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Semantics of templates in a compositional framework for building logics

Published online by Cambridge University Press:  03 September 2015

INGMAR DASSEVILLE ,
MATTHIAS VAN DER HALLEN ,
GERDA JANSSENS  and
MARC DENECKER
INGMAR DASSEVILLE
Affiliation:
KU Leuven (e-mail: [email protected])
MATTHIAS VAN DER HALLEN
Affiliation:
KU Leuven (e-mail: [email protected])
GERDA JANSSENS
Affiliation:
KU Leuven (e-mail: [email protected])
MARC DENECKER
Affiliation:
KU Leuven (e-mail: [email protected])
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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.

Keywords

compositionalitymodularitytemplatesmacrossemanticssecond order logic
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 15 , Special Issue 4-5: 31st International Conference on Logic Programming , July 2015 , pp. 681 - 695
Copyright
Copyright © Cambridge University Press 2015 

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