Effective Properties of Some First Order Intuitionistic Modal Logics

2000 ◽  
pp. 236-250
Author(s):  
Aida Pliuškevičienė
Keyword(s):  
Effective Properties ◽  
Modal Logics ◽  
First Order ◽  
Intuitionistic Modal Logics

Gentzen sequent calculi for some intuitionistic modal logics

2019 ◽  
Vol 27 (4) ◽  
pp. 596-623
Author(s):  
Zhe Lin ◽  
Minghui Ma
Keyword(s):  
Propositional Logic ◽  
Sequent Calculus ◽  
Modal Logics ◽  
Cut Elimination ◽  
Sequent Calculi ◽  
Intuitionistic Propositional Logic ◽  
Propositional Language ◽  
Intuitionistic Modal Logics ◽  
Subformula Property ◽  
Gentzen Sequent Calculus

Abstract Intuitionistic modal logics are extensions of intuitionistic propositional logic with modal axioms. We treat with two modal languages ${\mathscr{L}}_\Diamond $ and $\mathscr{L}_{\Diamond ,\Box }$ which extend the intuitionistic propositional language with $\Diamond $ and $\Diamond ,\Box $, respectively. Gentzen sequent calculi are established for several intuitionistic modal logics. In particular, we introduce a Gentzen sequent calculus for the well-known intuitionistic modal logic $\textsf{MIPC}$. These sequent calculi admit cut elimination and subformula property. They are decidable.

scholarly journals KRIPKE COMPLETENESS OF STRICTLY POSITIVE MODAL LOGICS OVER MEET-SEMILATTICES WITH OPERATORS

2019 ◽  
Vol 84 (02) ◽  
pp. 533-588 ◽  
Author(s):  
STANISLAV KIKOT ◽  
AGI KURUCZ ◽  
YOSHIHITO TANAKA ◽  
FRANK WOLTER ◽  
MICHAEL ZAKHARYASCHEV
Keyword(s):  
Computer Science ◽  
Monotone Operators ◽  
Modal Logics ◽  
Consequence Relations ◽  
First Order ◽  
Completeness Problem ◽  
Relational Structures ◽  
Kripke Frames

AbstractOur concern is the completeness problem for spi-logics, that is, sets of implications between strictly positive formulas built from propositional variables, conjunction and modal diamond operators. Originated in logic, algebra and computer science, spi-logics have two natural semantics: meet-semilattices with monotone operators providing Birkhoff-style calculi and first-order relational structures (aka Kripke frames) often used as the intended structures in applications. Here we lay foundations for a completeness theory that aims to answer the question whether the two semantics define the same consequence relations for a given spi-logic.

Simulating polyadic modal logics by monadic ones

2003 ◽  
Vol 68 (2) ◽  
pp. 419-462 ◽  
Author(s):  
George Goguadze ◽  
Carla Piazza ◽  
Yde Venema
Keyword(s):  
Modal Logics ◽  
Finite Model ◽  
Model Property ◽  
Finite Model Property ◽  
First Order ◽  
First Order Definability

AbstractWe define an interpretation of modal languages with polyadic operators in modal languages that use monadic operators (diamonds) only. We also define a simulation operator which associates a logic Λsim in the diamond language with each logic Λ in the language with polyadic modal connectives. We prove that this simulation operator transfers several useful properties of modal logics, such as finite/recursive axiomatizability, frame completeness and the finite model property, canonicity and first-order definability.

scholarly journals Problem Libraries for Non-Classical Logics

10.29007/mkdw ◽  
2018 ◽  
Author(s):  
Jens Otten ◽  
Thomas Raths
Keyword(s):  
Theorem Proving ◽  
General Problem ◽  
Crucial Role ◽  
Automated Theorem Proving ◽  
Modal Logics ◽  
First Order ◽  
Problem Library ◽  
Future Plans

Problem libraries for automated theorem proving (ATP) systems play a crucial role when developing, testing, benchmarking and evaluating ATP systems for classical and non-classical logics. We provide an overview of existing problem libraries for some important non-classical logics, namely first-order intuitionistic and first-order modal logics. We suggest future plans to extend these existing libraries and discuss ideas for a general problem library platform for non-classical logics.

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