Related papers: Sound and Relatively Complete Belief Hoare Logic f…
This paper presents an example of formal reasoning about the semantics of a Prolog program of practical importance (the SAT solver of Howe and King). The program is treated as a definite clause logic program with added control. The logic…
A logic is defined that allows to express information about statistical probabilities and about degrees of belief in specific propositions. By interpreting the two types of probabilities in one common probability space, the semantics given…
Speech Recognition searches to predict the spoken words automatically. These systems are known to be very expensive because of using several pre-recorded hours of speech. Hence, building a model that minimizes the cost of the recognizer…
In Bayesian statistics the precise point-null hypothesis $\theta=\theta_0$ can be tested by checking whether $\theta_0$ is contained in a credible set. This permits testing of $\theta=\theta_0$ without having to put prior probabilities on…
Local Completeness Logic (LCL) has been put forward as a program logic for proving both the correctness and incorrectness of program specifications. LCL is an abstract logic, parameterized by an abstract domain that allows combining over-…
Recently, a growing number of researchers have applied machine learning to assist users of interactive theorem provers. However, the expressive nature of underlying logics and esoteric structures of proof documents impede machine learning…
Empirical research in Natural Language Processing (NLP) has adopted a narrow set of principles for assessing hypotheses, relying mainly on p-value computation, which suffers from several known issues. While alternative proposals have been…
We introduce a modal logic for describing statistical knowledge, which we call statistical epistemic logic. We propose a Kripke model dealing with probability distributions and stochastic assignments, and show a stochastic semantics for the…
Nondeterministic choice is a useful program construct that provides a way to describe the behaviour of a program without specifying the details of possible implementations. It supports the stepwise refinement of programs, a method that has…
While software requirements are often expressed in natural language, verifying the correctness of a program against such requirements is a hard and underexplored problem. Large language models (LLMs) are promising candidates for addressing…
A principled approach to the design of program verification and con- struction tools is applied to separation logic. The control flow is modelled by power series with convolution as separating conjunction. A generic construction lifts…
In this thesis, we present two approaches to a rigorous mathematical and algorithmic foundation of quantitative and statistical inference in constraint-based natural language processing. The first approach, called quantitative constraint…
Probabilistic logic programs are logic programs where some facts hold with a specified probability. Here, we investigate these programs with a causal framework that allows counterfactual queries. Learning the program structure from…
This paper concerns the relation between imperative process algebra and rely/guarantee logic. An imperative process algebra is complemented by a rely/guarantee logic that can be used to reason about how data change in the course of a…
Clustering is part of unsupervised analysis methods that consist in grouping samples into homogeneous and separate subgroups of observations also called clusters. To interpret the clusters, statistical hypothesis testing is often used to…
This paper summarises the results obtained by the author and his collaborators in a program logic approach to the verification of quantum programs, including quantum Hoare logic, invariant generation and termination analysis for quantum…
We study the stability of posterior predictive inferences to the specification of the likelihood model and perturbations of the data generating process. In modern big data analyses, useful broad structural judgements may be elicited from…
As large language models (LLMs) continue to demonstrate remarkable abilities across various domains, computer scientists are developing methods to understand their cognitive processes, particularly concerning how (and if) LLMs internally…
The logic of hereditary Harrop formulas (HH) has proven useful for specifying a wide range of formal systems. This logic includes a form of hypothetical judgment that leads to dynamically changing sets of assumptions and that is key to…
Hoare-style verification provides a principled foundation for reasoning about the correctness of quantum programs, but existing approaches do not allow fully automatic verification. While automata-based verification scales well when…