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We prove a topological completeness theorem for the modal logic GLP containing operators $\langle\lambda\rangle$ for $\lambda \in$ Ord intended to capture progressively stronger notions of consistency in mathematical theories. We show that,…
Recently, there has been an increasing interest in the bottom-up evaluation of the semantics of logic programs with complex terms. The presence of function symbols in the program may render the ground instantiation infinite, and finiteness…
In order to properly test software, test data of a certain quality is needed. However, useful test data is often unavailable: Existing or hand-crafted data might not be diverse enough to enable desired test cases. Furthermore, using…
We introduce continuation semantics for both fixpoint modal logic (FML) and Computation Tree Logic* (CTL*), parameterised by a choice of branching type and quantitative predicate lifting. Our main contribution is proving that they are…
Chain-of-thought (CoT) is capable of eliciting models to explicitly generate reasoning paths, thus promoting reasoning accuracy and attracting increasing attention. Specifically, zero-shot CoT achieves remarkable improvements in a wide…
It is well known that, under certain conditions, it is possible to split logic programs under stable model semantics, i.e. to divide such a program into a number of different "levels", such that the models of the entire program can be…
LLMs used for code generation are typically guided by engineering constraints--technology choices, dependency restrictions, and architectural patterns--expressed in verbose natural language. We investigate whether compact, structured…
Recent advances in large language models (LLMs) have enabled agents to autonomously execute complex, long-horizon tasks, yet planning remains a primary bottleneck for reliable task execution. Existing methods typically fall into two…
An efficient and flexible engine for computing fixed points is critical for many practical applications. In this paper, we firstly present a goal-directed fixed point computation strategy in the logic programming paradigm. The strategy…
In this paper, we propose a Feasible Sequential Linear Programming (FSLP) algorithm applied to time-optimal control problems (TOCP) obtained through direct multiple shooting discretization. This method is motivated by TOCP with nonlinear…
Developing and maintaining CLP programs requires visualization and explanation tools. However, existing tools are built in an ad hoc way. Therefore porting tools from one platform to another is very difficult. We have shown in previous work…
Action description languages, such as A and B, are expressive instruments introduced for formalizing planning domains and planning problem instances. The paper starts by proposing a methodology to encode an action language (with conditional…
Signal temporal logic (STL) is a powerful formalism for specifying various temporal properties in dynamical systems. However, existing methods, such as mixed-integer programming and nonlinear programming, often struggle to efficiently solve…
Concolic testing is a popular software verification technique based on a combination of concrete and symbolic execution. Its main focus is finding bugs and generating test cases with the aim of maximizing code coverage. A previous approach…
Scaling training compute, measured in FLOPs, has long been shown to improve the accuracy of large language models, yet training remains resource-intensive. Prior work shows that increasing test-time compute (TTC)-for example through…
Inductive logic programming is a form of machine learning based on mathematical logic that generates logic programs from given examples and background knowledge. In this project, we extend the Popper ILP system to make use of multi-task…
We apply to logic programming some recently emerging ideas from the field of reduction-based communicating systems, with the aim of giving evidence of the hidden interactions and the coordination mechanisms that rule the operational…
Program completion is a translation from the language of logic programs into the language of first-order theories. Its original definition has been extended to programs that include integer arithmetic, accept input, and distinguish between…
One of the long-standing goals in optimisation and constraint programming is to describe a problem in natural language and automatically obtain an executable, efficient model. Large language models appear to bring this vision closer,…
Nomadic applications create replicas of shared objects that evolve independently while they are disconnected. When reconnecting, the system has to reconcile the divergent replicas. In the log-based approach to reconciliation, such as in the…