Related papers: Solving non-linear Horn clauses using a linear Hor…
A programming tactic involving polyhedra is reported that has been widely applied in the polyhedral analysis of (constraint) logic programs. The method enables the computations of convex hulls that are required for polyhedral analysis to be…
Constraint Logic Programming (CLP) and Hereditary Harrop formulas (HH) are two well known ways to enhance the expressivity of Horn clauses. In this paper, we present a novel combination of these two approaches. We show how to enrich the…
This Survey provides an overview of techniques in termination analysis for programs with numerical variables and transitions defined by linear constraints. This subarea of program analysis is challenging due to the existence of undecidable…
The differentiable implementation of logic yields a seamless combination of symbolic reasoning and deep neural networks. Recent research, which has developed a differentiable framework to learn logic programs from examples, can even acquire…
We present necessary and sufficient conditions for the termination of linear homogeneous programs. We also develop a complete method to check termination for this class of programs. Our complete characterization of termination for such…
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…
We consider the scenario in which a set of sources generate messages in a network and a receiver node demands an arbitrary linear function of these messages. We formulate an algebraic test to determine whether an arbitrary network can…
Reduction to the satisfiability problem for constrained Horn clauses (CHCs) is a widely studied approach to automated program verification. The current CHC-based methods for pointer-manipulating programs, however, are not very scalable.…
Evaluating consistency in large language models (LLMs) is crucial for ensuring reliability, particularly in complex, multi-step interactions between humans and LLMs. Traditional self-consistency methods often miss subtle semantic changes in…
We investigate the decidability and computational complexity of conservative extensions and the related notions of inseparability and entailment in Horn description logics (DLs) with inverse roles. We consider both query conservative…
Resolution lies at the foundation of both logic programming and type class context reduction in functional languages. Terminating derivations by resolution have well-defined inductive meaning, whereas some non-terminating derivations can be…
Many applications require conformance with specifications that constrain the use of resources, such as execution time, energy, bandwidth, etc. We have presented a configurable framework for static resource usage verification where…
The benefits of cutting planes based on the perspective function are well known for many specific classes of mixed-integer nonlinear programs with on/off structures. However, we are not aware of any empirical studies that evaluate their…
We present a general framework for balancing expressions (terms) in form of so called tree straight-line programs. The latter can be seen as circuits over the free term algebra extended by contexts (terms with a hole) and the operations…
We investigate the problem of extracting rules, expressed in Horn logic, from neural network models. Our work is based on the exact learning model, in which a learner interacts with a teacher (the neural network model) via queries in order…
This article addresses the following problems: 1) First, a nonlinearity analysis is made looking for the presence of nonlinearities in an early phase of the identification process. The level and the nature of the nonlinearities should be…
The relevance of polynomial formula classes to deductive efficiency motivated their search, and currently, a great number of such classes is known. Nonetheless, they have been exclusively sought in the setting of clausal form and…
In this article, we examine how clausal resolution can be applied to a specific, but widely used, non-classical logic, namely discrete linear temporal logic. Thus, we first define a normal form for temporal formulae and show how arbitrary…
This short paper describes a simple and intuitive Prolog program, a metainterpreter, that computes the bottom up meaning of a simple positive Horn clause definition. It involves a simple transformation of the object program rules into…
Modern software for propositional satisfiability problems gives a powerful automated reasoning toolkit, capable of outputting not only a satisfiable/unsatisfiable signal but also a justification of unsatisfiability in the form of resolution…