Related papers: Enumeration Problems Related to Ground Horn Theori…
Complexity theory provides a wealth of complexity classes for analyzing the complexity of decision and counting problems. Despite the practical relevance of enumeration problems, the tools provided by complexity theory for this important…
We establish proof-theoretic, constructive and coalgebraic foundations for proof search in coinductive Horn clause theories. Operational semantics of coinductive Horn clause resolution is cast in terms of coinductive uniform proofs; its…
In this note we compute values of global linear Harbourne constants over arbitrary fields for up to ten lines. These invariants have appeared recently in the discussions around the Bounded Negativity Conjecture. They seem to be of…
We introduce in this section an Algebraic and Combinatorial approach to the theory of Numbers. The approach rests on the observation that numbers can be identified with familiar combinatorial objects namely rooted trees, which we shall here…
Computing homology and cohomology is at the heart of many recent works and a key issue for topological data analysis. Among homological objects, homology generators are useful to locate or understand holes (especially for geometric…
Hyperproperties govern the behavior of a system or systems across multiple executions, and are being recognized as an important extension of regular temporal properties. So far, such properties have resisted comprehensive treatment by…
Horn functions form a subclass of Boolean functions and appear in many different areas of computer science and mathematics as a general tool to describe implications and dependencies. Finding minimum sized representations for such functions…
We present initial limit Datalog, a new extensible class of constrained Horn clauses for which the satisfiability problem is decidable. The class may be viewed as a generalisation to higher-order logic (with a simple restriction on types)…
Verifying programs that manipulate tree data structures often requires complex, ad-hoc proofs that are hard to generalize and automate. This paper introduces an automatic technique for analyzing such programs. Our approach combines automata…
We use machine learning to provide a tractable measure of the amount of predictable variation in the data that a theory captures, which we call its "completeness." We apply this measure to three problems: assigning certain equivalents to…
We prove a theorem which implies a quantum (multiplicative) analogue of the Horn conjecture, and also of the saturation conjecture. We obtain transversality statements for quantum schubert calculus in any characteristic and also determine…
This paper describes a framework for analysing matches in multiple data sets. The framework described is quite general and can be applied to a variety of problems where matches are to be found in data surveyed at a number of locations (or…
Autonomous systems that operate in a shared environment with people need to be able to follow the rules of the society they occupy. While laws are unique for one society, different people and institutions may use different rules to guide…
The symbol grounding problem asks how tokens like cat can be about cats, as opposed to mere shapes manipulated in a calculus. We recast grounding from a binary judgment into an audit across desiderata, each indexed by an evaluation tuple…
The features of a logically sound approach to a theory of statistical reasoning are discussed. A particular approach that satisfies these criteria is reviewed. This is seen to involve selection of a model, model checking, elicitation of a…
We report on work in progress on automatic procedures for proving properties of programs written in higher-order functional languages. Our approach encodes higher-order programs directly as first-order SMT problems over Horn clauses. It is…
We consider countable linear orders and study the quasi-order of convex embeddability and its induced equivalence relation. We obtain both combinatorial and descriptive set-theoretic results, and further extend our research to the case of…
We study approximations of theories both in general context and with respect to some natural classes of theories. Some kinds of approximations are considered, connections with finitely axiomatizable theories and minimal generating sets of…
Parameterised subgraph counting problems are the most thoroughly studied topic in the theory of parameterised counting, and there has been significant recent progress in this area. Many of the existing tractability results for parameterised…
In this tutorial, we will survey known results on the complexity of conjunctive query evaluation in different settings, ranging from Boolean queries over counting to more complex models like enumeration and direct access. A particular focus…