Related papers: Teaching Intuitionistic and Classical Propositiona…

I aim to promote an alternative agenda for teaching modal logic chiefly inspired by the relationships between modal logic and philosophy. The guiding idea for this proposal is a reappraisal of the interest of modal logic in philosophy,…

Machine learning models such as Transformers or LSTMs struggle with tasks that are compositional in nature such as those involving reasoning/inference. Although many datasets exist to evaluate compositional generalization, when it comes to…

While neural models show remarkable accuracy on individual predictions, their internal beliefs can be inconsistent across examples. In this paper, we formalize such inconsistency as a generalization of prediction error. We propose a…

We introduce a theorem proving approach to the specification and generation of temporal logical constraints for training neural networks. We formalise a deep embedding of linear temporal logic over finite traces (LTL$_f$) and an associated…

We consider the question of extending propositional logic to a logic of plausible reasoning, and posit four requirements that any such extension should satisfy. Each is a requirement that some property of classical propositional logic be…

This paper describes how automated deduction methods for natural language processing can be applied more efficiently by encoding context in a more elaborate way. Our work is based on formal approaches to context, and we provide a tableau…

Abductive reasoning, reasoning for inferring explanations for observations, is often mentioned in scientific, design-related and artistic contexts, but its understanding varies across these domains. This paper reviews how abductive…

Machine learning has shown much promise in helping improve the quality of medical, legal, and financial decision-making. In these applications, machine learning models must satisfy two important criteria: (i) they must be causal, since the…

Large language models (LLMs) have been shown to be capable of impressive few-shot generalisation to new tasks. However, they still tend to perform poorly on multi-step logical reasoning problems. Here we carry out a comprehensive evaluation…

Logic $L$ was introduced by Lewitzka [7] as a modal system that combines intuitionistic and classical logic: $L$ is a conservative extension of CPC and it contains a copy of IPC via the embedding $\varphi\mapsto\square\varphi$. In this…

This work presents a novel systematic methodology to analyse the capabilities and limitations of Large Language Models (LLMs) with feedback from a formal inference engine, on logic theory induction. The analysis is complexity-graded w.r.t.…

In this paper, we consider the complexity of propositional proofs of classical and intuitionistic tautologies. In fact, we describe a nondeterministic polynomial-time decision procedure for intuitionistic implicational tautologies. For this…

Propositional term modal logic is interpreted over Kripke structures with unboundedly many accessibility relations and hence the syntax admits variables indexing modalities and quantification over them. This logic is undecidable, and we…

Intuitionistic logic programming provides the notion of embedded implication in rule bodies, which can be used to reason about a current database modified by the antecedent. This can be applied to a system that translates SQL to Datalog to…

Existing debiasing techniques are typically training-based or require access to the model's internals and output distributions, so they are inaccessible to end-users looking to adapt LLM outputs for their particular needs. In this study, we…

The ability to derive underlying principles from a handful of observations and then generalize to novel situations -- known as inductive reasoning -- is central to human intelligence. Prior work suggests that language models (LMs) often…

Modern large language models (LLMs) employ diverse logical inference mechanisms for reasoning, making the strategic optimization of these approaches critical for advancing their capabilities. This paper systematically investigate the…

Defeasible logic is a rule-based nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts…

In this paper we will see deductive systems for classical propositional and predicate logic in the calculus of structures. Like sequent systems, they have a cut rule which is admissible. In addition, they enjoy a top-down symmetry and some…

In the literature, essence is formalized in two different ways, either de dicto, or de re. Following \cite{Marcos:2005}, we adopt its de dicto formalization: a formula is essential, if once it is true, it is necessarily true; otherwise, it…