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Adversarial examples -- inputs with imperceptible perturbations that fool neural networks -- remain one of deep learning's most perplexing phenomena despite nearly a decade of research. While numerous defenses and explanations have been…
In this paper we show how the defense relation among abstract arguments can be used to encode the reasons for accepting arguments. After introducing a novel notion of defenses and defense graphs, we propose a defense semantics together with…
Explainable Artificial Intelligence (XAI) systems, including intelligent agents, must be able to explain their internal decisions, behaviours and reasoning that produce their choices to the humans (or other systems) with which they…
Because contemporary large software systems are pervasively inconsistent, it is not safe to reason about them using classical logic. The goal of Direct Logic is to be a minimal fix to classical mathematical logic that meets the requirements…
Modal logics are widely used in multi-agent systems to reason about actions, abilities, norms, or epistemic states. Combined with description logic languages, they are also a powerful tool to formalise modal aspects of ontology-based…
Differentiable logics are a family of quantitative logics originated in the machine learning literature. Because of their origin, differentiable logics often come equipped with analytic properties that guarantee that they are…
Over the past few decades, non-monotonic reasoning has developed to be one of the most important topics in computational logic and artificial intelligence. Different ways to introduce non-monotonic aspects to classical logic have been…
Logical relations constitute a key method for reasoning about contextual equivalence of programs in higher-order languages. They are usually developed on a per-case basis, with a new theory required for each variation of the language or of…
The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues…
Type-free systems of logic are designed to consistently handle significant instances of self-reference. Some consistent type-free systems also have the feature of allowing the sort of general abstraction or comprehension principle that…
Multi-agent interactions between Large Language Model (LLM) agents have shown major improvements on diverse reasoning tasks. However, these involve long generations from multiple models across several rounds, making them expensive.…
Reasoning, a crucial ability for complex problem-solving, plays a pivotal role in various real-world settings such as negotiation, medical diagnosis, and criminal investigation. It serves as a fundamental methodology in the field 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…
Rational inference relations were introduced by Lehmann and Magidor as the ideal systems for drawing conclusions from a conditional base. However, there has been no simple characterization of these relations, other than its original…
An important open question in AI is what simple and natural principle enables a machine to reason logically for meaningful abstraction with grounded symbols. This paper explores a conceptually new approach to combining probabilistic…
Logical relations are one of the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be…
Classical decision theory models behaviour in terms of utility maximisation where utilities represent rational preference relations over outcomes. However, empirical evidence and theoretical considerations suggest that we need to go beyond…
These lecture notes give a statistical perspective on the foundations of reinforcement learning and interactive decision making. We present a unifying framework for addressing the exploration-exploitation dilemma using frequentist and…
A fundamental question asked in modal logic is whether a given theory is consistent. But consistent with what? A typical way to address this question identifies a choice of background knowledge axioms (say, S4, D, etc.) and then shows the…
This study intends to systematically disentangle pure logic reasoning and text understanding by investigating the contrast across abstract and contextualized logical problems from a comprehensive set of domains. We explore whether LLMs…