Related papers: Computing Abstract Distances in Logic Programs

Determinantal point processes (DPPs) are an important concept in random matrix theory and combinatorics. They have also recently attracted interest in the study of numerical methods for machine learning, as they offer an elegant "missing…

Abstraction logic is a new logic, serving as a foundation of mathematics. It combines features of both predicate logic and higher-order logic: abstraction logic can be viewed both as higher-order logic minus static types as well as…

Large Language Models have significantly advanced natural language processing tasks, but remain prone to generating incorrect or misleading but plausible arguments. This issue, known as hallucination, is particularly concerning in…

Boolean functions can be used to express the groundness of, and trace grounding dependencies between, program variables in (constraint) logic programs. In this paper, a variety of issues pertaining to the efficient Prolog implementation of…

The Abstraction and Reasoning Corpus (ARC) aims at benchmarking the performance of general artificial intelligence algorithms. The ARC's focus on broad generalization and few-shot learning has made it difficult to solve using pure machine…

In this paper, we present two alternative approaches to defining answer sets for logic programs with arbitrary types of abstract constraint atoms (c-atoms). These approaches generalize the fixpoint-based and the level mapping based answer…

We consider the problem of synthesizing programs with numerical constants that optimize a quantitative objective, such as accuracy, over a set of input-output examples. We propose a general framework for optimal synthesis of such programs…

We study transformational program logics for correctness and incorrectness that we extend to explicitly handle both termination and nontermination. We show that the logics are abstract interpretations of the right image transformer for a…

Programs must be correct with respect to their application domain. Yet, the program specification and verification approaches so far only consider correctness in terms of computations. In this work, we present a two-tier Hoare Logic that…

At its core, abstraction is the process of generalizing from specific instances to broader concepts or models, with the primary objective of reducing complexity while preserving properties essential to the intended purpose. It is…

Programs that process data that reside in files are widely used in varied domains, such as banking, healthcare, and web-traffic analysis. Precise static analysis of these programs in the context of software verification and transformation…

The success of Conflict Driven Clause Learning (CDCL) for Boolean satisfiability has inspired adoption in other domains. We present a novel lifting of CDCL to program analysis called Abstract Conflict Driven Learning for Programs (ACDLP).…

While large language models (LLMs) with reasoning capabilities are progressing rapidly on high-school math competitions and coding, can they reason effectively through complex, open-ended challenges found in frontier physics research? And…

Existing math datasets evaluate the reasoning abilities of large language models (LLMs) by either using the final answer or the intermediate reasoning steps derived from static examples. However, the former approach fails to surface model's…

Identifying semantically equivalent sentences is important for many cross-lingual and mono-lingual NLP tasks. Current approaches to semantic equivalence take a loose, sentence-level approach to "equivalence," despite previous evidence that…

Synthesizing programs from examples requires searching over a vast, combinatorial space of possible programs. In this search process, a key challenge is representing the behavior of a partially written program before it can be executed, to…

The ability to abstract, count, and use System~2 reasoning are well-known manifestations of intelligence and understanding. In this paper, we argue, using the example of the ``Look and Say" puzzle, that although deep neural networks can…

We propose relational linear programming, a simple framework for combing linear programs (LPs) and logic programs. A relational linear program (RLP) is a declarative LP template defining the objective and the constraints through the logical…

Verification of numerical accuracy properties in modern software remains an important and challenging task. This paper describes an original framework combining different solutions for numerical accuracy. First, we extend an existing…

Discrete mathematics is the foundation of computer science. It focuses on concepts and reasoning methods that are studied using math notations. It has long been argued that discrete math is better taught with programming, which takes…