Related papers: A Categorical Framework for Program Semantics and …
This thesis is expository in nature. We analyze the connection between abstract minions, which can be described as functors from the category of finite ordinals to sets, and concrete minions, which are sets $\mathrm{Pol}(A, B)$ of…
We study, in an abstract axiomatic setting, the notion of sectional category of a morphism. From this, we unify and generalize known results about this invariant in different settings as well as we deduce new applications.
Although the notion of a concept as a collection of objects sharing certain properties, and the notion of a conceptual hierarchy are fundamental to both Formal Concept Analysis and Description Logics, the ways concepts are described and…
Just like any other branch of mathematics, denotational semantics of programming languages should be formalised in type theory, but adapting traditional domain theoretic semantics, as originally formulated in classical set theory to type…
The aim of this article is to describe a new perspective on functoriality of persistent homology and explain its intrinsic symmetry that is often overlooked. A data set for us is a finite collection of functions, called measurements, with a…
Lawvere observed in his celebrated work on hyperdoctrines that the set-theoretic schema of comprehension can be elegantly expressed in the functorial language of categorical logic, as a comprehension structure on the functor…
Dependent pattern matching is a key feature in dependently typed programming. However, there is a theory-practice disconnect: while many proof assistants implement pattern matching as primitive, theoretical presentations give semantics to…
Causal abstraction provides a theoretical foundation for mechanistic interpretability, the field concerned with providing intelligible algorithms that are faithful simplifications of the known, but opaque low-level details of black box AI…
Functional ANOVA offers a principled framework for interpretability by decomposing a model's prediction into main effects and higher-order interactions. For independent features, this decomposition is well-defined, strongly linked with SHAP…
In this paper, we study whether transformer-based language models can extract predicate argument structure from simple sentences. We firstly show that language models sometimes confuse which predicates apply to which objects. To mitigate…
Abstract dialectical frameworks (ADFs) have been introduced as a formalism for modeling and evaluating argumentation allowing general logical satisfaction conditions. Different criteria used to settle the acceptance of arguments are called…
We give a formal treatment of simple type theories, such as the simply-typed $\lambda$-calculus, using the framework of abstract clones. Abstract clones traditionally describe first-order structures, but by equipping them with additional…
In this paper, we present an approach to define the semantics for object-oriented modeling languages. One important property of this semantics is to support underspecified and incomplete models. To this end, semantics is given as predicates…
Both syntactic and semantic structures are key linguistic contextual clues, in which parsing the latter has been well shown beneficial from parsing the former. However, few works ever made an attempt to let semantic parsing help syntactic…
The lambda calculus with constructors is an extension of the lambda calculus with variadic constructors. It decomposes the pattern-matching a la ML into a case analysis on constants and a commutation rule between case and application…
Categorization is a core component of human linguistic competence. We investigate how a transformer-based language model (LM) learns linguistic categories by comparing its behaviour over the course of training to behaviours which…
Structured recursion schemes such as folds and unfolds have been widely used for structuring both functional programs and program semantics. In this context, it has been customary to implement denotational semantics as folds over an…
The present work presents some results about the categorial relation between logics and its categories of structures. A (propositional, finitary) logic is a pair given by a signature and Tarskian consequence relation on its formula algebra.…
Abstract interpretation is a method to automatically find invariants of programs or pieces of code whose semantics is given via least fixed-points. Up-to techniques have been introduced as enhancements of coinduction, an abstract principle…
Current open-domain neural semantics parsers show impressive performance. However, closer inspection of the symbolic meaning representations they produce reveals significant weaknesses: sometimes they tend to merely copy character sequences…