Related papers: Partial Evaluation of Logic Programs in Vector Spa…
Traditional coding theory guarantees valid decoding only if a minority of symbols are adversarially manipulated. In contrast, the game of coding framework ensures reliable decoding, even in the presence of an adversarial majority. This…
Vector-based word representations help countless Natural Language Processing (NLP) tasks capture the language's semantic and syntactic regularities. In this paper, we present the characteristics of existing word embedding approaches and…
A computational limit of combining partial evaluation and program inversion is investigated. Using a reversible Turing machine interpreter, we show that the first Futamura and inversion projections can produce not only functionally but also…
Given a generic semidefinite program, specified by matrices with rational entries, each coordinate of its optimal solution is an algebraic number. We study the degree of the minimal polynomials of these algebraic numbers. Geometrically,…
The paper relates two variants of semantic models for natural language, logical functional models and compositional distributional vector space models, by transferring the logic and reasoning from the logical to the distributional models.…
Fuzzy logic programming is a growing declarative paradigm aiming to integrate fuzzy logic into logic programming. One of the most difficult tasks when specifying a fuzzy logic program is determining the right weights for each rule, as well…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus…
We present a method for verifying partial correctness properties of imperative programs that manipulate integers and arrays by using techniques based on the transformation of constraint logic programs (CLP). We use CLP as a metalanguage for…
Writing correct programs for weak memory models such as the C11 memory model is challenging because of the weak consistency guarantees these models provide. The first program logics for the verification of such programs have recently been…
The field of probabilistic logic programming (PLP) focuses on integrating probabilistic models into programming languages based on logic. Over the past 30 years, numerous languages and frameworks have been developed for modeling, inference…
We give an introduction to logic tailored for algebraists, explaining how proofs in linear logic can be viewed as algorithms for constructing morphisms in symmetric closed monoidal categories with additional structure. This is made explicit…
Logical inference algorithms for conditional independence (CI) statements have important applications from testing consistency during knowledge elicitation to constraintbased structure learning of graphical models. We prove that the…
In this report, we summarize the set partition enumeration problems and thoroughly explain the algorithms used to solve them. These algorithms iterate through the partitions in lexicographic order and are easy to understand and implement in…
We present a scheme for translating logic programs, which may use aggregation and arithmetic, into algebraic expressions that denote bag relations over ground terms of the Herbrand universe. To evaluate queries against these relations, we…
The demonstrated code-understanding capability of LLMs raises the question of whether they can be used for automated program verification, a task that demands high-level abstract reasoning about program properties that is challenging for…
Students of our department solve algebraic exercises in mathematical logic in a computerized environment. They construct transformations step by step and the program checks the syntax, equivalence of expressions and completion of the task.…
Several recent works have developed a new, probabilistic interpretation for numerical algorithms solving linear systems in which the solution is inferred in a Bayesian framework, either directly or by inferring the unknown action of the…
We introduce a lazy approach to the explanation-based approximation of probabilistic logic programs. It uses only the most significant part of the program when searching for explanations. The result is a fast and anytime approximate…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…