Related papers: A program logic for union bounds

We study transformational program logics for correctness and incorrectness that we extend to explicitly handle both termination and nontermination. We show that the logics are abstract interpretations of the right image transformer for a…

The framework of algorithmic knowledge assumes that agents use deterministic knowledge algorithms to compute the facts they explicitly know. We extend the framework to allow for randomized knowledge algorithms. We then characterize the…

Some approaches to increasing program reliability involve a disciplined use of programming languages so as to minimise the hazards introduced by error-prone features. This is realised by writing code that is constrained to a subset of the a…

Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…

The goal of inductive logic programming is to induce a logic program (a set of logical rules) that generalises training examples. Inducing programs with many rules and literals is a major challenge. To tackle this challenge, we introduce an…

We aim to create the highest possible quality of treatment-control matches for categorical data in the potential outcomes framework. Matching methods are heavily used in the social sciences due to their interpretability, but most matching…

We present a new algorithm for computing upper bounds on the number of executions of each program instruction during any single program run. The upper bounds are expressed as functions of program input values. The algorithm is primarily…

We propose a novel logic, called Frame Logic (FL), that extends first-order logic (with recursive definitions) using a construct Sp(.) that captures the implicit supports of formulas -- the precise subset of the universe upon which their…

This article aims to achieve two goals: to show that probability is not the only way of dealing with uncertainty (and even more, that there are kinds of uncertainty which are for principled reasons not addressable with probabilistic means);…

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…

The emergence of tools based on artificial intelligence has also led to the need of producing explanations which are understandable by a human being. In most approaches, the system is considered a black box, making it difficult to generate…

Interpolation is an important property of classical and many non-classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the the non-monotonic system of…

Standard approaches to probabilistic reasoning require that one possesses an explicit model of the distribution in question. But, the empirical learning of models of probability distributions from partial observations is a problem for which…

Predictive coding has emerged as an influential normative model of neural computation, with numerous extensions and applications. As such, much effort has been put into mapping PC faithfully onto the cortex, but there are issues that remain…

An uninterpreted program (UP) is a program whose semantics is defined over the theory of uninterpreted functions. This is a common abstraction used in equivalence checking, compiler optimization, and program verification. While simple, the…

We present a one-fits-all programmatic approach to reason about a plethora of objectives on probabilistic programs. The first ingredient is to add a reward-statement to the language. We then define a program transformation applying a…

The unification of logic and probability is a long-standing concern in AI, and more generally, in the philosophy of science. In essence, logic provides an easy way to specify properties that must hold in every possible world, and…

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 there is a long tradition of reasoning about (non)termination in program analysis, specialized logics are typically needed to give different termination criteria. This includes partial correctness, where termination is not guaranteed,…

Grover's algorithm relies on the superposition and interference of quantum mechanics, which is more efficient than classical computing in specific tasks such as searching an unsorted database. Due to the high complexity of quantum…