Rule-Generation Theorem and its Applications

Bulletin of the Section of Logic 47 (4):265-281 (2018)
  Copy   BIBTEX

Abstract

In several applications of sequent calculi going beyond pure logic, an introduction of suitably defined rules seems to be more profitable than addition of extra axiomatic sequents. A program of formalization of mathematical theories via rules of special sort was developed successfully by Negri and von Plato. In this paper a general theorem on possible ways of transforming axiomatic sequents into rules in sequent calculi is proved. We discuss its possible applications and provide some case studies for illustration.

Categories

Add categories

Keywords

Reprint years

DOI

10.18778/0138-0680.47.4.03

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,783

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

A conditional defense of plurality rule: generalizing May's theorem in a restricted informational environment.Robert E. Goodin & Christian List - 2006 - American Journal of Political Science 50 (4):940-949.
An alternative rule of disjunction in modal logic.Timothy Williamson - 1991 - Notre Dame Journal of Formal Logic 33 (1):89-100.
Reflecting rules: A note on generalizing the deduction theorem.Gillman Payette - 2015 - Journal of Applied Logic 13 (3):188-196.
Cantor theorem and friends, in logical form.Silvio Valentini - 2013 - Annals of Pure and Applied Logic 164 (4):502-508.
A New Normalization Strategy for the Implicational Fragment of Classical Propositional Logic.Luiz C. Pereira, Edward H. Haeusler, Vaston G. Costa & Wagner Sanz - 2010 - Studia Logica 96 (1):95-108.
Gleason-Type Theorem for Projective Measurements, Including Qubits: The Born Rule Beyond Quantum Physics.F. De Zela - 2016 - Foundations of Physics 46 (10):1293-1306.
A relative interpolation theorem for infinitary universal Horn logic and its applications.Alexej P. Pynko - 2006 - Archive for Mathematical Logic 45 (3):267-305.
Applications of cut-free infinitary derivations to generalized recursion theory.Arnold Beckmann & Wolfram Pohlers - 1998 - Annals of Pure and Applied Logic 94 (1-3):7-19.
The Problem of the Second Best: Conceptual Issues: Juha Räikkä.Juha Räikkä - 2000 - Utilitas 12 (2):204-218.
Gentzen formulations of two positive relevance logics.Aleksandar Kron - 1980 - Studia Logica 39 (4):381 - 403.
Do the right thing! Rule finitism, rule scepticism and rule following.Wes Sharrock & Graham Button - 1999 - Human Studies 22 (2-4):193-210.
Gentzen formulations of two positive relevance logics.Aleksandar Kron - 1981 - Studia Logica 40 (3):381 - 403.
A simplified proof of an impossibility theorem.Alfred F. Mackay - 1973 - Philosophy of Science 40 (2):175-177.
The Theorem of Convergence of Opinions and Hume's Problem.Chen Xiaoping - 2008 - Modern Philosophy 5:014.
Categorical Abstract Algebraic Logic: Bloom's Theorem for Rule-Based π-Institutions.George Voutsadakis - 2008 - Logic Journal of the IGPL 16 (3):233-248.

Analytics

Added to PP
2019-05-18

Downloads
11 (#1,133,540)

6 months
3 (#965,065)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Andrzej Indrzejczak
University of Lodz

Citations of this work

Free Logics are Cut-Free.Andrzej Indrzejczak - 2021 - Studia Logica 109 (4):859-886.
A novel approach to equality.Andrzej Indrzejczak - 2021 - Synthese 199 (1-2):4749-4774.

Add more citations

References found in this work

Proof Methods for Modal and Intuitionistic Logics.Melvin Fitting - 1985 - Journal of Symbolic Logic 50 (3):855-856.
Power and weakness of the modal display calculus.Marcus Kracht - 1996 - In Heinrich Wansing (ed.), Proof theory of modal logic. Boston: Kluwer Academic Publishers. pp. 93--121.
Simple cut elimination proof for hybrid logic.Andrezj Indrzejczak - 2016 - Logic and Logical Philosophy 25 (2):129-141.

Add more references