Natural Deduction, Hybrid Systems and Modal Logics

2010 ◽  
Author(s):  
Andrzej Indrzejczak
Keyword(s):  
Hybrid Systems ◽  
Natural Deduction ◽  
Modal Logics

Label-free natural deduction systems for intuitionistic and classical modal logics

2010 ◽  
Vol 20 (4) ◽  
pp. 373-421 ◽  
Author(s):  
Didier Galmiche ◽  
Yakoub Salhi
Keyword(s):  
Natural Deduction ◽  
Modal Logics ◽  
Label Free

scholarly journals From 2-Sequents and Linear Nested Sequents to Natural Deduction for Normal Modal Logics

2021 ◽  
Vol 22 (3) ◽  
pp. 1-29
Author(s):  
Simone Martini ◽  
Andrea Masini ◽  
Margherita Zorzi
Keyword(s):  
Natural Deduction ◽  
Modal Logics ◽  
Structural Rule ◽  
Elimination Rule ◽  
Accessibility Relation ◽  
Formal Systems ◽  
Explicit Reference ◽  
Deduction Rules ◽  
Nested Sequents ◽  
Normal Modal Logics

We extend to natural deduction the approach of Linear Nested Sequents and of 2-Sequents. Formulas are decorated with a spatial coordinate, which allows a formulation of formal systems in the original spirit of natural deduction: only one introduction and one elimination rule per connective, no additional (structural) rule, no explicit reference to the accessibility relation of the intended Kripke models. We give systems for the normal modal logics from K to S4. For the intuitionistic versions of the systems, we define proof reduction, and prove proof normalization, thus obtaining a syntactical proof of consistency. For logics K and K4 we use existence predicates (à la Scott) for formulating sound deduction rules.

Modal Logics and Topological Semantics for Hybrid Systems

1997 ◽  
Author(s):  
Sergei N. Artemov ◽  
Jennifer M. Davoren ◽  
A. Nerode
Keyword(s):  
Hybrid Systems ◽  
Modal Logics ◽  
Topological Semantics

scholarly journals Natural deduction rules for modal logics.

1972 ◽  
Vol 13 (4) ◽  
pp. 461-475 ◽  
Author(s):  
Thomas W. Satre
Keyword(s):  
Natural Deduction ◽  
Modal Logics ◽  
Deduction Rules
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