Related papers: Sound and Relatively Complete Belief Hoare Logic f…
We discuss proving correctness and completeness of definite clause logic programs. We propose a method for proving completeness, while for proving correctness we employ a method which should be well known but is often neglected. Also, we…
Mathematical proof aims to deliver confident conclusions, but a very similar process of deduction can be used to make uncertain estimates that are open to revision. A key ingredient in such reasoning is the use of a "default" estimate of…
Large Language Models (LLMs) are increasingly deployed across diverse domains, raising the need for rigorous reliability assessment methods. Existing benchmark-based evaluations primarily offer descriptive statistics of model accuracy over…
Separation logic is a recent extension of Hoare logic for reasoning about programs with references to shared mutable data structures. In this paper, we provide a new interpretation of the logic for a programming language with higher types.…
Argumentation problems are concerned with determining the acceptability of a set of arguments from their relational structure. When the available information is uncertain, probabilistic argumentation frameworks provide modelling tools to…
We define a new notion of conditional belief, which plays the same role for Dempster-Shafer belief functions as conditional probability does for probability functions. Our definition is different from the standard definition given by…
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…
This paper concerns the relation between process algebra and Hoare logic. We investigate the question whether and how a Hoare logic can be used for reasoning about how data change in the course of a process when reasoning equationally about…
Consistently checking the statistical significance of experimental results is the first mandatory step towards reproducible science. This paper presents a hitchhiker's guide to rigorous comparisons of reinforcement learning algorithms.…
LF is a dependent type theory in which many other formal systems can be conveniently embedded. However, correct use of LF relies on nontrivial metatheoretic developments such as proofs of correctness of decision procedures for LF's…
Large language models (LLMs) have shown significant potential in scientific disciplines such as biomedicine, particularly in hypothesis generation, where they can analyze vast literature, identify patterns, and suggest research directions.…
Language models are increasingly being used in important decision pipelines, so ensuring the correctness of their outputs is crucial. Recent work has proposed evaluating the "factuality" of claims decomposed from a language model generation…
G\"odel's Dialectica interpretation is a fundamental tool for the extraction of computational content from proofs, and plays a central role in today's proof mining program. In the past decades, it has also been studied from the perspective…
We introduce a new approach to modeling uncertainty based on plausibility measures. This approach is easily seen to generalize other approaches to modeling uncertainty, such as probability measures, belief functions, and possibility…
This paper provides a statistical method to test whether a system that performs a binary sequential hypothesis test is optimal in the sense of minimizing the average decision times while taking decisions with given reliabilities. The…
The Epistemic Halpern-Shoham logic (EHS) is a temporal-epistemic logic that combines the interval operators of the Halpern-Shoham logic with epistemic modalities. The semantics of EHS is based on interpreted systems whose labelling function…
Advances in the general capabilities of large language models (LLMs) have led to their use for information retrieval, and as components in automated decision systems. A faithful representation of probabilistic reasoning in these models may…
Inductive reasoning enables humans to infer abstract rules from limited examples and apply them to novel situations. In this work, we compare an LLM-based hypothesis search framework with direct program generation approaches on few-shot…
Program logics are a powerful formal method in the context of program verification. Can we develop a counterpart of program logics in the context of language verification? This paper proposes language logics, which allow for statements of…
As language models (LMs) become integral to fields like healthcare, law, and journalism, their ability to differentiate between fact, belief, and knowledge is essential for reliable decision-making. Failure to grasp these distinctions can…