Related papers: Knowledge of Uncertain Worlds: Programming with Lo…

Classical higher-order logic, when utilized as a meta-logic in which various other (classical and non-classical) logics can be shallowly embedded, is well suited for realising a universal logic reasoning approach. Universal logic reasoning…

Large language models have shown unprecedented abilities in generating linguistically coherent and syntactically correct natural language output. However, they often return incorrect and inconsistent answers to input questions. Due to the…

A logic program is an executable specification. For example, merge sort in pure Prolog is a logical formula, yet shows creditable performance on long linked lists. But such executable specifications are a compromise: the logic is distorted…

Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the…

There are many different semantics for general logic programs (i.e. programs that use negation in the bodies of clauses). Most of these semantics are Turing complete (in a sense that can be made precise), implying that they are undecidable.…

Knowledge refactoring compresses a logic program by introducing new rules. Current approaches struggle to scale to large programs. To overcome this limitation, we introduce a constrained optimisation refactoring approach. Our first key idea…

The inclusion of universal quantification and a form of implication in goals in logic programming is considered. These additions provide a logical basis for scoping but they also raise new implementation problems. When universal and…

We define a new decidable logic for expressing and checking invariants of programs that manipulate dynamically-allocated objects via pointers and destructive pointer updates. The main feature of this logic is the ability to limit the…

In everyday life it happens that a person has to reason about what other people think and how they behave, in order to achieve his goals. In other words, an individual may be required to adapt his behaviour by reasoning about the others'…

Many real world domains require the representation of a measure of uncertainty. The most common such representation is probability, and the combination of probability with logic programs has given rise to the field of Probabilistic Logic…

Defeasible reasoning is a simple but efficient approach to nonmonotonic reasoning that has recently attracted considerable interest and that has found various applications. Defeasible logic and its variants are an important family of…

In this paper, we introduce a set of tools for providing user-friendly explanations in an explanation-based constraint programming system. The idea is to represent the constraints of a problem as an hierarchy (a tree). Users are then…

Probabilistic Logic Programming is an effective formalism for encoding problems characterized by uncertainty. Some of these problems may require the optimization of probability values subject to constraints among probability distributions…

Uncertain information is being taken into account in an increasing number of application fields. In the meantime, abduction has been proved a powerful tool for handling hypothetical reasoning and incomplete knowledge. Probabilistic logical…

Matching Logic is a framework for specifying programming language semantics and reasoning about programs. Its formulas are called patterns and are built with variables, symbols, connectives and quantifiers. A pattern is a combination of…

The logic of definitions is a family of logics for encoding and reasoning about judgments, which are atomic predicates specified by inference rules. A definition associates an atomic predicate with a logical formula, which may itself depend…

Testing algorithms across a wide range of problem instances is crucial to ensure the validity of any claim about one algorithm's superiority over another. However, when it comes to inference algorithms for probabilistic logic programs,…

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…

The logic programming paradigm provides the basis for a new intensional view of higher-order notions. This view is realized primarily by employing the terms of a typed lambda calculus as representational devices and by using a richer form…

In the practical deployment of machine learning (ML) models, missing data represents a recurring challenge. Missing data is often addressed when training ML models. But missing data also needs to be addressed when deciding predictions and…