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We present a method for verifying partial correctness properties of imperative programs that manipulate integers and arrays by using techniques based on the transformation of constraint logic programs (CLP). We use CLP as a metalanguage for…
Higher-order constructs extend the expressiveness of first-order (Constraint) Logic Programming ((C)LP) both syntactically and semantically. At the same time assertions have been in use for some time in (C)LP systems helping programmers…
A logic is defined that allows to express information about statistical probabilities and about degrees of belief in specific propositions. By interpreting the two types of probabilities in one common probability space, the semantics given…
In this paper we consider Epistemic Logic Programs, which extend Answer Set Programming (ASP) with "epistemic operators" and "epistemic negation", and a recent approach to the semantics of such programs in terms of World Views. We propose…
Evaluating an explanation's faithfulness is desired for many reasons such as trust, interpretability and diagnosing the sources of model's errors. In this work, which focuses on the NLI task, we introduce the methodology of…
This paper defines an argumentation semantics for extended logic programming and shows its equivalence to the well-founded semantics with explicit negation. We set up a general framework in which we extensively compare this semantics to…
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…
We predict credit applications with off-the-shelf, interchangeable black-box classifiers and we explain single predictions with counterfactual explanations. Counterfactual explanations expose the minimal changes required on the input data…
Though the truths of logic and pure mathematics are objective and independent of any contingent facts or laws of nature, our knowledge of these truths depends entirely on our knowledge of the laws of physics. Recent progress in the quantum…
Explanation mechanisms from the field of Counterfactual Thinking are a widely-used paradigm for Explainable Artificial Intelligence (XAI), as they follow a natural way of reasoning that humans are familiar with. However, all common…
Joint Vision-Language Embedding models such as CLIP typically fail at understanding negation in text queries, for example, failing to distinguish "no" in the query: "a plain blue shirt with no logos". Prior work has largely addressed this…
The Boolean logic of subsets, usually presented as `propositional logic,' is considered as being "classical" while intuitionistic logic and the many sublogics and off-shoots are "non-classical." But there is another mathematical logic, the…
We develop a model of abduction in abstract argumentation, where changes to an argumentation framework act as hypotheses to explain the support of an observation. We present dialogical proof theories for the main decision problems (i.e.,…
Explaining why an answer is in the result of a query or why it is missing from the result is important for many applications including auditing, debugging data and queries, and answering hypothetical questions about data. Both types of…
Logic programming has long being advocated for legal reasoning, and several approaches have been put forward relying upon explicit representation of the law in logic programming terms. In this position paper we focus on the PROLEG…
A belief base revision is developed. The belief base is represented using Unified Answer Set Programs which is capable of representing imprecise and uncertain information and perform nonomonotonic reasoning with them. The base revision…
The distinction between strong negation and default negation has been useful in answer set programming. We present an alternative account of strong negation, which lets us view strong negation in terms of the functional stable model…
This paper presents an example of formal reasoning about the semantics of a Prolog program of practical importance (the SAT solver of Howe and King). The program is treated as a definite clause logic program with added control. The logic…
Machines are being increasingly used in decision-making processes, resulting in the realization that decisions need explanations. Unfortunately, an increasing number of these deployed models are of a 'black-box' nature where the reasoning…
The ability to generalise from a small number of examples is a fundamental challenge in machine learning. To tackle this challenge, we introduce an inductive logic programming (ILP) approach that combines negation and predicate invention.…