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A compositional typed higher-order logic with definitions

Book Contribution - Book Chapter Conference Contribution

Expressive KR languages are built by integrating different language constructs, or extendinga language with new language constructs. This process is difficult if non-truth-functional ornon-monotonic constructs are involved. What is needed is a compositional principle.This paper presents a compositional principle for defining logics by modular composition oflogical constructs, and applies it to build a higher order logic integrating typed lambda calculusand rule sets under a well-founded or stable semantics. Logical constructs are formalized astriples of a syntactical rule, a semantical rule, and a typing rule. The paper describes howsyntax, typing and semantics of the logic are composed from the set of its language constructs.The base semantical concept is the infon: mappings from structures to values in these structures.Semantical operators of language constructs operate on infons and allow to construct the infonsof compound expressions from the infons of its subexpressions. This conforms to Frege’s principleof compositionality.
Book: Technical Communications of the 32nd International Conference on Logic Programming
Pages: 14:1 - 14:1
Publication year:2016