{"type":"ScholarlyArticle","title":"Declarative Programming of Search Problems with Built-in Arithmetic","authors":[{"name":"Eugenia Ternovskaia","slug":"eugenia-ternovskaia","given":"Eugenia","family":"Ternovskaia","affiliation":""},{"name":"David G. Mitchell","slug":"david-g-mitchell","given":"David G.","family":"Mitchell","affiliation":""}],"abstract":"We address the problem of providing a logical formalization of arithmetic in declarative modelling languages for NP search problems. The challenge is to simultaneously allow quantification over an infinite domain such as the natural numbers, provide natural modelling facilities, and control expressive power of the language. To address the problem, we introduce an extension of the model expansion (MX) based framework to finite structures embedded in an infinite secondary structure, together with double-guarded logics for representing MX specifications for these structures. The logics also contain multi-set functions (aggregate operations). Our main result is that these logics capture the complexity class NP on small-cost arithmetical structures.Eugenia Ternovska, David G. Mitchell","doi":null,"url":"https://ijcai.org/proceedings/2009/160","pdf":"https://ijcai.org/proceedings/2009/0160.pdf","markdown":"https://ijcai.org/proceedings/2009/160.md","bibtex":"https://ijcai.org/proceedings/2009/bibtex/160","volume":{"slug":"2009","title":"Proceedings of the Twenty-First International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2009","url":"https://ijcai.org/proceedings/2009/","year":2009,"location":"Pasadena, California, USA","dates":"","editors":"Hiroaki Kitano","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":160,"pages":{"first":942,"last":946},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}