Related papers: Representing Isabelle in LF
We present modular implicits, an extension to the OCaml language for ad-hoc polymorphism inspired by Scala implicits and modular type classes. Modular implicits are based on type-directed implicit module parameters, and elaborate…
The Isabelle proof assistant comes equipped with a very powerful tactic for term simplification. While tremendously useful, the results of simplifying a term do not always match the user's expectation: sometimes, the resulting term is not…
Vision-Language-Action Models (VLAs) have shown remarkable progress towards embodied intelligence. While their architecture partially resembles that of Large Language Models (LLMs), VLAs exhibit higher complexity due to their multi-modal…
Intuitionistic modal logics (IMLs) extend intuitionistic propositional logic with modalities such as the box and diamond connectives. Advances in the study of IMLs have inspired several applications in programming languages via the…
We make the case for language models over logical forms (LFLMs), arguing that such models are more data-efficient than their textual counterparts. To that end, we introduce the Graph-based Formal-Logical Distributional Semantics (GFoLDS)…
Natural language understanding applications such as interactive planning and face-to-face translation require extensive inferencing. Many of these inferences are based on the meaning of particular open class words. Providing a…
We show that in a locally lambda-presentable category, every lambda(m)-injectivity class (i.e., the class of all the objects injective with respect to some class of lambda-presentable morphisms) is a weakly reflective subcategory determined…
With the fast-growing number of classification models being produced every day, numerous model interpretation and comparison solutions have also been introduced. For example, LIME and SHAP can interpret what input features contribute more…
This paper presents State Algebra, a novel framework designed to represent and manipulate propositional logic using algebraic methods. The framework is structured as a hierarchy of three representations: Set, Coordinate, and Row…
Inductive logic programming (ILP) has been a deeply influential paradigm in AI, enjoying decades of research on its theory and implementations. As a natural descendent of the fields of logic programming and machine learning, it admits the…
The paper introduces a new modular action language, ALM, and illustrates the methodology of its use. It is based on the approach of Gelfond and Lifschitz (1993; 1998) in which a high-level action language is used as a front end for a logic…
Definitions of new symbols merely abbreviate expressions in logical frameworks, and no new facts (regarding previously defined symbols) should hold because of a new definition. In Isabelle/HOL, definable symbols are types and constants. The…
Large Language Models (LLMs) are increasingly being used in education, yet their correctness alone does not capture the quality, reliability, or pedagogical validity of their problem-solving behavior, especially in mathematics, where…
The growing complexity and diversity of models used in the engineering of dependable systems implies that a variety of formal methods, across differing abstractions, paradigms, and presentations, must be integrated. Such an integration…
This works is motivated by a real-world case study where it is necessary to integrate and relate existing ontologies through meta- modelling. For this, we introduce the Description Logic ALCQM which is obtained from ALCQ by adding…
Integrating diverse formalisms into modular knowledge representation systems offers increased expressivity, modeling convenience and computational benefits. We introduce concepts of abstract modules and abstract modular systems to study…
Model interpretability is an increasingly important component of practical machine learning. Some of the most common forms of interpretability systems are example-based, local, and global explanations. One of the main challenges in…
Once one has enriched LFG's formal machinery with the linear logic mechanisms needed for semantic interpretation as proposed by Dalrymple et. al., it is natural to ask whether these make any existing components of LFG redundant. As…
We define a modular multi-concept extension of the lexicographic closure semantics for defeasible description logics with typicality. The idea is that of distributing the defeasible properties of concepts into different modules, according…
Neural networks are widely regarded as black-box models, creating significant challenges in understanding their inner workings, especially in natural language processing (NLP) applications. To address this opacity, model explanation…