Related papers: Logic for approximate entailment in ordered univer…

Although conventional logical systems based on logical calculi have been successfully used in mathematics and beyond, they have definite limitations that restrict their application in many cases. For instance, the principal condition for…

Large language models (LLMs) struggle in knowledge-intensive tasks, as retrievers often overfit to surface similarity and fail on queries involving complex logical relations. The capacity for logical analysis is inherent in model…

A sound and complete embedding of conditional logics into classical higher-order logic is presented. This embedding enables the application of off-the-shelf higher-order automated theorem provers and model finders for reasoning within and…

While Large Language Models (LLMs) have found success in real-world applications, their underlying explanatory process is still poorly understood. This paper proposes IBE-Eval, a framework inspired by philosophical accounts on Inference to…

Reconciling the tension between inductive learning and deductive reasoning in first-order relational domains is a longstanding challenge in AI. We study the problem of answering queries in a first-order relational probabilistic logic…

A policy describes the conditions under which an action is permitted or forbidden. We show that a fragment of (multi-sorted) first-order logic can be used to represent and reason about policies. Because we use first-order logic, policies…

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 the context of the Semantic Web, several approaches to the combination of ontologies, given in terms of theories of classical first-order logic and rule bases, have been proposed. They either cast rules into classical logic or limit the…

We study logic for reasoning with if-then formulas describing dependencies between attributes of objects which are observed in consecutive points in time. We introduce semantic entailment of the formulas, show its fixed-point…

Sequential propositional logic deviates from ordinary propositional logic by taking into account that during the sequential evaluation of a propositional statement,atomic propositions may yield different Boolean values at repeated…

Argumentation is the process of constructing arguments about propositions, and the assignment of statements of confidence to those propositions based on the nature and relative strength of their supporting arguments. The process is modelled…

Epistemic reasoning requires agents to infer the state of the world from partial observations and information about other agents' knowledge. Prior work evaluating LLMs on canonical epistemic puzzles interpreted their behavior through a…

Ordered logics and type systems have been used in a variety of applications including computational linguistics, memory allocation, stream processing, logical frameworks, parametricity, and enforcing security protocols. In most…

Predicate Logic with Definitions (PLD or D-logic) is a modification of first-order logic intended mostly for practical formalization of mathematics. The main syntactic constructs of D-logic are terms, formulas and definitions. A definition…

Generating logical form equivalents of human language is a fresh way to employ neural architectures where long short-term memory effectively captures dependencies in both encoder and decoder units. The logical form of the sequence usually…

Event relations are crucial for narrative understanding and reasoning. Governed by nuanced logic, event relation extraction (ERE) is a challenging task that demands thorough semantic understanding and rigorous logical reasoning. In this…

Open-domain question answering (Open-QA) is a common task for evaluating large language models (LLMs). However, current Open-QA evaluations are criticized for the ambiguity in questions and the lack of semantic understanding in evaluators.…

Deep and shallow embeddings of non-classical logics in classical higher-order logic have been explored, implemented, and used in various reasoning tools in recent years. This paper presents a method for the simultaneous deployment of deep…

Argumentation is a process of evaluating and comparing a set of arguments. A way to compare them consists in using a ranking-based semantics which rank-order arguments from the most to the least acceptable ones. Recently, a number of such…

Large language models (LLMs) have revolutionized natural language processing, but their ability to process long sequences is fundamentally limited by the context window size during training. Existing length extrapolation methods often…