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We advocate a declarative approach to proving properties of logic programs. Total correctness can be separated into correctness, completeness and clean termination; the latter includes non-floundering. Only clean termination depends on the…
With one exception, our previous work on recurrence extraction and denotational semantics has focused on a source language that supports inductive types and structural recursion. The exception handles general recursion via an initial…
The capability of making interpretable and self-explanatory decisions is essential for developing responsible machine learning systems. In this work, we study the learning to explain problem in the scope of inductive logic programming…
Large Language Models (LLMs) demonstrate strong in-context learning abilities, yet their effectiveness in text classification depends heavily on prompt design and incurs substantial computational cost. Conformal In-Context Learning (CICLe)…
Incorrectness Separation Logic (ISL) is a proof system designed to automate verification and detect bugs in programs manipulating heap memories. In this study, we extend ISL to support variable-length array predicates and pointer…
Program slicing has been mainly studied in the context of imperative languages, where it has been applied to a wide variety of software engineering tasks, like program understanding, maintenance, debugging, testing, code reuse, etc. This…
ACL2 has long supported user-defined simplifiers, so-called metafunctions and clause processors, which are installed when corresponding rules of class :meta or :clause-processor are proved. Historically, such simplifiers could access the…
The lambda calculus since more than half a century is a model and foundation of functional programming languages. However, lambda expressions can be evaluated with different reduction strategies and thus, there is no fixed cost model nor…
In-context learning (ICL) is one of the most powerful and most unexpected capabilities to emerge in recent transformer-based large language models (LLMs). Yet the mechanisms that underlie it are poorly understood. In this paper, we…
Some approaches to increasing program reliability involve a disciplined use of programming languages so as to minimise the hazards introduced by error-prone features. This is realised by writing code that is constrained to a subset of the a…
Demonstration ordering, which is an important strategy for in-context learning (ICL), can significantly affects the performance of large language models (LLMs). However, most of the current approaches of ordering require high computational…
Large Language Models (LLMs) have demonstrated remarkable performance in various NLP tasks, including semantic parsing, which translates natural language into formal code representations. However, the reverse process, translating code into…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
We show how categorial deduction can be implemented in higher-order (linear) logic programming, thereby realising parsing as deduction for the associative and non-associative Lambek calculi. This provides a method of solution to the parsing…
Recent years have witnessed a significant increase in the performance of Vision and Language tasks. Foundational Vision-Language Models (VLMs), such as CLIP, have been leveraged in multiple settings and demonstrated remarkable performance…
Many recent analyses for conventional imperative programs begin by transforming programs into logic programs, capitalising on existing LP analyses and simple LP semantics. We propose using logic programs as an intermediate program…
This paper shows that the semantics of programs with aggregates implemented by the solvers clingo and dlv can be characterized as extended First-Order formulas with intensional functions in the logic of Here-and-There. Furthermore, this…
The earlier paper "Introduction to clarithmetic I" constructed an axiomatic system of arithmetic based on computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html), and proved its soundness and extensional completeness with respect…
The relationship between communicated language and intended meaning is often probabilistic and sensitive to context. Numerous strategies attempt to estimate such a mapping, often leveraging recursive Bayesian models of communication. In…
The aim of the Alma project is the design of a strongly typed constraint programming language that combines the advantages of logic and imperative programming. The first stage of the project was the design and implementation of Alma-0, a…