how the concept of ‘composite choices’ (combinations of probabilistic and belief facts) in CaLPs aligns with ‘belief worlds,’ making it possible to adapt existing PLP inference systems for CaLPs.
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- Advancing Constraint Logic Programming: A Unified Approach to Negation with Semirings
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The theoretical foundations laid out in the paper suggest that practical implementations of CaLPs are feasible. By extending systems like ProbLog and cplint/PITA, researchers can develop tools that can reason with both traditional probabilities and interval-based beliefs. This allows for more robust and nuanced decision-making in AI applications, such as the UAV example where it needs to combine visual classifications with RFID signals and location data to identify stolen vehicles. This advancement promises to enhance AI’s ability to handle the complexities of real-world uncertainty, moving beyond the limitations of point-probabilities to embrace a more comprehensive understanding of knowledge and evidence.
