Related papers: Higher-order Logic as Lingua Franca -- Integrating…
Many theories of semantic interpretation use lambda-term manipulation to compositionally compute the meaning of a sentence. These theories are usually implemented in a language such as Prolog that can simulate lambda-term operations with…
Argumentation frameworks ($AF$s) have been extensively developed, but existing higher-order bipolar $AF$s suffer from critical limitations: attackers and supporters are restricted to arguments, multi-valued and fuzzy semantics lack unified…
Logic is the main formal language to perform automated reasoning, and it is further a human-interpretable language, at least for small formulae. Learning and optimising logic requirements and rules has always been an important problem in…
The paper presents a comprehensive analysis of the European AI Act in terms of its logical modalities, with the aim of preparing its formal representation, for example, within the logic-pluralistic Knowledge Engineering Framework and…
We propose a formal model of reasoning limitations in large neural net models for language, grounded in the depth of their neural architecture. By treating neural networks as linear operators over logic predicate space we show that each…
Deontic logic is a very well researched branch of mathematical logic and philosophy. Various kinds of deontic logics are discussed for different application domains like argumentation theory, legal reasoning, and acts in multi-agent…
Dialogical argumentation is an important cognitive activity by which agents exchange arguments and counterarguments as part of some process such as discussion, debate, persuasion and negotiation. Whilst numerous formal systems have been…
Deep learning is very effective at jointly learning feature representations and classification models, especially when dealing with high dimensional input patterns. Probabilistic logic reasoning, on the other hand, is capable to take…
Ontology is a popular method for knowledge representation in different domains, including the legal domain, and description logics (DL) is commonly used as its description language. To handle reasoning based on inconsistent DL-based legal…
We endow prioritised default logic (PDL) with argumentation semantics using the ASPIC+ framework for structured argumentation, and prove that the conclusions of the justified arguments are exactly the prioritised default extensions.…
We introduce a variation on Barthe et al.'s higher-order logic in which formulas are interpreted as predicates over open rather than closed objects. This way, concepts which have an intrinsically functional nature, like continuity,…
The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a…
Advances in natural language processing have resulted in increased capabilities with respect to multiple tasks. One of the possible causes of the observed performance gains is the introduction of increasingly sophisticated text…
Weighted monadic second-order logic is a weighted extension of monadic second-order logic that captures exactly the behaviour of weighted automata. Its semantics is parameterized with respect to a semiring on which the values that weighted…
Structured reasoning over natural language inputs remains a core challenge in artificial intelligence, as it requires bridging the gap between unstructured linguistic expressions and formal logical representations. In this paper, we propose…
We propose a novel framework that leverages large language models (LLMs) to guide the rank selection in tensor network models for higher-order data analysis. By utilising the intrinsic reasoning capabilities and domain knowledge of LLMs,…
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 present a logical separability analysis for a functional quantum computation language. This logic is inspired by previous works on logical analysis of aliasing for imperative functional programs. Both analyses share similarities notably…
Logical frameworks provide natural and direct ways of specifying and reasoning within deductive systems. The logical framework LF and subsequent developments focus on finitary proof systems, making the formalization of circular proof…
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…