Efficient representation of piecewise linear functions into Łukasiewicz logic modulo satisfiability

IF 0.4 4区 计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS Mathematical Structures in Computer Science Pub Date : 2022-05-17 DOI:10.1017/S096012952200010X
Sandro Preto, M. Finger
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引用次数: 1

Abstract

Abstract This work concerns the representation of a class of continuous functions into Logic, so that one may automatically reason about properties of these functions using logical tools. Rational McNaughton functions may be implicitly represented by logical formulas in Łukasiewicz Infinitely-valued Logic by constraining the set of allowed valuations; such a restriction contemplates only those valuations that satisfy specific formulas. This work investigates two approaches to such depiction, called representation modulo satisfiability. Furthermore, a polynomial-time algorithm that builds this representation is presented, producing a pair of formulas consisting of the representative formula and the constraining one, given as input a rational McNaughton function in a suitable encoding. An implementation of the algorithm is discussed.
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分段线性函数的有效表示成Łukasiewicz逻辑模可满足性
摘要这项工作涉及一类连续函数在逻辑中的表示,以便使用逻辑工具自动推理这些函数的性质。Rational McNaughton函数可以通过约束允许估值的集合,由Łukasiewicz无穷值逻辑中的逻辑公式隐式表示;这种限制只考虑那些满足特定公式的估值。这项工作研究了两种描述方法,称为表示模可满足性。此外,还提出了一种建立这种表示的多项式时间算法,产生了一对由代表公式和约束公式组成的公式,并以适当的编码将有理McNaughton函数作为输入。讨论了该算法的实现。
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来源期刊
Mathematical Structures in Computer Science
Mathematical Structures in Computer Science 工程技术-计算机:理论方法
CiteScore
1.50
自引率
0.00%
发文量
30
审稿时长
12 months
期刊介绍: Mathematical Structures in Computer Science is a journal of theoretical computer science which focuses on the application of ideas from the structural side of mathematics and mathematical logic to computer science. The journal aims to bridge the gap between theoretical contributions and software design, publishing original papers of a high standard and broad surveys with original perspectives in all areas of computing, provided that ideas or results from logic, algebra, geometry, category theory or other areas of logic and mathematics form a basis for the work. The journal welcomes applications to computing based on the use of specific mathematical structures (e.g. topological and order-theoretic structures) as well as on proof-theoretic notions or results.
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