Related papers: Higher-order Logic as Lingua Franca -- Integrating…
Real-valued logics underlie an increasing number of neuro-symbolic approaches, though typically their logical inference capabilities are characterized only qualitatively. We provide foundations for establishing the correctness and power of…
Description logics (DLs) are standard knowledge representation languages for modelling ontologies, i.e. knowledge about concepts and the relations between them. Unfortunately, DL ontologies are difficult to learn from data and…
We examine the class of languages that can be defined entirely in terms of provability in an extension of the sorted type theory (Ty_n) by embedding the logic of phonologies, without introduction of special types for syntactic entities.…
We develop a classical propositional logic for reasoning about combinatory logic. We define its syntax, axiomatic system and semantics. The syntax and axiomatic system are presented based on classical propositional logic, with typed…
We seize the opportunity of the publication of selected papers from the \emph{Logic, categories, semantics} workshop in the \emph{Journal of Applied Logic} to survey some current trends in logic, namely intuitionistic and linear type…
Large Language Models (LLMs) have rapidly transformed the landscape of artificial intelligence, enabling natural language interfaces and dynamic orchestration of software components. However, their reliance on probabilistic inference limits…
We present a framework, named the Montagovian generative lexicon, for computing the semantics of natural language sentences, expressed in many sorted higher order logic. Word meaning is depicted by lambda terms of second order lambda…
The integration of structured hierarchical embeddings into transformer-based architectures introduces a refined approach to lexical representation, ensuring that multi-scale semantic relationships are preserved without compromising…
We present a generic framework that facilitates object level reasoning with logics that are encoded within the Higher Order Logic theorem proving environment of HOL Light. This involves proving statements in any logic using intuitive…
Recent Large Language Models (LLMs) have significantly advanced natural language processing and automated decision-making. However, these models still encounter difficulties when performing complex reasoning tasks involving logical…
Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…
The increasing incorporation of Artificial Intelligence in the form of automated systems into decision-making procedures highlights not only the importance of decision theory for automated systems but also the need for these decision…
Multi-agent large language model frameworks are promising for complex multi step reasoning, yet existing systems remain weak for scientific and knowledge intensive domains due to static prompts and agent roles, rigid workflows, and…
The paper introduces a propositional linguistic logic that serves as the basis for automated uncertain reasoning with linguistic information. First, we build a linguistic logic system with truth value domain based on a linear symmetrical…
Logical relations built on top of an operational semantics are one of the most successful proof methods in programming language semantics. In recent years, more and more expressive notions of operationally-based logical relations have been…
Explainable AI is an emerging field providing solutions for acquiring insights into automated systems' rationale. It has been put on the AI map by suggesting ways to tackle key ethical and societal issues. Existing explanation techniques…
Deductive reasoning plays a pivotal role in the formulation of sound and cohesive arguments. It allows individuals to draw conclusions that logically follow, given the truth value of the information provided. Recent progress in the domain…
We argue that grammatical analysis is a viable alternative to concept spotting for processing spoken input in a practical spoken dialogue system. We discuss the structure of the grammar, and a model for robust parsing which combines…
Ontologies formalise how the concepts from a given domain are interrelated. Despite their clear potential as a backbone for explainable AI, existing ontologies tend to be highly incomplete, which acts as a significant barrier to their more…
Deep learning is bringing remarkable contributions to the field of argumentation mining, but the existing approaches still need to fill the gap toward performing advanced reasoning tasks. In this position paper, we posit that…