Graphical Sequent Calculi for Modal Logics

Ma M.; A. Pietarinen

doi:10.4204/EPTCS.243.7

Publications

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Graphical Sequent Calculi for Modal Logics

P. 91–103.

Ma M., Pietarinen A.

The syntax of modal graphs is defined in terms of the continuou

s cut and broken cut following

Charles Peirce’s notation in the gamma part of his graphical

logic of existential graphs. Graphical

calculi for normal modal logics are developed based on a refo

rmulation of the graphical calculus

for classical propositional logic. These graphical calcul

i are of the nature of deep inference. The

relationship between graphical calculi and sequent calcul

i for modal logics is shown by translations

between graphs and modal formulas.

Language: English

DOI

Keywords: Modal Logic Graphical Sequent Calculi

In book

Electronic Proceedings in Theoretical Computer Science

Vol. 243. , [б.и.], 2017.

Two Types of Filtrations for wK4 and Its Relatives

Kudinov A., Shapirovsky I., Studia Logica 2025 P. 1–25

We study the finite model property of subframe logics with expressible transitive reflexive closure modality. For m > 0, let Lm be the logic defined by axiom ♦^{m+1}p → ♦p ∨ p. We construct quotient filtrations for the logics Lm, which implies that these logics and their tense counterparts have the finite model property. Then, we construct selective filtrations ...

Added: October 14, 2025

Влияние аксиомы связности на сложность модальной логики.

Kudinov A., Мясников К. М., Математика и теоретические компьютерные науки 2025 Т. 3 № 2 С. 58–84

The paper proves that for weakly transitive logics with the universal modality, whose formula satisfiability problem is in PSPACE, adding the connectedness axiom does not increase the complexity. Furthermore, an explicit algorithm solving this problem is presented. ...

Added: October 14, 2025

Advances in Modal Logic

College Publications, 2020.

Logic deals with the fundamental notions of truth and falsity. Modal logic arose from the philosophical study of “modes of truth” with the two most common modes being “necessarily true” and “possibly true”. Nowadays modal logic is used to reason about knowledge, about obligations, about programs and about time, among others. Actual research in modal logic spans ...

Added: August 27, 2020

Grammar Logics in Nested Sequent Calculus: Proof Theory and Decision Procedures

Tiu A., Ianovski E., Goré R., , in: Advances in Modal LogicIssue 9.: L.: College Publications, 2012. P. 516–537.

A grammar logic refers to an extension of the multi-modal logic K in which the modal axioms are generated from a formal grammar. We consider a proof theory, in nested sequent calculus, of grammar logics with converse, i.e., every modal operator [a] comes with a converse [¯a]. Extending previous works on nested sequent systems for ...

Added: February 25, 2019

Advances in Modal Logic

College Publications, 2016.

Logic deals with the fundamental notions of truth and falsity. Modal logic arose from the philosophical study of “modes of truth” with the two most common modes being “necessarily true” and “possibly true”. Research in modal logic now spans the spectrum from philosophy, computer science and mathematics using techniques from relational structures, universal algebra, topology, ...

Added: September 20, 2018

Advances in Modal Logic

College Publications, 2018.

Logic deals with the fundamental notions of truth and falsity. Modal logic arose from the philosophical study of “modes of truth” with the two most common modes being “necessarily true” and “possibly true”. Research in modal logic now spans philosophy, computer science, and mathematics, using techniques from relational structures, universal algebra, topology, and proof theory. These ...

Added: September 20, 2018

Gamma graph calculi for modal logics

Ma M., Pietarinen A., Synthese 2017 Vol. 195 No. 8 P. 3621–3650

We describe Peirce’s 1903 system of modal gamma graphs, its transformation rules of inference, and the interpretation of the broken-cut modal operator. We show that Peirce proposed the normality rule in his gamma system. We then show how various normal modal logics arise from Peirce’s assumptions concerning the broken-cut notation. By developing an algebraic semantics ...

Added: September 16, 2018