Efficient representation of piecewise linear functions into Łukasiewicz logic modulo satisfiability. (17th October 2022)

• Record Type: Journal Article
• Authors: Preto, Sandro; Finger, Marcelo
• Is Part Of: Mathematical structures in computer science. Volume 32:Number 9(2022)
• Page Start: 1119
• Page End: 1144
• Publication Date: 2022-10-17
• Subjects: Function representation -- Łukasiewicz Infinitely-valued Logic -- rational McNaughton functions -- piecewise linear functions; Computer science -- Mathematics -- Periodicals; 004.015105
• DOI: 10.1017/S096012952200010X
• Languages: English
• ISSNs: 0960-1295

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.