Related papers: Connecting Proof Theory and Knowledge Representati…
Cut-elimination is the bedrock of proof theory. It is the algorithm that eliminates cuts from a sequent calculus proof that leads to cut-free calculi and applications. Cut-elimination applies to many logics irrespective of their semantics.…
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…
We develop a second-order extension of intuitionistic modal logic, allowing quantification over propositions, both syntactically and semantically. A key feature of second-order logic is its capacity to define positive connectives from the…
Sequence classification is the supervised learning task of building models that predict class labels of unseen sequences of symbols. Although accuracy is paramount, in certain scenarios interpretability is a must. Unfortunately, such…
This paper presents and discusses several methods for reasoning from inconsistent knowledge bases. A so-called argumentative-consequence relation taking into account the existence of consistent arguments in favor of a conclusion and the…
Chain-of-Thought (CoT) prompting plays an indispensable role in endowing large language models (LLMs) with complex reasoning capabilities. However, CoT currently faces two fundamental challenges: (1) Sufficiency, which ensures that the…
In many model-based diagnosis applications it is impossible to provide such a set of observations and/or measurements that allow to identify the real cause of a fault. Therefore, diagnosis systems often return many possible candidates,…
Rule-based reasoning, a fundamental type of legal reasoning, enables us to draw conclusions by accurately applying a rule to a set of facts. We explore causal language models as rule-based reasoners, specifically with respect to…
Finding counterevidence to statements is key to many tasks, including counterargument generation. We build a system that, given a statement, retrieves counterevidence from diverse sources on the Web. At the core of this system is a natural…
Understanding the laws that govern a phenomenon is the core of scientific progress. This is especially true when the goal is to model the interplay between different aspects in a causal fashion. Indeed, causal inference itself is…
In this paper, we establish the foundations of a novel logical framework for the {\pi}-calculus, based on the deduction-as-computation paradigm. Following the standard proof-theoretic interpretation of logic programming, we represent…
Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In…
This thesis embarks on a comprehensive exploration of formal computational models that underlie typed programming languages. We focus on programming calculi, both functional (sequential) and concurrent, as they provide a compelling rigorous…
We study reasoning with existential rules to perform query answering over streams of data. On static databases, this problem has been widely studied, but its extension to rapidly changing data has not yet been considered. To bridge this…
Sequential hypothesis testing asks for decision rules that update as data arrive. A natural goal is \emph{eventual correctness}: the rule may change its mind early on, but it should make only finitely many wrong decisions almost surely.…
Scientists have long aimed to discover meaningful formulae which accurately describe experimental data. A common approach is to manually create mathematical models of natural phenomena using domain knowledge, and then fit these models to…
Large language models make remarkable progress in reasoning capabilities. Existing works focus mainly on deductive reasoning tasks (e.g., code and math), while another type of reasoning mode that better aligns with human learning, inductive…
Commonsense reasoning has long been considered as one of the holy grails of artificial intelligence. Most of the recent progress in the field has been achieved by novel machine learning algorithms for natural language processing. However,…
It is commonly agreed that the success of future proof assistants will rely on their ability to incorporate computations within deduction in order to mimic the mathematician when replacing the proof of a proposition P by the proof of an…
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.,…