Related papers: A Type System Theory for Higher-Order Intensional …
We present a new approach to HPSG processing: compiling HPSG grammars expressed as type constraints into definite clause programs. This provides a clear and computationally useful correspondence between linguistic theories and their…
This paper develops a formal logic for guises based on the work of H\'ector-Neri Casta\~neda, who understood relations from an internalist viewpoint, following Leibniz. We introduce a syntax, model theory, and proof theory for an…
This work proposes a dependent type theory that combines functions and session-typed processes (with value dependencies) through a contextual monad, internalising typed processes in a dependently-typed lambda-calculus. The proposed…
The definitional equality of an intensional type theory is its test of type compatibility. Today's systems rely on ordinary evaluation semantics to compare expressions in types, frustrating users with type errors arising when evaluation…
Software engineers are faced with the challenge of creating control algorithms for increasingly complex dynamic systems, such as the management of communication network topologies. To support rapid prototyping for these increasingly complex…
Gradual typing is an approach to integrating static and dynamic typing within the same language, and puts the programmer in control of which regions of code are type checked at compile-time and which are type checked at run-time. In this…
We present Dependent JavaScript (DJS), a statically-typed dialect of the imperative, object-oriented, dynamic language. DJS supports the particularly challenging features such as run-time type-tests, higher-order functions, extensible…
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…
A standard intensional account of probabilistic computation represents a randomized program as a deterministic computation that consumes an explicit random tape. This yields a two-layer perspective: an intensional layer that makes reuse of…
Multi-label classification problems with thousands of classes are hard to solve with in-context learning alone, as language models (LMs) might lack prior knowledge about the precise classes or how to assign them, and it is generally…
The differentiable implementation of logic yields a seamless combination of symbolic reasoning and deep neural networks. Recent research, which has developed a differentiable framework to learn logic programs from examples, can even acquire…
We present an approach to type theory in which the typing judgments do not have explicit contexts. Instead of judgments of shape "Gamma |- A : B", our systems just have judgments of shape "A : B". A key feature is that we distinguish free…
Text-to-image generative models have demonstrated remarkable capabilities in generating high-quality images based on textual prompts. However, crafting prompts that accurately capture the user's creative intent remains challenging. It often…
This work presents a novel systematic methodology to analyse the capabilities and limitations of Large Language Models (LLMs) with feedback from a formal inference engine, on logic theory induction. The analysis is complexity-graded w.r.t.…
HolPy is an interactive theorem proving system implemented in Python. It uses higher-order logic as the logical foundation. Its main features include a pervasive use of macros in producing, checking, and storing proofs, a JSON-based format…
Topological collections allow to consider uniformly many data structures in programming languages and are handled by functions defined by pattern matching called transformations. We present two type systems for languages with topological…
Type theories can be formalized using the intrinsically (hard) or the extrinsically (soft) typed style. In large libraries of type theoretical features, often both styles are present, which can lead to code duplication and integration…
SPEEDY is an Eclipse-based IDE for exploring techniques that assist users in generating correct specifications, particularly including invariant inference algorithms and tools. It integrates with several back-end tools that propose…
Harnessing the power of dependently typed languages can be difficult. Programmers must manually construct proofs to produce well-typed programs, which is not an easy task. In particular, migrating code to these languages is challenging.…
Autonomous systems embedded with machine learning modules often rely on deep neural networks for classifying different objects of interest in the environment or different actions or strategies to take for the system. Due to the…