Open AccessGrounding rules and (hyper-)isomorphic formulas
Author(s) -
Francesca Poggiolesi
Publication year - 2020
Publication title -
australasian journal of logic
Language(s) - English
Resource type - Journals
ISSN - 1448-5052
DOI - 10.26686/ajl.v17i1.5694
Subject(s) - meaning (existential) , mathematics , rule of inference , semantics (computer science) , inference , proof theoretic semantics , link (geometry) , domain (mathematical analysis) , algebra over a field , calculus (dental) , epistemology , pure mathematics , computer science , artificial intelligence , operational semantics , combinatorics , programming language , computational semantics , philosophy , mathematical analysis , medicine , dentistry
An oft-defended claim of a close relationship between Gentzen inference rules and the meaning of the connectives they introduce and eliminate has given rise to a whole domain called proof-theoretic semantics, see Schroeder- Heister (1991); Prawitz (2006). A branch of proof-theoretic semantics, mainly developed by Dosen (2019); Dosen and Petric (2011), isolates in a precise mathematical manner formulas (of a logic L) that have the same meaning. These isomorphic formulas are defined to be those that behave identically in inferences. The aim of this paper is to investigate another type of recently discussed rules in the literature, namely grounding rules, and their link to the meaning of the connectives they provide the grounds for. In particular, by using grounding rules, we will refine the notion of isomorphic formulas through the notion of hyper-isomorphic formulas. We will argue that it is actually the notion of hyper-isomorphic formulas that identify those formulas that have the same meaning.