Related papers: Satisfiability Modulo Theory Meets Inductive Logic…
Fuzzy answer set programming (FASP) combines two declarative frameworks, answer set programming and fuzzy logic, in order to model reasoning by default over imprecise information. Several connectives are available to combine different…
Inductive Logic Programming (ILP) is a principled approach for generalizing regularities from data and constructing hypotheses as interpretable logic programs. However, a key limitation is its reliance on expert-crafted language bias - the…
Integer Linear Programming (ILP) provides a viable mechanism to encode explicit and controllable assumptions about explainable multi-hop inference with natural language. However, an ILP formulation is non-differentiable and cannot be…
This paper studies Linear Temporal Logic over Finite Traces (LTLf) where proposition letters are replaced with first-order formulas interpreted over arbitrary theories, in the spirit of Satisfiability Modulo Theories. The resulting logic,…
Numerous real-world decision-making problems can be formulated and solved using Mixed-Integer Linear Programming (MILP) models. However, the transformation of these problems into MILP models heavily relies on expertise in operations…
Generating rational and generally accurate responses to tasks, often accompanied by example demonstrations, highlights Large Language Model's (LLM's) remarkable In-Context Learning (ICL) capabilities without requiring updates to the model's…
The vast quantity of data generated and captured every day has led to a pressing need for tools and processes to organize, analyze and interrelate this data. Automated reasoning and optimization tools with inherent support for data could…
Numerous recent prompt optimization approaches like chain-of-thought, have been demonstrated to significantly improve the quality of content generated by large language models (LLMs). In-context learning (ICL), a recent paradigm where a few…
Recent work on loglinear models in probabilistic constraint logic programming is applied to first-order probabilistic reasoning. Probabilities are defined directly on the proofs of atomic formulae, and by marginalisation on the atomic…
With the technology of the time, Kowalski's seminal 1974 paper {\em Predicate Logic as a Programming Language} was a breakthrough for the use of logic in computer science. It introduced two fundamental ideas: on the declarative side, the…
Satisfiability modulo theories (SMT) solving has become a critical part of many static analyses, including symbolic execution, refinement type checking, and model checking. We propose Formulog, a domain-specific language that makes it…
In-Context Learning (ICL) enables pretrained LLMs to adapt to downstream tasks by conditioning on a small set of input-output demonstrations, without any parameter updates. Although there have been many theoretical efforts to explain how…
In the contexts of automated reasoning (AR) and formal verification (FV), important decision problems are effectively encoded into Satisfiability Modulo Theories (SMT). In the last decade efficient SMT solvers have been developed for…
Knowledge Representation and Reasoning and Machine Learning are two important fields in AI. Nonmonotonic logic programming (NMLP) and Answer Set Programming (ASP) provide formal languages for representing and reasoning with commonsense…
Pre-trained language models (PLMs) have made significant advances in natural language inference (NLI) tasks, however their sensitivity to textual perturbations and dependence on large datasets indicate an over-reliance on shallow…
In modern industry, dynamic environments and the complexity of modular and reconfigurable resources require automated planning of process sequences. Capability-based planning approaches address this by automatically generating plans from…
Inductive Logic Programming (ILP) systems learn generalised, interpretable rules in a data-efficient manner utilising existing background knowledge. However, current ILP systems require training examples to be specified in a structured…
Inductive reasoning is an essential capability for large language models (LLMs) to achieve higher intelligence, which requires the model to generalize rules from observed facts and then apply them to unseen examples. We present MIRAGE, a…
In-context learning (ICL) can significantly enhance the complex reasoning capabilities of large language models (LLMs), with the key lying in the selection and ordering of demonstration examples. Previous methods typically relied on simple…
The ability to generalise from a small number of examples is a fundamental challenge in machine learning. To tackle this challenge, we introduce an inductive logic programming (ILP) approach that combines negation and predicate invention.…