Semantics of templates in a compositional framework for building logics. Issue 4 (3rd September 2015)

• Record Type: Journal Article
• Authors: DASSEVILLE, INGMAR; VAN DER HALLEN, MATTHIAS; JANSSENS, GERDA; DENECKER, MARC
• Editors: Eiter, Thomas; Toni, Francesca
• Is Part Of: Theory and practice of logic programming. Volume 15:Issue 4/5(2015)
• Page Start: 681
• Page End: 695
• Publication Date: 2015-09-03
• Subjects: compositionality, -- modularity, -- templates, -- macros, -- semantics, -- second order logic; Logic programming -- Periodicals; Artificial intelligence -- Computer programs -- Periodicals; Constraint programming (Computer science) -- Periodicals; 005.115
• DOI: 10.1017/S1471068415000319
• Languages: English
• ISSNs: 1471-0684

Abstract

Abstract: There is a growing need for abstractions in logic specification languages such as FO(·) and ASP. One technique to achieve these abstractions are templates (sometimes called macros). While the semantics of templates are virtually always described through a syntactical rewriting scheme, we present an alternative view on templates as second order definitions. To extend the existing definition construct of FO(·) to second order, we introduce a powerful compositional framework for defining logics by modular integration of logic constructs specified as pairs of one syntactical and one semantical inductive rule. We use the framework to build a logic of nested second order definitions suitable to express templates. We show that under suitable restrictions, the view of templates as macros is semantically correct and that adding them does not extend the descriptive complexity of the base logic, which is in line with results of existing approaches.