Related papers: Reducing Higher-order Recursion Scheme Equivalence…
The task of assigning internationally accepted commodity codes (aka HS codes) to traded goods is a critical function of customs offices. Like court decisions made by judges, this task follows the doctrine of precedent and can be nontrivial…
This paper introduces a model theory for resolution on Higher Order Hereditarily Harrop formulae (HOHH), the logic underlying the Lambda-Prolog programming language, and proves soundness and completeness of resolution. The semantics and the…
We address the problem of verifying automatically procedural programs manipulating parametric-size arrays of integers, encoded as a constrained Horn clauses solving problem. We propose a new algorithmic method for synthesizing loop…
Tree transductions are binary relations of finite trees. For tree transductions defined by non-deterministic top-down tree transducers, inclusion, equivalence and synthesis problems are known to be undecidable. Adding origin semantics to…
We study the model-checking problem for recursion schemes: does the tree generated by a given higher-order recursion scheme satisfy a given logical sentence. The problem is known to be decidable for sentences of the MSO logic. We prove…
An algorithm is proposed for solving optimization problems arising in neural network training for supervised learning. The unique feature of the algorithm is the use of an auxiliary loss, in addition to the original loss employed for model…
Type checking algorithms and theorem provers rely on unification algorithms. In presence of type families or higher-order logic, higher-order (pre)unification (HOU) is required. Many HOU algorithms are expressed in terms of…
This paper presents a Hoare-style calculus for formal reasoning about reconfiguration programs of distributed systems. Such programs create and delete components and/or interactions (connectors) while the system components change state…
This contribution examines optimization problems that involve stochastic dominance constraints. These problems have uncountably many constraints. We develop methods to solve the optimization problem by reducing the constraints to a finite…
Constraint Handling Rules (CHR) is a rule-based programming language that rewrites collections of constraints. It is typically embedded into a general-purpose language. There exists a plethora of implementation for numerous host languages.…
Markov chain Monte Carlo (MCMC) sampling of densities restricted to linearly constrained domains is an important task arising in Bayesian treatment of inverse problems in the natural sciences. While efficient algorithms for uniform polytope…
We explore the sense in which the existing constructions for higher-order maps on quantum theory based on causality constraints and compositionality constraints respectively, coincide. More precisely, we construct a functor F : Caus(C) ->…
We present a generic framework that facilitates object level reasoning with logics that are encoded within the Higher Order Logic theorem proving environment of HOL Light. This involves proving statements in any logic using intuitive…
Best rank-one approximation is one of the most fundamental tasks in tensor computation. In order to fully exploit modern multi-core parallel computers, it is necessary to develop decoupling algorithms for computing the best rank-one…
Similar to a tree grammar, a Horn theory can be used to describe an infinite set of terms. In this paper, we present a class of Horn theories such that the set of definable predicates is closed wrt. conjunction and such that the…
First-order resolution has been used for type inference for many years, including in Hindley- Milner type inference, type-classes, and constrained data types. Dependent types are a new trend in functional languages. In this paper, we show…
Constraint Handling Rules (CHR) is a declarative committed-choice programming language with a strong relationship to linear logic. Its generalization CHR with Disjunction (CHRv) is a multi-paradigm declarative programming language that…
Hierarchical text classification (HTC) is a special sub-task of multi-label classification (MLC) whose taxonomy is constructed as a tree and each sample is assigned with at least one path in the tree. Latest HTC models contain three…
The direct deep learning simulation for multi-scale problems remains a challenging issue. In this work, a novel higher-order multi-scale deep Ritz method (HOMS-DRM) is developed for thermal transfer equation of authentic composite materials…
We introduce constraints necessary for type checking a higher-order concurrent constraint language, and solve them with an incremental algorithm. Our constraint system extends rational unification by constraints x$\subseteq$ y saying that…