Related papers: Towards Reasoning About Properties of Imperative P…
Differentiable Logics are deployed in neuro-symbolic learning tasks as a way of embedding logical constraints in the training objective of neural networks. A differentiable logic consists of a syntax to write logical properties and a…
We describe a general approach to deriving linear-time logics for a wide variety of state-based, quantitative systems, by modelling the latter as coalgebras whose type incorporates both branching and linear behaviour. Concretely, we define…
Linear Temporal Logic (LTL) is the standard specification language for reactive systems and is successfully applied in industrial settings. However, many shortcomings of LTL have been identified in the literature, among them the limited…
Reasoning is a fundamental component of language understanding. Recent prompting techniques, such as chain of thought, have consistently improved LLMs' performance on various reasoning tasks. Nevertheless, there is still little…
We present a theory of parameterized dynamic logic, namely DLp, for specifying and reasoning about a rich set of program models based on their transitional behaviours. Different from most dynamic logics that deal with regular expressions or…
Rule-based reasoning, a fundamental type of legal reasoning, enables us to draw conclusions by accurately applying a rule to a set of facts. We explore causal language models as rule-based reasoners, specifically with respect to…
Convincing someone of the truth value of a premise requires understanding and articulating the core logical structure of the argument which proves or disproves the premise. Understanding the logical structure of an argument refers to…
We introduce APPL (Abstract Program Property Logic), a unifying Hoare-style logic that subsumes standard Hoare logic, incorrectness logic, and several variants of Hyper Hoare logic. APPL provides a principled foundation for abstract program…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
Term rewriting systems have a simple syntax and semantics and facilitate proofs of correctness. However, they are not as popular in industry or academia as imperative languages. We define a term rewriting based abstract programming language…
One can perform equational reasoning about computational effects with a purely functional programming language thanks to monads. Even though equational reasoning for effectful programs is desirable, it is not yet mainstream. This is partly…
We analyse the expressiveness of the two-valued semantics of abstract argumentation frameworks, normal logic programs and abstract dialectical frameworks. By expressiveness we mean the ability to encode a desired set of two-valued…
Existing refinement calculi provide frameworks for the stepwise development of imperative programs from specifications. This paper presents a refinement calculus for deriving logic programs. The calculus contains a wide-spectrum logic…
Scientific ideation aims to propose novel solutions within a given scientific context. Existing LLM-based agentic approaches emulate human research workflows, yet inadequately model scientific reasoning, resulting in surface-level…
We demonstrate experimental results with LLMs that address robotics task planning problems. Recently, LLMs have been applied in robotics task planning, particularly using a code generation approach that converts complex high-level…
Large Language Models (LLMs) have demonstrated strong capabilities in natural language understanding and reasoning. However, their ability to perform exact, deterministic computation remains unclear. In this work, we systematically evaluate…
Causal reasoning, the ability to identify cause-and-effect relationship, is crucial in human thinking. Although large language models (LLMs) succeed in many NLP tasks, it is still challenging for them to conduct complex causal reasoning…
We present probabilistic logic programming under inheritance with overriding. This approach is based on new notions of entailment for reasoning with conditional constraints, which are obtained from the classical notion of logical entailment…
Program correctness (in imperative and functional programming) splits in logic programming into correctness and completeness. Completeness means that a program produces all the answers required by its specification. Little work has been…
Types in logic programming have focused on conservative approximations of program semantics by regular types, on one hand, and on type systems based on a prescriptive semantics defined for typed programs, on the other. In this paper, we…