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Distributive Full Nonassociative Lambek Calculus with S4-Modalities Is Context-Free
[chapter]

2012
*
Lecture Notes in Computer Science
*

In our

doi:10.1007/978-3-642-31262-5_11
fatcat:nzxxxs7nqnaxhbgclayh7oc7ti
*systems**modal*axioms are replaced by*some*structural rules.*Cut*elimination holds*for**some*pure*logics*considered here, but not*for**logics*enriched with assumptions (consequence relations). ... It may be helpful to compare rules*for*♦ with rules*for*·, and rules*for*↓ with rules*for*an implication, say /. It is natural to consider*some**modal*axioms as in classical*modal**logic*. ... Now we show that the validity problem*for*K t 1,2 is in PSPACE. Our method is to show that K t 1,2 is embedded into K.t in polynomial time. ...##
###
Cut-free sequent and tableau systems for propositional Diodorean modal logics

1994
*
Studia Logica: An International Journal for Symbolic Logic
*

We present sound, (weakly) complete and

doi:10.1007/bf01057938
fatcat:snmgz5cr7fc6vnxthziv5quyq4
*cut*-*free*tableau*systems**for*the propositional normal*modal**logics**S4*:3,*S4*:3:1 and*S4*:14. ... Each tableau*system*has a*cut*-*free*sequent analogue proving that Gentzen's*cut*-elimination theorem holds*for*these latter*systems*. The techniques are due to Hintikka and Rautenberg. ... Acknowledgements: I have had many invaluable discussions with Ian Gent, Harold Simmons and Thomas Forster about matters*modal*. ...##
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S4 enriched multimodal categorial grammars are context-free

2007
*
Theoretical Computer Science
*

enriched with residuated

doi:10.1016/j.tcs.2007.07.027
fatcat:gkftxweqavgohmkihbllz2v5xi
*modalities*, weakly recognize exactly the context-*free*languages. ... We extend this result, proving that categorial grammars based on NL*S4*, the enrichment of NL3 by the axioms 4 and T , weakly recognize exactly the context-*free*languages. ... Acknowledgements The author wishes to thank the referees and the editor*for*their encouragement, and*for*their insightful comments regarding the content and presentation of this paper. ...##
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Proof Search in Nested Sequent Calculi
[chapter]

2015
*
Lecture Notes in Computer Science
*

Fact The nested sequent calculus with

doi:10.1007/978-3-662-48899-7_39
fatcat:xn3q2hdsvnfzbigipp7wghoiu4
*modal*rules R and L is sound and*cut*-*free*complete*for**modal**logic*K. ... Fact The nested sequent calculus with*modal*rules R and L is sound and*cut*-*free*complete*for**modal**logic*K. ... Future work: applicability of this approach to*logics*based on non-classical propositional*logic*such as constructive*modal**logics*; our methods work*for**logics*which are not based on a*cut*-*free*sequent ...##
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Termination of Derivations in a Fragment of Transitive Distributed Knowledge Logic

2008
*
Informatica
*

Hilbert-Style and Gentzen-Style Calculi

doi:10.15388/informatica.2008.232
fatcat:tbpew6tncbcwvf6i2qcrt6pm6m
*for*the*Logic**S4*n D The*logic**S4*n D is obtained from the multi-*modal**logic**S4*n by adding distributed knowledge operator D (see, e.g., (Fagin and Vardi, 1986; ...*For*a fragment of this*logic*loop-check-*free*sequent calculus is proposed. ...*For**modal**logic*KT loop-check-*free*sequent calculus is presented in (Heuerding et al., 1996) using sequents with two halves. ...##
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A Polynomial Translation of S4 into T and Contraction-Free Tableaux for S4

1997
*
Logic Journal of the IGPL
*

In order to obtain a complete contraction

doi:10.1093/jigpal/5.2.287
fatcat:isaz3ze7j5dmbp2emmytdknk2y
*free*fragment of the sequent calculus*for**S4*, Mints's translation of*modal*formulae into*modal*clauses is used. ... We use tableau proof-*systems*to show that Fitting's translation of the transitive*modal**logic**S4*into T can be constructed in deterministic polynomial time. ... Acknowledgments The authors thank the readers of a rst version of this paper*for*their relevant comments. ...##
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On the Decidability of Certain Semi-Lattice Based Modal Logics
[chapter]

2017
*
Lecture Notes in Computer Science
*

Sequent calculi are proof

doi:10.1007/978-3-319-66902-1_3
fatcat:ccmk2zszmjbcrddy4p36e2zwji
*systems*that are exceptionally suitable*for*proving the decidability of a*logic*. ... The version that is published in the proceedings*contains*multiple typesetting errors (such as missing or replaced symbols)*for*mysterious reasons. ... I am grateful to the organizers of the TABLEAUX, FroCoS and ITP conferences*for*their invitation*for*me to speak at those conferences, which triggered the writing of this paper. ...##
###
Page 2428 of Mathematical Reviews Vol. , Issue 94e
[page]

