Federico Pailos
Universidad de Buenos Aires (UBA)
In this paper, we present a way to translate the metainferences of a mixed metainferential system into formulae of an extended-language system, called its associated σ-system. To do this, the σ-system will contain new operators (one for each standard), called the σ operators, which represent the notions of "belonging to a (given) standard". We first prove, in a model-theoretic way, that these translations preserve (in)validity. That is, that a metainference is valid in the base system if and only if its translation is a tautology of its corresponding σ-system. We then use these results to obtain other key advantages. Most interestingly, we provide a recipe for building unlabeled sequent calculi for σ-systems. We then exemplify this with a σ-system useful for logics of the ST family, and prove soundness and completeness for it, which indirectly gives us a calculus for the metainferences of all those mixed systems. Finally, we respond to some possible objections and show how our σ-framework can shed light on the “obeying” discussion within mixed metainferential contexts
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

 PhilArchive page | Other versions
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Paradoxes and Failures of Cut.David Ripley - 2013 - Australasian Journal of Philosophy 91 (1):139 - 164.

View all 18 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Simple Cut Elimination Proof for Hybrid Logic.Andrezj Indrzejczak - 2016 - Logic and Logical Philosophy 25 (2):129-141.
A Note on the Sequent Calculi.Franco Parlamento & Flavio Previale - forthcoming - Review of Symbolic Logic:1-15.
Sequent Calculi for SCI.Szymon Chlebowski - 2018 - Studia Logica 106 (3):541-563.
Cut-Free Calculi and Relational Semantics for Temporal STIT Logics.Tim Lyon & Kees van Berkel - 2019 - In Francesco Calimeri, Nicola Leone & Marco Manna (eds.), Logics in Artificial Intelligence. Springer International Publishing. pp. 803 - 819.
Cuts, Gluts and Gaps.Vincent Degauquier - 2012 - Logique Et Analyse 55 (218):229-240.
A Survey of Nonstandard Sequent Calculi.Andrzej Indrzejczak - 2014 - Studia Logica 102 (6):1295-1322.
Decision Procedures for Some Strong Hybrid Logics.Andrzej Indrzejczak & Michał Zawidzki - 2013 - Logic and Logical Philosophy 22 (4):389-409.


Added to PP index

Total views
31 ( #368,644 of 2,507,400 )

Recent downloads (6 months)
31 ( #28,935 of 2,507,400 )

How can I increase my downloads?


My notes