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Description of modal logics inheriting admissible rules for S4

1999
*
Logic Journal of the IGPL
*

Using this condition we describe all tabular

doi:10.1093/jigpal/7.5.655
fatcat:4fahyok2hraydfyhm653mms2qq
*modal**logics*inheriting*inference**rules**admissible**for**S4*. ... We give a necessary and sufficient condition*for*any*modal**logic*with fmp to inherit all*inference**rules**admissible*in*S4*. ... First we recall a simple general fact: Lemma 4.1 A tabular*modal**logic*λ := λ(F 1 · · · F n ) extending*S4*,*preserves*all*inference**rules**admissible**for**S4*iff each*logic*λ(F i ) does. Proof. ...##
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Uniform Interpolation and Propositional Quantifiers in Modal Logics

2007
*
Studia Logica: An International Journal for Symbolic Logic
*

The method is based on a simulation of certain quantifiers ranging over propositional variables and uses a terminating sequent calculus

doi:10.1007/s11225-007-9021-5
fatcat:zafkuihx7zaxhhnv3phwvgpmii
*for*which structural*rules*are*admissible*. ... We shall present such a proof of the uniform interpolation theorem*for*normal*modal**logics*K and T. It provides an explicit algorithm constructing the interpolants. ... Ghilardi and Zawadowski in [9] proved that uniform interpolation fails*for**modal**logic**S4*. It follows immediately that it fails*for**modal**logic*K4 as well. ...##
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Page 2074 of Mathematical Reviews Vol. , Issue 98D
[page]

1998
*
Mathematical Reviews
*

We show that a

*modal**logic*4 with FMP above*S4**preserves*all*inference**rules**admissible**for**S4*iff 4 has the so-called co-cover property. It turns out that there are 2*°*logics*of this kind. ... (RS-KRAS; Krasnoyarsk)*Modal**logics**preserving**admissible**for**S4**inference**rules*. (English summary) Computer science*logic*(Kazimierz, 1994), 512-526, Lecture Notes in Comput. ...##
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Page 6407 of Mathematical Reviews Vol. , Issue 95k
[page]

1995
*
Mathematical Reviews
*

Summary: “The main result of this paper is a complete semantic description of all

*modal**logics*with the finite model property (fmp) that*preserve*all*inference**rules**admissible**for*$4: a*modal**logic*A ... (RS-KRAS; Krasnoyarsk)*Preserving*of*admissible**inference**rules*in*modal**logic*. (English summary)*Logical*foundations of computer science (St. Petersburg, 1994), 304-315, Lecture Notes in Comput. ...##
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Rules admissible in transitive temporal logic TS4, sufficient condition

2010
*
Theoretical Computer Science
*

The paper 1 develops a technique

doi:10.1016/j.tcs.2010.09.012
fatcat:pwmfwrjvovaqjgn4fhhqzsdnt4
*for*computation*inference**rules**admissible*in temporal*logic*T*S4*. ... The main result of the paper is a sufficient condition*for**admissibility**inference**rules*in T*S4*. ... So, T*S4*, despite being defined by the same class of frames as the*modal**logic**S4*, does not always admit*rules**admissible*in*S4*. ...##
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Logics with the universal modality and admissible consecutions

2007
*
Journal of Applied Non-Classical Logics
*

In this paper 1 we study

doi:10.3166/jancl.17.383-396
fatcat:64synuhvpbajlmttsdinhkwklu
*admissible*consecutions (*inference**rules*) in multi-*modal**logics*with the universal*modality*. ... We consider extensions of multi-*modal**logic**S4*n augmented with the universal*modality*.*Admissible*consecutions form the largest class of*rules*, under which a*logic*(as a set of theorems) is closed. ... Acknowledgements I would like to thank Valentin Shehtman*for*his idea to extend our previous research (Golovanov et al., 2005) to arbitrary multi-*modal**logics*with universal*modality*. References ...##
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A Linear-Logical Reconstruction of Intuitionistic Modal Logic S4

2019
*
International Conference on Rewriting Techniques and Applications
*

We propose a

doi:10.4230/lipics.fscd.2019.20
dblp:conf/rta/FukudaY19
fatcat:qjz4e6bymbb3vnqwbmgtic7u2m
*modal*linear*logic*to reformulate intuitionistic*modal**logic**S4*(IS4) in terms of linear*logic*, establishing an*S4*-version of Girard translation from IS4 to it. ... While the Girard translation from intuitionistic*logic*to linear*logic*is well-known, its extension to*modal**logic*is non-trivial since a naive combination of the*S4**modality*and the exponential*modality*... We follow the proof*for*propositional linear*logic*by Lincoln et al. [9] . To show the*admissibility*of Cut, we consider the*admissibility*of the following cut*rules*: Γ !A Γ , (!A) n B ! ...##
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Page 2193 of Mathematical Reviews Vol. , Issue 2001D
[page]

