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We propose an automated deduction method which allows us to produce proofs close to the human intuition and practice. This method is based on tableaux, which generate more natural proofs than similar methods relying on clausal forms, and…
Deep learning methods capable of handling relational data have proliferated over the last years. In contrast to traditional relational learning methods that leverage first-order logic for representing such data, these deep learning methods…
We examine the interplay between projectivity (in the sense that was introduced by S.~Ghilardi) and uniform post-interpolant for the classical and intuitionistic propositional logic. More precisely, we explore whether a projective…
Assumption-based Argumentation (ABA) is advocated as a unifying formalism for various forms of non-monotonic reasoning, including logic programming. It allows capturing defeasible knowledge, subject to argumentative debate. While, in much…
The Iltis project provides an interactive, web-based system for teaching the foundations of formal methods. It is designed with the objective to allow for simple inclusion of new educational tasks; to pipeline such tasks into more complex…
We study syllogistic reasoning in LLMs from the logical and natural language perspectives. In process, we explore fundamental reasoning capabilities of the LLMs and the direction this research is moving forward. To aid in our studies, we…
Logical frameworks and meta-languages form a common substrate for representing, implementing and reasoning about a wide variety of deductive systems of interest in logic and computer science. Their design, implementation and their use in…
Abduction, first proposed in the setting of classical logics, has been studied with growing interest in the logic programming area during the last years. In this paper we study abduction with penalization in the logic programming framework.…
This book chapter establishes connections between the interactive proof tool Isabelle and classical tableau and resolution technology. Isabelle's classical reasoner is described and demonstrated by an extended case study: the Church-Rosser…
Interactive theorem provers based on dependent type theory have the flexibility to support both constructive and classical reasoning. Constructive reasoning is supported natively by dependent type theory and classical reasoning is typically…
This work introduces a framework for quantifying the information content of logical propositions through the use of implication hypergraphs. We posit that a proposition's informativeness is primarily determined by its relationships with…
We explore end-to-end trained differentiable models that integrate natural logic with neural networks, aiming to keep the backbone of natural language reasoning based on the natural logic formalism while introducing subsymbolic vector…
This paper presents Abduction and Argumentation as two principled forms for reasoning, and fleshes out the fundamental role that they can play within Machine Learning. It reviews the state-of-the-art work over the past few decades on the…
This article presents a formalism inspired by Dennett's notion of the intentional stance. Whereas Dennett's treatment of these concepts is informal, we aim to provide a more formal analogue. We introduce a framework based on stochastic…
Interactive theorem provers have developed dramatically over the past four decades, from primitive beginnings to today's powerful systems. Here, we focus on Isabelle/HOL and its distinctive strengths. They include automatic proof search,…
We consider the problem of how to verify the security of probabilistic oblivious algorithms formally and systematically. Unfortunately, prior program logics fail to support a number of complexities that feature in the semantics and…
Recently, a growing number of researchers have applied machine learning to assist users of interactive theorem provers. However, the expressive nature of underlying logics and esoteric structures of proof documents impede machine learning…
Logical frameworks and meta-languages form a common substrate for representing, implementing and reasoning about a wide variety of deductive systems of interest in logic and computer science. Their design, implementation and their use in…
We introduce a neuro-symbolic natural logic framework based on reinforcement learning with introspective revision. The model samples and rewards specific reasoning paths through policy gradient, in which the introspective revision algorithm…
We introduce a novel learning and planning framework that replaces traditional reward-based optimisation with constructive logical inference. In our model, actions, transitions, and goals are represented as logical propositions, and…