1994
*
Mathematical Reviews
*

Xiang Li (PRC-GUIZ; Guiyang)
94e:03019 03B45 03F05
Shimura, Tatsuya

*Cut*-*free**systems**for**some**modal**logics**containing**S4*. Rep. Math.*Logic*No. 26 (1992), 39-65 (1993). ... The author presents several*cut*-*free*Gentzen-type sequent calculi corresponding to*some*extensions of the Lewis*modal**system**S4*. ...##
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Relational Hypersequent S4 and B are Cut-Free Hypersequent Incomplete
[article]

2021
*
arXiv
*
pre-print

We show that relational hypersequent K4,

arXiv:2108.12095v1
fatcat:tpckhy3w2bfj7ffbywbmegax2q
*S4*, KB and RB, investigated in Parisi (2020) and Burns and Zach (2020) are*cut*-*free*hypersequent incomplete. ... In addition, the former two are also*cut*-*free*sequent and formula incomplete. ... We begin in Section 2 by providing a brief overview of*some*of the criteria considered in the literature*for*"good" proof*systems**for**modal**logics*. ...##
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Page 16 of Mathematical Reviews Vol. , Issue 98A
[page]

1998
*
Mathematical Reviews
*

of

*S4*into T and contraction-*free*tableaux*for**S4*. ... The paper deals with nonstandard sequent calculi*for**some*com- mon*modal**logics*; the main questions addressed are soundness, completeness and*cut*elimination. ...##
###
Page 1684 of Mathematical Reviews Vol. 55, Issue 6
[page]

1978
*
Mathematical Reviews
*

“every occurrence of” before “

*modal*’’; p. 138, 1. 5, put “*free*in «” before “within”; p. 185, 1. 7, put “*containing*a as its only*free*variable” before the period ; p. 354, answer 6.4(b), put “gq”*for*... Algebraic models*for**modal**logics*are presented in Chapter 17. ...##
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Taming Displayed Tense Logics Using Nested Sequents with Deep Inference
[chapter]

2009
*
Lecture Notes in Computer Science
*

We outline such a procedure

doi:10.1007/978-3-642-02716-1_15
fatcat:hsfl4p376jbchgt2yd4unuj3du
*for*the deep-sequent*system*DKt and its*S4*extension. ... The*cut*elimination proof*for*SKt uses a proof substitution technique similar to that used in*cut*elimination*for*display*logics*. ... Acknowledgment: We thank the anonymous referees*for*their helpful comments on an earlier draft of the paper. ...##
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An $$ \mathcal{O} $$ ((n · log n)3)-Time Transformation from Grz into Decidable Fragments of Classical First-Order Logic
[chapter]

2000
*
Lecture Notes in Computer Science
*

Instead, we use the syntactic relationships between

doi:10.1007/3-540-46508-1_10
fatcat:vwos635zrrbxzhs6vpicyhnuna
*cut*-*free*sequent-style calculi*for*Grz,*S4*and T. We rst translate Grz into T, and then we use the relational translation from T into FO 2 . ... The provability*logic*Grz is characterized by a class of*modal*frames that is not rst-order de nable. ... known*cut*-*free*Gentzen*systems**for*these*logics*(see e.g . 11] ). ...##
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Justified common knowledge

2006
*
Theoretical Computer Science
*

*Systems*T J n ,

*S4*J n , and S5 J n are specified as T n ,

*S4*n , and S5 n , with the

*modalities*K 1 , . . . , K n augmented by

*S4*with the

*modality*J, together with the principle:

*for*all i = 1, . . . ... We show that in standard situations, when the base epistemic

*systems*are T,

*S4*, and S5, the resulting justified common knowledge

*systems*are normal

*modal*

*logics*, which places them within the scope of well-developed ... Otherwise,

*for*

*some*finite subset of , ٛ and, by

*modal*

*logic*rules, ٛ J ; hence J ∈ -a contradiction. Take a maximal consistent set

*containing*∪ {¬ }. ...

##
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Realization Theorems for Justification Logics: Full Modularity
[chapter]

2015
*
Lecture Notes in Computer Science
*

A constructive proof of a realization theorem typically relies on a

doi:10.1007/978-3-319-24312-2_16
fatcat:s6dznxculjgevpuz6njzvw3cuu
*cut*-*free*sequent-style proof*system**for*the corresponding*modal**logic*. ... A uniform realization theorem*for*all the*modal**logics*of the socalled*modal*cube, i.e.,*for*the extensions of the basic*modal**logic*K with any subset of the axioms d, t, b, 4, and 5, has been proven using ... The authors are indebted to Agata Ciabattoni*for*making this research possible. ...
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