2001
*
Mathematical Reviews
*

We also prove that self-

*admissible**rules*are always*admissible**for*what are, in a sense, canonical log- ics such as*S4*or IPC regarding the type of algebra generating*rules*.” 2001d:03056 03B45 Sturm, Holger ... The main result of our paper is a complete description of all self-*admissible*quasi-characterizing*inference**rules*. ...##
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Page 3851 of Mathematical Reviews Vol. , Issue 2000f
[page]

2000
*
Mathematical Reviews
*

The authors investigate

*admissible**rules*of*inference*in proposi- tional*logics*, that is, those which are stable with respect to any substitution and*preserve*the set of theorems of*logic*. As A. I. ... It is known that three of the five pretabular extensions of the*modal**logic*$4 and one of the three such extensions of Int have finite bases*for**admissible**rules*, while the remaining pretabular*logics*...##
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Page 802 of Mathematical Reviews Vol. , Issue 2003B
[page]

2003
*
Mathematical Reviews
*

., Dordrecht, 1999; see MR 2002b:03001]

*for*classical proposi- tional*logic*and labelled*rules**for**S4*of M. ...*Admissibility*of*logical**inference**rules*, North-Holland, Amsterdam, 1997; MR 981:03035]. ...##
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A Linear-logical Reconstruction of Intuitionistic Modal Logic S4
[article]

2019
*
arXiv
*
pre-print

We propose a "

arXiv:1904.10605v1
fatcat:oalwlgh6wjaj3pbshdvjwcuram
*modal*linear*logic*" to reformulate intuitionistic*modal**logic**S4*(IS4) in terms of linear*logic*, establishing an*S4*-version of Girard translation from IS4 to it. ... While the Girard translation from intuitionistic*logic*to linear*logic*is well-known, its extension to*modal**logic*is non-trivial since a naive combination of the*S4**modality*and the exponential*modality*... We follow the proof*for*propositional linear*logic*by Lincoln et al. [9] . To show the*admissibility*of Cut, we consider the*admissibility*of the following cut*rules*: Γ !A Γ , (!A) n B ! ...##
###
Hintikka multiplicities in matrix decision methods for some propositional modal logics
[chapter]

1997
*
Lecture Notes in Computer Science
*

This work is a study of the inter-translatability of two closely related proof methods, i.e. tableau (or sequent) and connection based, in the case of the propositional

doi:10.1007/bfb0027410
fatcat:lvauiob6u5djviia7d3bxasr7a
*modal**logics*K, K4, T,*S4*, paying ... in order to reduce as much as possible the search space*for*proofs. ... The authors wish to thank the anonymous referees of previous works*for*their suggestion to work in this direction and Alain Heuerding*for*useful discussions on this topic. ...##
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Frege systems for extensible modal logics

2006
*
Annals of Pure and Applied Logic
*

We prove a similar result

doi:10.1016/j.apal.2006.04.001
fatcat:mqjlbj4g7zbqbony6yobwfq7o4
*for*an infinite family of normal*modal**logics*, including K4, GL,*S4*, and S4Grz . ... Mints and Kojevnikov [11] have recently shown p-equivalence of Frege systems*for*the Intuitionistic Propositional Calculus (IPC ) in the standard language, building on a description of*admissible**rules*... In a similar spirit, bases of*admissible**rules**for*some*modal**logics*were constructed by Jeřábek [9] . ...##
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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. ... Our first calculus SKt is a variant of Kashima's calculus*for*Kt, which can also be seen as a display calculus, and uses "shallow"*inference*whereby*inference**rules*are only applied to the top-level nodes ... Acknowledgment: We thank the anonymous referees*for*their helpful comments on an earlier draft of the paper. ...##
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Does the deduction theorem fail for modal logic?

2011
*
Synthese
*

Various sources in the literature claim that the deduction theorem does not hold

doi:10.1007/s11229-011-9905-9
fatcat:govwc36ncfda5jljby4chnms7a
*for*normal*modal*or epistemic*logic*, whereas others present versions of the deduction theorem*for*several normal*modal*systems ... A contractionand cut-free sequent calculus equivalent to the Hilbert system*for*basic*modal**logic*shows the standard failure argument untenable by proving the underivability of 2A from A. ... Acknowledgements We thank Giovanna Corsi, Per Lindström, Paolo Maffezioli, Per Martin-Löf, Grisha Mints, Peter Pagin, Stephen Read, Gabriel Sandu, Sergei Soloviev, and Göran Sundholm*for*discussions and ...
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