Publication
What is a logic translation?
Till Mossakowski; Razvan Diaconescu; Andrzej Tarlecki
In: Logica Universalis, Vol. 3, No. 1, Pages 95-124, Birkhäuser, Basel, 2009.
Abstract
We study logic translations from an abstract perspective, without any commitment to the structure of sentences and the nature of logical entailment, which also means that we cover both proof- theoretic and model-theoretic entailment. We show how logic translations induce notions of logical expressiveness, consistency strength and sublogic, leading to an explanation of paradoxes that have been described in the literature. Connectives and quantifiers, although not present in the definition of logic and logic translation, can be recovered by their abstract properties and are preserved and reflected by translations under suitable conditions.