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Formal deductive systems are very common in computer science. They are used to represent logics, programming languages, and security systems. Moreover, writing programs that manipulate them and that reason about them is important and…
This paper investigates the use of symmetric monoidal closed (SMC) structure for representing syntax with variable binding, in particular for languages with linear aspects. In our setting, one first specifies an SMC theory T, which may…
In classical logic, nonBoolean fluents, such as the location of an object, can be naturally described by functions. However, this is not the case in answer set programs, where the values of functions are pre-defined, and nonmonotonicity of…
Recent years have witnessed a renewed interest in Boolean function in explaining binary classifiers in the field of explainable AI (XAI). The standard approach of Boolean function is propositional logic. We present a modal language of a…
In machine learning (ML), researchers and engineers seem to be at odds. System implementers would prefer models to be declarative, with detailed type information and semantic restrictions that allow models to be optimised, rearranged and…
There is a growing need for abstractions in logic specification languages such as FO(.) and ASP. One technique to achieve these abstractions are templates (sometimes called macros). While the semantics of templates are virtually always…
Human languages use a wide range of grammatical categories to constrain which words or phrases can fill certain slots in grammatical patterns and to express additional meanings, such as tense or aspect, through morpho-syntactic means. These…
Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such…
This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…
Many semantical aspects of programming languages, such as their operational semantics and their type assignment calculi, are specified by describing appropriate proof systems. Recent research has identified two proof-theoretic features that…
Many of the existing approaches for program comprehension rely on the linguistic information found in source code, such as identifier names and comments. Semantic clustering is one such technique for modularization of the system that relies…
Cross-lingual representations of words enable us to reason about word meaning in multilingual contexts and are a key facilitator of cross-lingual transfer when developing natural language processing models for low-resource languages. In…
We have proposed going beyond traditional ontologies to use rich semantics implemented in programming languages for modeling. In this paper, we discuss the application of executable semantic models to two examples, first a structured…
Linearity and ramification constraints have been widely used to weaken higher-order (primitive) recursion in such a way that the class of representable functions equals the class of polytime functions. We show that fine-tuning these two…
We develop a unified categorical theory of substructural abstract syntax with variable binding and single-variable (capture-avoiding) substitution. This is done for the gamut of context structural rules given by exchange (linear theory)…
Vision-language fine-tuning has emerged as an efficient paradigm for constructing multimodal foundation models. While textual context often highlights semantic relationships within an image, existing fine-tuning methods typically overlook…
The approach to reasoning about structural operational semantics style specifications supported by the Abella system is discussed. This approach uses lambda tree syntax to treat object language binding and encodes binding related properties…
Models are heavily used in software engineering and together with their systems they evolve over time. Thus, managing their changes is an important challenge for system maintainability. Existing approaches to model differencing concentrate…
The present article is the first of a series whose goal is to define a logical formalism in which it is possible to reason about genetics. In this paper, we introduce the main concepts of our language whose domain of discourse consists of a…
We present a categorical framework for formal systems in which inference rules with $m$ metavariables over a category of syntax $\mathscr{S}$, taken to be a cartesian PROP, are represented by operations of arity $k \to n$ equipped with…