# Reasoning in Non-Probabilistic Uncertainty: Logic Programming and Neural-Symbolic Computing as Examples

## TL;DR

This paper explores non-probabilistic approaches to reasoning under uncertainty, demonstrating that logic-based methods like logic programming and neural-symbolic systems can effectively handle certain types of uncertainty that probabilistic methods cannot address.

## Contribution

It provides theoretical and practical evidence that logic-based methods are viable alternatives for reasoning with non-probabilistic uncertainty, illustrated through two paradigmatic examples.

## Key findings

- Logic programming with Kleene semantics supports discourse reasoning.
- Neural-symbolic Input/Output logic handles uncertainty in normative contexts.
- Non-probabilistic methods can address types of uncertainty beyond probabilistic scope.

## Abstract

This article aims to achieve two goals: to show that probability is not the only way of dealing with uncertainty (and even more, that there are kinds of uncertainty which are for principled reasons not addressable with probabilistic means); and to provide evidence that logic-based methods can well support reasoning with uncertainty. For the latter claim, two paradigmatic examples are presented: Logic Programming with Kleene semantics for modelling reasoning from information in a discourse, to an interpretation of the state of affairs of the intended model, and a neural-symbolic implementation of Input/Output logic for dealing with uncertainty in dynamic normative contexts.