Related papers: Learning logic programs by explaining their failur…

The programming language Prolog makes declarative programming possible, at least to a substantial extent. Programs may be written and reasoned about in terms of their declarative semantics. All the advantages of declarative programming are…

For over two decades Separation Logic has been arguably the most popular framework for reasoning about heap-manipulating programs, as well as reasoning about shared resources and permissions. Separation Logic is often extended to include…

This paper outlines a general formal framework for reasoning systems, intended to support future analysis of inference architectures across domains. We model reasoning systems as structured tuples comprising phenomena, explanation space,…

Large language models (LLMs) have revolutionized many areas (e.g. natural language processing, software engineering, etc.) by achieving state-of-the-art performance on extensive downstream tasks. Aiming to achieve robust and general…

Deep learning is very effective at jointly learning feature representations and classification models, especially when dealing with high dimensional input patterns. Probabilistic logic reasoning, on the other hand, is capable to take…

Probabilistic Logic Programming (PLP) languages, like ProbLog, naturally support reasoning under uncertainty, while maintaining a declarative and interpretable framework. Meanwhile, counterfactual reasoning (i.e., answering ``what if''…

Inductive logic programming (ILP) is a form of machine learning. The goal of ILP is to induce a hypothesis (a set of logical rules) that generalises training examples. As ILP turns 30, we provide a new introduction to the field. We…

Inductive Logic Programming (ILP) combines rule-based and statistical artificial intelligence methods, by learning a hypothesis comprising a set of rules given background knowledge and constraints for the search space. We focus on extending…

We introduce DeepProbLog, a neural probabilistic logic programming language that incorporates deep learning by means of neural predicates. We show how existing inference and learning techniques of the underlying probabilistic logic…

Making errors is part of the programming process -- even for the most seasoned professionals. Novices in particular are bound to make many errors while learning. It is well known that traditional (compiler/interpreter) programming error…

In the logic programming paradigm, a program is defined by a set of methods, each of which can be executed when specific conditions are met during the current state of an execution. The semantics of these programs can be elegantly…

Possibilistic logic programs (poss-programs) under stable models are a major variant of answer set programming (ASP). While its semantics (possibilistic stable models) and properties have been well investigated, the problem of inductive…

Machine learning methods are being increasingly applied in sensitive societal contexts, where decisions impact human lives. Hence it has become necessary to build capabilities for providing easily-interpretable explanations of models'…

In inductive learning of a broad concept, an algorithm should be able to distinguish concept examples from exceptions and noisy data. An approach through recursively finding patterns in exceptions turns out to correspond to the problem of…

Transformer large language models (LLMs) have sparked admiration for their exceptional performance on tasks that demand intricate multi-step reasoning. Yet, these models simultaneously show failures on surprisingly trivial problems. This…

Fermi Problems (FPs) are mathematical reasoning tasks that require human-like logic and numerical reasoning. Unlike other reasoning questions, FPs often involve real-world impracticalities or ambiguous concepts, making them challenging even…

In recent years, there has been an increasing interest in exploiting logically specified background knowledge in order to obtain neural models (i) with a better performance, (ii) able to learn from less data, and/or (iii) guaranteed to be…

Identifying and resolving logic errors can be one of the most frustrating challenges for novices programmers. Unlike syntax errors, for which a compiler or interpreter can issue a message, logic errors can be subtle. In certain conditions,…

The differentiable implementation of logic yields a seamless combination of symbolic reasoning and deep neural networks. Recent research, which has developed a differentiable framework to learn logic programs from examples, can even acquire…

Probabilistic logic programs are logic programs in which some of the facts are annotated with probabilities. This paper investigates how classical inference and learning tasks known from the graphical model community can be tackled for…