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

Zhe Lin
2012 Lecture Notes in Computer Science  
In our 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.  ... 
doi:10.1007/978-3-642-31262-5_11 fatcat:nzxxxs7nqnaxhbgclayh7oc7ti

Cut-free sequent and tableau systems for propositional Diodorean modal logics

Rajeev Gor�
1994 Studia Logica: An International Journal for Symbolic Logic  
We present sound, (weakly) complete and 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.  ... 
doi:10.1007/bf01057938 fatcat:snmgz5cr7fc6vnxthziv5quyq4

S4 enriched multimodal categorial grammars are context-free

Andrew R. Plummer
2007 Theoretical Computer Science  
enriched with residuated 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.  ... 
doi:10.1016/j.tcs.2007.07.027 fatcat:gkftxweqavgohmkihbllz2v5xi

Proof Search in Nested Sequent Calculi [chapter]

Björn Lellmann, Elaine Pimentel
2015 Lecture Notes in Computer Science  
Fact The nested sequent calculus with 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  ... 
doi:10.1007/978-3-662-48899-7_39 fatcat:xn3q2hdsvnfzbigipp7wghoiu4

Termination of Derivations in a Fragment of Transitive Distributed Knowledge Logic

Regimantas Pliuškevičius, Aida Pliuškevičienė
2008 Informatica  
Hilbert-Style and Gentzen-Style Calculi 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.  ... 
doi:10.15388/informatica.2008.232 fatcat:tbpew6tncbcwvf6i2qcrt6pm6m

A Polynomial Translation of S4 into T and Contraction-Free Tableaux for S4

S. Cerrito
1997 Logic Journal of the IGPL  
In order to obtain a complete contraction 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.  ... 
doi:10.1093/jigpal/5.2.287 fatcat:isaz3ze7j5dmbp2emmytdknk2y

On the Decidability of Certain Semi-Lattice Based Modal Logics [chapter]

Katalin Bimbó
2017 Lecture Notes in Computer Science  
Sequent calculi are proof 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.  ... 
doi:10.1007/978-3-319-66902-1_3 fatcat:ccmk2zszmjbcrddy4p36e2zwji

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.  ... 

Relational Hypersequent S4 and B are Cut-Free Hypersequent Incomplete [article]

Kai Tanter
2021 arXiv   pre-print
We show that relational hypersequent K4, 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.  ... 
arXiv:2108.12095v1 fatcat:tpckhy3w2bfj7ffbywbmegax2q

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.  ... 

Taming Displayed Tense Logics Using Nested Sequents with Deep Inference [chapter]

Rajeev Goré, Linda Postniece, Alwen Tiu
2009 Lecture Notes in Computer Science  
We outline such a procedure 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.  ... 
doi:10.1007/978-3-642-02716-1_15 fatcat:hsfl4p376jbchgt2yd4unuj3du

An $$ \mathcal{O} $$ ((n · log n)3)-Time Transformation from Grz into Decidable Fragments of Classical First-Order Logic [chapter]

Stéphane Demri, Rajeev Goré
2000 Lecture Notes in Computer Science  
Instead, we use the syntactic relationships between 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] ).  ... 
doi:10.1007/3-540-46508-1_10 fatcat:vwos635zrrbxzhs6vpicyhnuna

Justified common knowledge

Sergei Artemov
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 ∪ {¬ }.  ... 
doi:10.1016/j.tcs.2006.03.009 fatcat:4mxemi3reneclkeohqktuhmnam

Realization Theorems for Justification Logics: Full Modularity [chapter]

Annemarie Borg, Roman Kuznets
2015 Lecture Notes in Computer Science  
A constructive proof of a realization theorem typically relies on a 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.  ... 
doi:10.1007/978-3-319-24312-2_16 fatcat:s6dznxculjgevpuz6njzvw3cuu
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