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Description of modal logics inheriting admissible rules for S4
1999
Logic Journal of the IGPL
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Using this condition we describe all tabular 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. ...
doi:10.1093/jigpal/7.5.655
fatcat:4fahyok2hraydfyhm653mms2qq
Uniform Interpolation and Propositional Quantifiers in Modal Logics
2007
Studia Logica: An International Journal for Symbolic Logic
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The method is based on a simulation of certain quantifiers ranging over propositional variables and uses a terminating sequent calculus 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. ...
doi:10.1007/s11225-007-9021-5
fatcat:zafkuihx7zaxhhnv3phwvgpmii
Page 2074 of Mathematical Reviews Vol. , Issue 98D
[page]
1998
Mathematical Reviews
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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. ...
Page 6407 of Mathematical Reviews Vol. , Issue 95k
[page]
1995
Mathematical Reviews
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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. ...
Rules admissible in transitive temporal logic TS4, sufficient condition
2010
Theoretical Computer Science
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The paper 1 develops a technique 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. ...
doi:10.1016/j.tcs.2010.09.012
fatcat:pwmfwrjvovaqjgn4fhhqzsdnt4
Logics with the universal modality and admissible consecutions
2007
Journal of Applied Non-Classical Logics
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In this paper 1 we study 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 ...
doi:10.3166/jancl.17.383-396
fatcat:64synuhvpbajlmttsdinhkwklu
A Linear-Logical Reconstruction of Intuitionistic Modal Logic S4
2019
International Conference on Rewriting Techniques and Applications
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We propose a 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 ! ...
doi:10.4230/lipics.fscd.2019.20
dblp:conf/rta/FukudaY19
fatcat:qjz4e6bymbb3vnqwbmgtic7u2m
Page 2193 of Mathematical Reviews Vol. , Issue 2001D
[page]
2001
Mathematical Reviews
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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. ...
Page 3851 of Mathematical Reviews Vol. , Issue 2000f
[page]
2000
Mathematical Reviews
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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 ...
Page 802 of Mathematical Reviews Vol. , Issue 2003B
[page]
2003
Mathematical Reviews
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., 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]. ...
A Linear-logical Reconstruction of Intuitionistic Modal Logic S4
[article]
2019
arXiv
pre-print
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We propose a "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 ! ...
arXiv:1904.10605v1
fatcat:oalwlgh6wjaj3pbshdvjwcuram
Hintikka multiplicities in matrix decision methods for some propositional modal logics
[chapter]
1997
Lecture Notes in Computer Science
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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 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. ...
doi:10.1007/bfb0027410
fatcat:lvauiob6u5djviia7d3bxasr7a
Frege systems for extensible modal logics
2006
Annals of Pure and Applied Logic
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We prove a similar result 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] . ...
doi:10.1016/j.apal.2006.04.001
fatcat:mqjlbj4g7zbqbony6yobwfq7o4
Taming Displayed Tense Logics Using Nested Sequents with Deep Inference
[chapter]
2009
Lecture Notes in Computer Science
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We outline such a procedure 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. ...
doi:10.1007/978-3-642-02716-1_15
fatcat:hsfl4p376jbchgt2yd4unuj3du
Does the deduction theorem fail for modal logic?
2011
Synthese
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Various sources in the literature claim that the deduction theorem does not hold 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 ...
doi:10.1007/s11229-011-9905-9
fatcat:govwc36ncfda5jljby4chnms7a
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