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Logic can be made useful for programming and for databases independently of logic programming. To be useful in this way, logic has to provide a mechanism for the definition of new functions and new relations on the basis of those given in…
The ability of Large Language Models (LLMs) to perform reasoning tasks such as deduction has been widely investigated in recent years. Yet, their capacity to generate proofs-faithful, human-readable explanations of why conclusions…
This study presents data format of episodic memory for artificial intelligence and cognitive science. The data format, named cognitive-logs, enables rigour and flexible logical reasoning. Cognitive-logs consist of a set of relational and…
Logical relations are one of the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be…
In the Declarative Networking paradigm, Datalog-like languages are used to express distributed computations. Whereas recently formal operational semantics for these languages have been developed, a corresponding declarative semantics has…
We introduce Plan*RAG, a novel framework that enables structured multi-hop reasoning in retrieval-augmented generation (RAG) through test-time reasoning plan generation. While existing approaches such as ReAct maintain reasoning chains…
Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly, on even very simple programs,…
The containment problem of Datalog queries is well known to be undecidable. There are, however, several Datalog fragments for which containment is known to be decidable, most notably monadic Datalog and several "regular" query languages on…
Substructural logics are formal logical systems that omit familiar structural rules of classical and intuitionistic logic such as contraction, weakening, exchange (commutativity), and associativity. This leads to a resource-sensitive…
Logic is the main formal language to perform automated reasoning, and it is further a human-interpretable language, at least for small formulae. Learning and optimising logic requirements and rules has always been an important problem in…
Quantitative reasoning is a critical skill to analyze data, yet the assessment of such ability remains limited. To address this gap, we introduce the Quantitative Reasoning with Data (QRData) benchmark, aiming to evaluate Large Language…
This paper is a reflexion on the computability of natural language semantics. It does not contain a new model or new results in the formal semantics of natural language: it is rather a computational analysis of the logical models and…
Following the recent successful examples of large technology companies, many modern enterprises seek to build knowledge graphs to provide a unified view of corporate knowledge and to draw deep insights using machine learning and logical…
In the context of large language models (LLMs), current advanced reasoning methods have made impressive strides in various reasoning tasks. However, when it comes to logical reasoning tasks, major challenges remain in both efficacy and…
Materialisation facilitates Datalog reasoning by precomputing all consequences of the facts and the rules so that queries can be directly answered over the materialised facts. However, storing all materialised facts may be infeasible in…
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…
We have designed a new logic programming language called LM (Linear Meld) for programming graph-based algorithms in a declarative fashion. Our language is based on linear logic, an expressive logical system where logical facts can be…
The generation of comprehensible explanations is an essential feature of modern artificial intelligence systems. In this work, we consider probabilistic logic programming, an extension of logic programming which can be useful to model…
Solving complex reasoning tasks may involve visual understanding, domain knowledge retrieval, numerical calculation, and multi-step reasoning. Existing methods augment large language models (LLMs) with external tools but are restricted to…
Large Language Models (LLMs) have shown promise as robotic planners but often struggle with long-horizon and complex tasks, especially in specialized environments requiring external knowledge. While hierarchical planning and…