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Weight constraint and aggregate programs are among the most widely used logic programs with constraints. In this paper, we relate the semantics of these two classes of programs, namely the stable model semantics for weight constraint…
How can we perform computations over natural language representations to solve tasks that require symbolic and numeric reasoning? We propose natural language embedded programs (NLEP) as a unifying framework for addressing math/symbolic…
Algebraic characterization of logic programs has received increasing attention in recent years. Researchers attempt to exploit connections between linear algebraic computation and symbolic computation in order to perform logical inference…
Constrained clustering has been well-studied for algorithms such as $K$-means and hierarchical clustering. However, how to satisfy many constraints in these algorithmic settings has been shown to be intractable. One alternative to encode…
In contrast to the prevailing view in the literature, it is shown that even extremely stiff sets of ordinary differential equations may be solved efficiently by explicit methods if limiting algebraic solutions are used to stabilize the…
We present a new approach to termination analysis of numerical computations in logic programs. Traditional approaches fail to analyse them due to non well-foundedness of the integers. We present a technique that allows to overcome these…
Many of the existing approaches for program comprehension rely on the linguistic information found in source code, such as identifier names and comments. Semantic clustering is one such technique for modularization of the system that relies…
Neural solvers have achieved impressive progress in addressing simple routing problems, particularly excelling in computational efficiency. However, their advantages under complex constraints remain nascent, for which current…
The neural network has become an integral part of modern software systems. However, they still suffer from various problems, in particular, vulnerability to adversarial attacks. In this work, we present a novel program reasoning framework…
Dealing with context dependent knowledge has led to different formalizations of the notion of context. Among them is the Contextualized Knowledge Repository (CKR) framework, which is rooted in description logics but links on the reasoning…
Embedding knowledge graphs (KGs) into continuous vector spaces is a focus of current research. Early works performed this task via simple models developed over KG triples. Recent attempts focused on either designing more complicated triple…
Programming languages and techniques based on logic and constraints, such as the Constraint Handling Rules (CHR), can support many common programming tasks that can be expressed in the form of a search for feasible or optimal solutions.…
This paper describes the COINS (COnstraint-based INteractive Solving) system: a conflict-based constraint solver. It helps understanding inconsistencies, simulates constraint additions and/or retractions (without any propagation),…
A complete approach to reasoning under uncertainty requires support for incremental and interactive formulation and revision of, as well as reasoning with, models of the problem domain capable of representing our uncertainty. We present a…
Utilizing a quantum system for reservoir computing has recently received a lot of attention. Key challenges are related to how on can optimally en- and decode classical information, as well as what constitutes a good reservoir. Our main…
We extract verified algorithms for exact real number computation from constructive proofs. To this end we use a coinductive representation of reals as streams of binary signed digits. The main objective of this paper is the formalisation of…
Kernel methods are powerful for machine learning, as they can represent data in feature spaces that similarities between samples may be faithfully captured. Recently, it is realized that machine learning enhanced by quantum computing is…
Numerical reasoning over documents, which demands both contextual understanding and logical inference, is challenging for low-capacity local models deployed on computation-constrained devices. Although such complex reasoning queries could…
Relational programming enables program synthesis through a verifier-to-solver approach. An earlier paper introduced a functional conversion that mitigated some of the inherent performance overhead. However, the conversion was inelegant: it…
Building meaningful interoperation with external software units requires performing the conceptual interoperability analysis that starts with identifying the conceptual interoperability constraints of each software unit, then it compares…