A general framework for minimisation-based belief change is presented. A problem instance is made up of an undirected graph, where a formula is associated with each vertex. For example, vertices may represent spatial locations, points in time, or some other notion of locality. Information is shared between vertices via a process of minimisation over the graph. We give equivalent semantic and sy...

A general framework for minimisation-based belief change is presented. A problem instance is made up of an undirected graph, where a formula is associated with each vertex. For example, vertices may represent spatial locations, points in time, or some other notion of locality. Information is shared between vertices via a process of minimisation over the graph. We give equivalent semantic and sy...

We discuss a proof-producing compiler which translates first order recursion equations, defined in higher order logic, to assembly language. The front end of the compiler is based on a series of source-tosource translations, starting with a semantic CPS translation and culminating in graph-colouring register allocation. Equality of the original program and the result of register allocation is p...

We propose a deep learning-based approach to the problem of premise selection: selecting mathematical statements relevant for proving a given conjecture. We represent a higher-order logic formula as a graph that is invariant to variable renaming but still fully preserves syntactic and semantic information. We then embed the graph into a vector via a novel embedding method that preserves the inf...

In this paper we describe the semantic analysis of differential equations given in the ubiquitous formats MathML and OpenMath. The analysis is integrated in a deployed Web indexing framework. Starting from basic classifications for differential equations the proposed system architecture is amenable to extensions for further reconstruction of mathematical content on the Web. The syntactic analys...

The semantic tableaux system is a procedure to decide whether or not a given formula is valid. The system also works for nding minimal models of formulas. In this paper, we apply this function to circumscription. We show that we can obtain the minimal models of circumscription just by checking the models produced by the system, and hence we do not need to check all possible models of it. We als...

We introduce a natural Turing-complete extension of first-order logic FO. The extension adds two novel features to FO. The first one of these is the capacity to add new points to models and new tuples to relations. The second one is the possibility of recursive looping when a formula is evaluated using a semantic game. We first define a game-theoretic semantics for the logic and then prove that...

Recent advances in decision procedures and constraint solvers can enable a new generation of formal specification languages. In this paper we present a new semantic foundation for formal specifications, called open-world logic programming, which integrates with state-of-theart solvers. Analysis, verification, and synthesis problems on open-world logic programs can be converted to constraints by...

Recent advances in deep learning have enabled state-of-the-art performance detecting medium and large-size objects. However, small object detection remains challenging primarily due to the scarcity of information. This paper proposes an end-to-end fusion network that integrates hand-crafted features address this limitation. A module based on semantic context information is designed enhance feat...